罗斯公司理财答案第六版(英文)
Chapter 2: Accounting Statements and Cash Flow 2.1
Assets
Current assets
Cash $ 4,000
Accounts receivable 8,000
Total current assets $ 12,000
Fixed assets
Machinery $ 34,000
Patents 82,000
Total fixed assets $116,000
Total assets $128,000
Liabilities and equity
Current liabilities
Accounts payable $ 6,000
Taxes payable 2,000
Total current liabilities $ 8,000
Long-term liabilities
Bonds payable $7,000
Stockholders equity
Common stock ($100 par) $ 88,000
Capital surplus 19,000
Retained earnings 6,000
Total stockholders equity $113,000
Total liabilities and equity $128,000
2.2
One year ago Today Long-term debt $50,000,000 $50,000,000
Preferred stock 30,000,000 30,000,000
Common stock 100,000,000 110,000,000
Retained earnings 20,000,000 22,000,000
Total $200,000,000 $212,000,000
2.3
Income Statement
$500,000 Less: Cost of goods sold $200,000
Administrative expenses 100,000 300,000
Earnings before interest and taxes $200,000
Less: Interest expense 50,000
Earnings before Taxes $150,000
Taxes 51,000
Net income $99,000
a.
Income Statement
The Flying Lion Corporation
19X1 19X2
Net sales $800,000 $500,000
Cost of goods sold (560,000) (320,000)
Operating expenses (75,000) (56,000)
Depreciation (300,000) (200,000)
Earnings before taxes $(135,000) $(76,000)
Taxes* 40,500 22,800
Net income $(94,500) $(53,200)
* The problem states that Flying Lion has other profitable operations. Flying Lion can take advantage of tax losses by deducting the tax liabilities in the other operations that have
taxable profits. If Flying Lion did not have other operations and tax losses could not be
carried forward or backward, then taxes in each of these years would have been zero.
b. C ash flow during 19X2 = -$94,500 + $300,000 = $205,500
Cash flow during 19X1 = -$53,200 + $200,000 = $146,800
2.5 The main difference between accounting profit and cash flow is that non-cash costs, such as
depreciation expense, are included in accounting profits. Cash flows do not consider costs that do not represent actual expenditures. Cash flows deduct the entire cost of an
investment at the time the cash flow occurs.
2.6 a. Net operating income = Sales - Cost of goods sold - Selling expenses - Depreciation
= $1,000,000 - $300,000 - $200,000 - $100,000
= $400,000
b. E arnings before taxes = Net operating income - Interest expense
= $400,000 - 0.1 ($1,000,000)
= $300,000
c. Net income = Earnings before taxes - Taxes
= $300,000 - 0.35 ($300,000)
= $195,000
d. C ash flow = Net income + Depreciation + Interest expense
= $195,000 + $100,000 + $100,000
= $395,000
Total Cash Flow of
the Stancil Company
Cash flows from the firm
Capital spending $(1,000)
Additions to working capital (4,000)
Total $(5,000)
Cash flows to investors of the firm
Short-term debt $(6,000)
Long-term debt (20,000)
Equity (Dividend - Financing) 21,000
Total $(5,000)
2.8 a. The changes in net working capital can be computed from:
Sources of net working capital
Net income $100
Depreciation 50
Increases in long-term debt 75
Total sources $225
Uses of net working capital
Dividends $50
Increases in fixed assets* 150
Total uses $200
Additions to net working capital $25
*Includes $50 of depreciation.
b.
Cash flow from the firm
Operating cash flow $150
Capital spending (150)
Additions to net working capital (25)
Total $(25)
Cash flow to the investors
Debt $(75)
Equity 50
Total $(25)。
罗斯《公司理财》英文习题答案DOCchap028
公司理财习题答案第二十八章Chapter 28: Cash Management28.1 Firms need to hold cash to:a. Satisfy the transaction needs. For example, cash is collected from sales and newfinancing and disbursed as wages, salaries, trade debts, taxes and dividends.b. Maintain compensating balances. A minimum required compensating balance atbanks providing credit service to the firm may impose a lower limit on the level ofcash a firm holds.28.2 a. Decrease. Examine the Baumol model. As the interest rate (k) increases, the optimalcash balance must also rise.b. Increase. Examine the Baumol model. As brokerage costs (F, the per transactioncosts) rise, the optimal balance increases.c. Decrease. Clearly, if the bank lowers its compensating balance requirement, a firmwill not be required to hold as much of its assets as cash.d. Decrease. If the cost of borrowing falls, a firm need not hold as much of its assets ascash because the cost of running short, i.e. the cost to borrow to fill cash needs, islower.e. Increase. As a firm’s credit rating falls, its cost to borrow increases. Thus, the firmcannot as easily afford to run short of cash and its cash balance must be higher.f. Decrease. Introduction of direct banking fees would increase the fixed costsassociated with holding cash. As fixed costs rise, the optimal balance must also rise.28.3 The average weekly cash balance is $20,750 [ ($24,000 + $34,000 + $10,000 +$15,000)/ 4].With monthly compounding, the return that the firm can earn on its average balance is$20,750 [[( 1 + 0.12/12)12 - 1] = $2,631.62Your answer may differ if you made different assumptions about the interest payments.28.4 a. The total amount of cash that will be disbursed during the year is:$345,000 * 12 = $4,140,000 Using the optimal cash balance formula,193,243$07.0)000,140,4)(500($2K 2FT*C ===$243,193 should be kept as cash. The balance, $556,807 (=$800,000-$243,193),should be invested in marketable securities.b. The number of times marketable securities will be sold during the next twelvemonths is $4,140,000 / $243,193 = 17 times28.5C*2FT K T KC *2F 7.5%(20mil)25,0007.5%200.01$3,000(mil)Average w eekly disbursement 3,00052$57.69mil222===⨯⨯=⨯===28.6 Use the Miller-Orr formula. The target cash balance = Z*3F 4K L 23=+σ The upper limit = H*=3Z*-2LThe daily opportunity cost = K= 1.0836510.000211-=Z*3($600)($1,440,00)4(0.000211)3$20,000$34,536H *$63,608=+== The average cash balance:C *4Z *L34($34,536)$20,0003$39,381=-=-=28.7 a.Z g*Hg 2L g 3200,0002100,0003$133,333Z s *Hs 2L s 3300,0002150,0003$200,000=+=+⨯==+=+⨯=b. Gold Star:()()s Z *L 4K /3F 133,333100,00040.00026132,0006,444,251K 1.1010.000261g 2g g3g g 3g 365=-=-⨯⨯⨯≈=-=Silver Star:()()s Z *L 4K /3F 200,000150,00040.00023632,000K 1.0910.000236g 2g g3g g 3g 365=-=-⨯⨯⨯≈=-=15733333,,So, Silver Star Co. has a more volatile daily cash flow.28.8 Garden Groves float = 150 ($15,000) = $2,250,000Increase in collected cash balance if a 3 day lockbox is installed = 3($2,250,000)= $6,750,000Annual earnings from this amount = $6,750,000 x 0.075 = $506,250The system should be installed if its cost is below this amount.Variable cost $ 0.5 x 150 x 365 = $27,375 Fixed cost = 80,000Total cost =$107,375The lockbox system should be installed. The net earnings from the use of the system are $398,875 (= $506,250 - $107,375)公司理财习题答案第二十八章28.9 To make the system profitable, the net earnings of installing the lockbox system must benon-negative. The lower limit for acceptability is zero profits.Let N be the number of customers per day.Earnings = ($4,500) (N) (2) (0.06) = $540 x NCosts:Variable cost: N (365) ($0.25) = $91.25 x NFixed cost: $15,000Equate Earnings to total costs:N = 33.43Salisbury Stakes needs at least 34 customers per day for the lockbox system to beprofitable.28.10 Disbursement float = $12,000 x 5 = $60,000Collection float = -$15,000 x 3 = -$45,000Net float = $60,000 - $45,000 = $15,000If funds are collected in four days rather than three, disbursement float will not change.Collection float will change to -$60,000. This change makes the net float equal to zero.28.11 a. Reduction in outstanding cash balances = $100,000 x 3 days = $300,000b. Return on savings = $300,000 (0.12) = $360,000c. Maximum monthly charge = $36,000 / 12 = $3,000Note: The calculation in part b assumes annual compounding. The answer in part cdoes not account for the time value of money. With monthly compounding of theinterest earned, the return on savings at the end of the year is$300,000 [(1.01)12 - 1] = $38,047.51The present value of this amount is $38,047.51 / (1.01) 12 = $33,765.23Compute the monthly payment as an annuity with a discount rate of 1% per periodfor twelve periods. That annuity factor is 11.2551. Thus, the payment is$33,765.23 = (Payment) (11.2551)Payment = $3,000Notice, as long as the treatment of the cash flows is the same, the payment is thesame.28.12 The cash savings are the earnings from the interest bearing account. Assuming dailycompounding, the three-day return to the delayed payment is($200,000)[(1.0004)3-1] = $240.096The interest rate for two weeks is 0.5615% (=(1.0004)14-1).Therefore, the present value of this annuity is($240.096)11(1.005615)260.005615$5,793.12 -=⎡⎣⎢⎢⎢⎢⎤⎦⎥⎥⎥⎥The Walter Company will save $5,793.12 per year.28.13 If the Miller Company divides the eastern region, collections will be accelerated by oneday freeing up $4 million per day. Compensating balances will be increased by $100,000 [=2($300,000)-$500,000]. The net effect is to have $3,900,000 to invest. If T-bills pay 7%per year, the annual net savings from the division of the eastern region is $3,900,000 x 0.07 = $273,000.28.14 Lockbox: interest saved = 7,500 x 250 x 1.5 x0.0003 = $843.75Annual saving (Annual charge) = 843.75 x 365 - 30,000 - 0.3 x 250 x 365= $250,593.75Annual saving (Concentration Banking) = 7,500 x 250 x1 x 0.0003 x 365= 562.5 x 365 = $205,312.5So the lockbox system is recommended.28.15 The important characteristics of short-term marketable securities are:i. maturityii. default riskiii. marketabilityiv. taxability。
罗斯《公司理财》英文习题答案DOCchap018
Chapter 18: Dividend Policy: Why Does It Matter?18.1 February 16: Declaration date - the board of directors declares a dividend payment thatwill be made on March 14.February 24: Ex-dividend date - the shares trade ex dividend on and after this date.Sellers before this date receive the dividend. Purchasers on or after thisdate do not receive the dividend.February 26: Record date - the declared dividends are distributable to shareholders of record on this date.March 14: Payable date - the checks are mailed.18.2Based on Miller and Modigliani reasoning, the stock will sell for $8.75. This is the same priceyoupurchased the stock. When the stock goes ex-dividend the stock is expected to fall $0.75 a share.18.3 a. If the dividend is declared, the price of the stock will drop on the ex-dividenddate by the value of the dividend, $5. It will then trade for $95.b. If it is not declared, the price will remain at $100.c. Mann’s outflows for investments are $2,000,000. These outflows occ urimmediately. One year from now, the firm will realize $1,000,000 in netincome and it will pay $500,000 in dividends. Since the only immediatefinancing need is for the investments, Mann must finance $2,000,000 throughthe sale of shares worth $100. It must sell $2,000,000 / $100 = 20,000 shares.d. The MM model is not realistic since it does not account for taxes, brokeragefees, uncertainty over future cash flows, investors’ preferences, signaling effects,and agency costs.18.4 a. The ex-dividend date is Feb. 27, which is two business days before the record date.b. The stock price should drop by $1.25 on the ex-dividend date.18.5 Knowing that share price can be expressed as the present value of expected futuredividends does not make dividend policy relevant. Under the growing perpetuitymodel, if overall corporate cash flows are unchanged, then a change in dividend policy only changes the timing of the dividends. The PV of those dividends is the same. This is true because, given that future earnings are held constant, dividend policy simplyrepresents a transfer between current and future stockholders.In a more realistic context and assuming a finite holding period, the value of the shares should represent the future stock price as well as the dividends. Any cash flow not paid as a dividend will be reflected in the future stock price. As such the PV of the flowswill not change with shifts in dividend policy; dividend policy is still irrelevant.18.6 a. The price is the PV of the dividends,$2 .$17..$1511553751152+=b. The current value of your shares is ($15)(500) = $7,500. The annuity youreceive must solve$7,500X1.15X1.152 =+;You desire $4,613.3721 each year. You will receive $1,000 in dividends in the first year, so you must sell enough shares to generate $3,613.3721. The end-of-year price at which you will sell your shares is the PV of the liquidating dividend, $17.5375 / 1.15 = $15.25, so you must sell 236.942 shares. The173 / 6remaining shares will each earn the liquidating dividend. At the end of thesecond year, you will receive $4,613.38 [= (500 - 236.942) x $17.5375].(Rounding causes the discrepancies).18.7 a. The value is the PV of the cash flows.Value = $32,000 + $1,545,600 / 1.12 = $1,412,000b. The current price of $141.20 per share will fall by the value of the dividend to $138.c. i. According to MM, it cannot be true that the low dividend is depressing theprice. Since dividend policy is irrelevant, the level of the dividend shouldnot matter. Any funds not distributed as dividends add to the value of thefirm hence the stock price. These directors merely want to change the timingof the dividends (more now, less in the future). As the calculations belowindicate, the value of the firm is unchanged by their proposal. Therefore,share price will be unchanged.To pay the $4.25 dividend, new shares, which total $10,500 (-$42,500 -$32,000) in value, must be sold. Those shares must also earn 12% so thevalue of the old shareholders’ interest one year hence will fall $11,760(=10,500 x 1.12). Under this scenario, the current value of the firm is Value= $42,500 + $1,533,840 / 1.12 = $1,412,000ii. The new shareholders are not entitled to receive the current dividend. They will receive only the value of the equity one year hence. The PV of thoseflows is $1,533,840 / 1.12 = $1,369,500, so the share price will be $136.95and 76.67 shares will be sold.18.8 a. (1.2 + 15) / 1 = $16.2Expected share price is $16.2.b. He can invest the dividends into the Gibson stock.Dividends that he gets = $1.2 million x 50% x 1,000 / 1,000,000 = $600Expected share price after dividend = (0.6 + 15) / 1 =$15.6Number of shares that Jeff needs to buy = 600 / 15.6 = 3818.9 Alternative 1: Dividends are paid out to the shareholders now.2 (1-31%) (1+7% (1-31%))3 = $1.59 millionAlternative 2: NBM invests cash in the financial assets:i. T-bill2 (1+7% (1-35%))3 (1-31%) = $1.58 millionii. Preferred stock2 {1+11% [1-(1-30%) x 35%]3} (1-31%) = $1.75 millionThe after-tax cash flow for the shareholders is maximized when the firm invests thecash in the preferred stocks.18.10 You should not expect to find either low dividend, high growth stocks or tax-freemunicipal bonds in the University of Pennsylvania’s portfolio. Since the universitydoes not pay taxes on investment income, it will want to invest in securities, whichprovide the highest pre-tax return. Since tax-free municipal bonds generally providelower returns than taxable securities, there is no reason for the university to holdmunicipal bonds.The Litzenberger-Ramaswamy research (discussed in the section on empirical evidence) found that high dividend stocks pay higher pre-tax returns than risk comparable lowdividend stocks because of the taxes on dividend income. Since the University ofPennsylvania does not pay taxes, it would be wise to invest in high dividend stocksrather than low dividend stocks in the same risk class.18.11 a. If T C = T0 then (P e - P b) / D =1. The stock price will fall by the amount of thedividend.b. If T C = 0 and T0 0 then (P e - P b) / D =1 - T0. The stock price will fall by theafter-tax proceeds from the dividend.c. In a, there was no tax disadvantage to dividends. Thus, investors are indifferentbetween buying the stock at P b and receiving the dividend or waiting, buying thestock at P e and receiving a subsequent capital gain. When only the dividend istaxed, after-tax proceeds must be equated for investors to be indifferent. Sincethe after-tax proceeds from the dividend are D (1 - T0), the price will fall by thatamount.d. No, Elton and Gruber’s paper is not a prescription for dividend policy. In aworld with taxes, a firm should never issue stock to pay a dividend, but thepresence of taxes does not imply that firms should not pay dividends fromexcess cash. The prudent firm, when faced with other financial considerationsand legal constraints may choose to pay dividends.18.12 a. Let x be the ordinary income tax rate. The individual receives an after-taxdividend of $1,000(1-x) which she invests in Treasury bonds. The T-bond willgenerate after-tax cash flows to the investor of $1,000 (1 - x)[1+0.08(1-x)].If the firm invests the money, its proceeds are $1,000 [1 + 0.08 (1-0.35)]To be indifferent, the investor’s proceeds must be the same whether she investsthe after-tax dividend or receives the proceeds from the firm’s investment andpays taxes on that amount.1,000 (1 - x) [1 + 0.08 (1 - x)] = (1 - x) {1,000 [1 + 0.08 (1 - 0.35)]}x = 0.35Note: This argument does not depend upon the length of time the investment isheld.b.Yes, this is a reasonable answer. She is only indifferent if the after-tax proceedsfrom the $1,000 investment in identical securities are identical; that occurs onlywhen the tax rates are identical.c. Since both investors will receive the same pre-tax return, you would expect thesame answer as in part a. Yet, because Carlson enjoys a tax benefit frominvesting in stock, the tax rate on ordinary income, which induces indifference,is much lower.1,000 (1 - x) [1 + 0.12(1 - x)] = (1 - x) {1,000 [1 + 0.12 (1 – 0.3) (0.35)]}x = 24.5%d. It is a compelling argument, but there are legal constraints, which deter firmsfrom investing large sums in stock of other companies.18.13 The fallacy behind both groups’ arguments is that they are considering dividends theonly return on a stock. They ignored capital gains. If dividends are controlled, firmsare likely to decrease their dividends. When dividends are reduced, the companiesretain more income, which causes share price to increase. That increase in share price will add to the investors’ capital gains. Sin ce dividends and capital gains are both ways of compensating investors, if transaction costs are negligible and there are no taxes,investors will be indifferent between the two forms of compensation.175 / 618.14 a. The after-tax expected return on Grebe stock is 4 / 20 = 0.2. Since Deaton stockis in the same risk class, it will be priced to yield the same after-tax expectedreturn.0.2(20P)(1T g)4(0.75)P;T g0P$19.170=--+= =b. If T g = 25%, the after-tax expected return on Grebe stock is (4) (1-0.25) / 20 =0.15. Deaton’s price will be0.15(20P)(0.75)4(0.75)PP$200=-+ =c. In this MM world, when the tax rates are identical, there is no tax disadvantageto the dividend. Investors are indifferent between $1 in capital gains and $1 individends. Hence, Deaton’s price will also be $20.18.15 P (Payall) = [100 + 25 (1-25%)] / (1 + 25%) = $95P (Payless) = [100 + 25 (50%) + 25 (50%) (1 - 25%)] / (1 + 25%) = $97.5P (Paynone) = $10018.16 a. Dividend yield: 4.5 / 50.50 = 0.0891b. The pricing of bonds was discussed in an earlier chapter. Whenever a bond isselling at par, the yield to maturity is the coupon rate. So, the yield on theDuPont bonds is 11%.c. After-tax shield = (Pre-tax yield) (1 - T)Preferred stock Debti. GM’s pension fund; T=0 8.91% 11.00%ii. GM; T=.34 8.00% 7.26%iii Roger Smith; T = 0.28 6.42% 7.92% *GM is exempt from 70% of taxes on dividend income, therefore, its effectivetax rate is (0.3) (0.34) = 0.102.d. Corporations, which are exempt from 70% of taxes on dividend income, wouldhold the preferred stock.18.17 The bird-in-the-hand argument is based upon the erroneous assumption that increaseddividends make a firm less risky. If capital spending and investment spending areunchanged, the firm’s overall c ash flows are not affected by the dividend policy.18.18 This argument is theoretically correct. In the real world with transaction costs ofsecurity trading, home-made dividends can be more expensive than dividends directlypaid out by the firms. However, the existence of financial intermediaries such asmutual funds reduces the transaction costs for individuals greatly. Thus, as a whole,the desire for current income shouldn’t be a major factor favoring high-current-dividend policy.18.19 To minimize her tax burden, your aunt should divest herself of high dividend yieldstocks and invest in low dividend yield stock. Or, if possible, she should keep her highdividend stocks, borrow an equivalent amount of money and invest that money in a taxdeferred account.18.20 This is not evidence on investor preferences. A rise in stock price when the currentdividend is increased may reflect expectations that future earnings, cash flows, etc. will rise. The better performance of the 115 companies, which raised their payouts, mayalso reflect a signal by management through the dividends that the firms were expected to do well in the future.18.21 Virginia Power’s investors probably were not aware of the cash flow crunch. Thus, theprice drop was due to the negative information about the cost overruns. Even if they were suspicious that there were overruns, the announcement would still cause a drop in price because it removed all uncertainty about overruns and indicated their magnitude.18.22 As the firm has been paying out regular dividends for more than 10 years, the currentsevere cut in dividends can cause the shareholders to lower their expectations oncurrent and future cash flows of the firm. It then results in the drop in the stock price.18.23 a. Cap’s past behavior suggests a preference for capital gains while Widow Jonesexhibits a preference for current income.b. Cap could show the widow how to construct homemade dividends through thesale of stock. Of course, Cap will also have to convince her that she lives in anMM world. Remember that homemade dividends can only be constructed underthe MM assumptions.c.Widow Jones may still not invest in Neotech because of the transaction costsinvolved in constructing homemade dividends. Also the Widow may desire theuncertainty resolution which comes with high dividend stocks.18.24 The capital investment needs of small, growing companies are very high. Therefore,payment of dividends could curtail their investment opportunities. Their other option is to issue stock to pay the dividend thereby incurring issuance costs. In either case, the companies and thus their investors are better off with a zero dividend policy during the firms’ rapid growth phases. This fact makes these firms attract ive only to low dividend clienteles.This example demonstrates that dividend policy is relevant when there are issuancecosts. Indeed, it may be relevant whenever the assumptions behind the MM model are not met.18.25 Unless there is an unsatisfied high dividend clientele, a firm cannot improve its shareprice by switching policies. If the market is in equilibrium, the number of people who desire high dividend payout stocks should exactly equal the number of such stocksavailable. The supplies and demands of each clientele will be exactly met inequilibrium. If the market is not in equilibrium, the supply of high dividend payoutstocks may be less than the demand. Only in such a situation could a firm benefit froma policy shift.18.26 a. Div1 = Div0 + s (t EPS1 - Div0)= 1.25 + 0.3 (0.4 x 4.5 -1.25)= 1.415b. Div1 = Div0 + s (t EPS1 - Div0)= 1.25 + 0.6 (0.4 x 4.5 - 1.25)= 1.58Note: Part “a” is more conservative since the adjustment rate is lower.18.27 This finding implies that firms use initial dividends to “signal” their potentialgrowth and positive NPV prospects to the stock market. The initiation of177 / 6regular cash dividends also serves to convince the market that their high currentearnings are not temporary.[文档可能无法思考全面，请浏览后下载，另外祝您生活愉快，工作顺利，万事如意!]。
(公司理财)英文版罗斯公司理财习题答案C
CHAPTER 20INTERNATIONAL CORPORATE FINANCEAnswers to Concepts Review and Critical Thinking Questions1. a.The dollar is selling at a premium because it is more expensive in the forward market than inthe spot market (SFr 1.53 versus SFr 1.50).b.The franc is expected to depreciate relative to the dollar because it will take more francs to buyone dollar in the future than it does today.c.Inflation in Switzerland is higher than in the United States, as are nominal interest rates.2.The exchange rate will increase, as it will take progressively more pesos to purchase a dollar. This isthe relative PPP relationship.3. a.The Australian dollar is expected to weaken relative to the dollar, because it will take moreA$ in the future to buy one dollar than it does today.b.The inflation rate in Australia is higher.c.Nominal interest rates in Australia are higher; relative real rates in the two countries are thesame.4. A Yankee bond is most accurately described by d.5. No. For example, if a country’s currency strengthens, imports become cheaper (good), but its exportsbecome more expensive for others to buy (bad). The reverse is true for currency depreciation.6.Additional advantages include being closer to the final consumer and, thereby, saving ontransportation, significantly lower wages, and less exposure to exchange rate risk. Disadvantages include political risk and costs of supervising distant operations.7.One key thing to remember is that dividend payments are made in the home currency. Moregenerally, it may be that the owners of the multinational are primarily domestic and are ultimately concerned about their wealth denominated in their home currency because, unlike a multinational, they are not internationally diversified.8. a.False. If prices are rising faster in Great Britain, it will take more pounds to buy the sameamount of goods that one dollar can buy; the pound will depreciate relative to the dollar.b.False. The forward market would already reflect the projected deterioration of the euro relativeto the dollar. Only if you feel that there might be additional, unanticipated weakening of the euro that isn’t reflected in forward rates today, will the forward hedge protect you against additional declines.c.True. The market would only be correct on average, while you would be correct all the time.9. a.American exporters: their situation in general improves because a sale of the exported goods fora fixed number of euros will be worth more dollars.American importers: their situation in general worsens because the purchase of the imported goods for a fixed number of euros will cost more in dollars.b.American exporters: they would generally be better off if the British government’s intentionsresult in a strengthened pound.American importers: they would generally be worse off if the pound strengthens.c.American exporters: they would generally be much worse off, because an extreme case of fiscalexpansion like this one will make American goods prohibitively expensive to buy, or else Brazilian sales, if fixed in cruzeiros, would become worth an unacceptably low number of dollars.American importers: they would generally be much better off, because Brazilian goods will become much cheaper to purchase in dollars.10.IRP is the most likely to hold because it presents the easiest and least costly means to exploit anyarbitrage opportunities. Relative PPP is least likely to hold since it depends on the absence of market imperfections and frictions in order to hold strictly.11.It all depends on whether the forward market expects the same appreciation over the period andwhether the expectation is accurate. Assuming that the expectation is correct and that other traders do not have the same information, there will be value to hedging the currency exposure.12.One possible reason investment in the foreign subsidiary might be preferred is if this investmentprovides direct diversification that shareholders could not attain by investing on their own. Another reason could be if the political climate in the foreign country was more stable than in the home country. Increased political risk can also be a reason you might prefer the home subsidiary investment. Indonesia can serve as a great example of political risk. If it cannot be diversified away, investing in this type of foreign country will increase the systematic risk. As a result, it will raise the cost of the capital, and could actually decrease the NPV of the investment.13.Yes, the firm should undertake the foreign investment. If, after taking into consideration all risks, aproject in a foreign country has a positive NPV, the firm should undertake it. Note that in practice, the stated assumption (that the adjustment to the discount rate has taken into consideration all political and diversification issues) is a huge task. But once that has been addressed, the net present value principle holds for foreign operations, just as for domestic.14.If the foreign currency depreciates, the U.S. parent will experience an exchange rate loss when theforeign cash flow is remitted to the U.S. This problem could be overcome by selling forward contracts. Another way of overcoming this problem would be to borrow in the country where the project is located.15.False. If the financial markets are perfectly competitive, the difference between the Eurodollar rateand the U.S. rate will be due to differences in risk and government regulation. Therefore, speculating in those markets will not be beneficial.16.The difference between a Eurobond and a foreign bond is that the foreign bond is denominated in thecurrency of the country of origin of the issuing company. Eurobonds are more popular than foreign bonds because of registration differences. Eurobonds are unregistered securities.Solutions to Questions and ProblemsNOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.Basicing the quotes from the table, we get:a.$50(€0.7870/$1) = €39.35b.$1.2706c.€5M($1.2706/€) = $6,353,240d.New Zealand dollare.Mexican pesof.(P11.0023/$1)($1.2186/€1) = P13.9801/€This is a cross rate.g.The most valuable is the Kuwait dinar. The least valuable is the Indonesian rupiah.2. a.You would prefer £100, since:(£100)($.5359/£1) = $53.59b.You would still prefer £100. Using the $/£ exchange rate and the SF/£ exchange rate to find theamount of Swiss francs £100 will buy, we get:(£100)($1.8660/£1)(SF .8233) = SF 226.6489ing the quotes in the book to find the SF/£ cross rate, we find:(SF 1.2146/$1)($0.5359/£1) = SF 2.2665/£1The £/SF exchange rate is the inverse of the SF/£ exchange rate, so:£1/SF .4412 = £0.4412/SF 13. a.F180= ¥104.93 (per $). The yen is selling at a premium because it is more expensive in theforward market than in the spot market ($0.0093659 versus $0.009530).b.F90 = $1.8587/£. The pound is selling at a discount because it is less expensive in the forwardmarket than in the spot market ($0.5380 versus $0.5359).c.The value of the dollar will fall relative to the yen, since it takes more dollars to buy one yen inthe future than it does today. The value of the dollar will rise relative to the pound, because it will take fewer dollars to buy one pound in the future than it does today.4. a.The U.S. dollar, since one Canadian dollar will buy:(Can$1)/(Can$1.26/$1) = $0.7937b.The cost in U.S. dollars is:(Can$2.19)/(Can$1.26/$1) = $1.74Among the reasons that absolute PPP doe sn’t hold are tariffs and other barriers to trade, transactions costs, taxes, and different tastes.c.The U.S. dollar is selling at a discount, because it is less expensive in the forward market thanin the spot market (Can$1.22 versus Can$1.26).d.The Canadian dollar is expected to appreciate in value relative to the dollar, because it takesfewer Canadian dollars to buy one U.S. dollar in the future than it does today.e.Interest rates in the United States are probably higher than they are in Canada.5. a.The cross rate in ¥/£ terms is:(¥115/$1)($1.70/£1) = ¥195.5/£1b.The yen is quoted too low relative to the pound. Take out a loan for $1 and buy ¥115. Use the¥115 to purchase pounds at the cross-rate, which will give you:¥115(£1/¥185) = £0.6216Use the pounds to buy back dollars and repay the loan. The cost to repay the loan will be:£0.6216($1.70/£1) = $1.0568You arbitrage profit is $0.0568 per dollar used.6.We can rearrange the interest rate parity condition to answer this question. The equation we will useis:R FC = (F T– S0)/S0 + R USUsing this relationship, we find:Great Britain: R FC = (£0.5394 – £0.5359)/£0.5359 + .038 = 4.45%Japan: R FC = (¥104.93 – ¥106.77)/¥106.77 + .038 = 2.08%Switzerland: R FC = (SFr 1.1980 – SFr 1.2146)/SFr 1.2146 + .038 = 2.43%7.If we invest in the U.S. for the next three months, we will have:$30M(1.0045)3 = $30,406,825.23If we invest in Great Britain, we must exchange the dollars today for pounds, and exchange the pounds for dollars in three months. After making these transactions, the dollar amount we would have in three months would be:($30M)(£0.56/$1)(1.0060)3/(£0.59/$1) = $28,990,200.05We should invest in U.S.ing the relative purchasing power parity equation:F t = S0 × [1 + (h FC– h US)]tWe find:Z3.92 = Z3.84[1 + (h FC– h US)]3h FC– h US = (Z3.92/Z3.84)1/3– 1h FC– h US = .0069Inflation in Poland is expected to exceed that in the U.S. by 0.69% over this period.9.The profit will be the quantity sold, times the sales price minus the cost of production. Theproduction cost is in Singapore dollars, so we must convert this to U.S. dollars. Doing so, we find that if the exchange rates stay the same, the profit will be:Profit = 30,000[$145 – {(S$168.50)/(S$1.6548/$1)}]Profit = $1,295,250.18If the exchange rate rises, we must adjust the cost by the increased exchange rate, so:Profit = 30,000[$145 – {(S$168.50)/1.1(S$1.6548/$1)}]Profit = $1,572,954.71If the exchange rate falls, we must adjust the cost by the decreased exchange rate, so:Profit = 30,000[$145 – {(S$168.50)/0.9(S$1.6548/$1)}]Profit = $955,833.53To calculate the breakeven change in the exchange rate, we need to find the exchange rate that make the cost in Singapore dollars equal to the selling price in U.S. dollars, so:$145 = S$168.50/S TS T = S$1.1621/$1S T = –.2978 or –29.78% decline10. a.If IRP holds, then:F180 = (Kr 6.43)[1 + (.08 – .05)]1/2F180 = Kr 6.5257Since given F180 is Kr6.56, an arbitrage opportunity exists; the forward premium is too high.Borrow Kr1 today at 8% interest. Agree to a 180-day forward contract at Kr 6.56. Convert the loan proceeds into dollars:Kr 1 ($1/Kr 6.43) = $0.15552Invest these dollars at 5%, ending up with $0.15931. Convert the dollars back into krone as$0.15931(Kr 6.56/$1) = Kr 1.04506Repay the Kr 1 loan, ending with a profit of:Kr1.04506 – Kr1.03868 = Kr 0.00638b.To find the forward rate that eliminates arbitrage, we use the interest rate parity condition, so:F180 = (Kr 6.43)[1 + (.08 – .05)]1/2F180 = Kr 6.525711.The international Fisher effect states that the real interest rate across countries is equal. We canrearrange the international Fisher effect as follows to answer this question:R US– h US = R FC– h FCh FC = R FC + h US– R USa.h AUS = .05 + .035 – .039h AUS = .046 or 4.6%b.h CAN = .07 + .035 – .039h CAN = .066 or 6.6%c.h TAI = .10 + .035 – .039h TAI = .096 or 9.6%12. a.The yen is expected to get stronger, since it will take fewer yen to buy one dollar in the futurethan it does today.b.h US– h JAP (¥129.76 – ¥131.30)/¥131.30h US– h JAP = – .0117 or –1.17%(1 – .0117)4– 1 = –.0461 or –4.61%The approximate inflation differential between the U.S. and Japan is – 4.61% annually.13. We need to find the change in the exchange rate over time, so we need to use the relative purchasingpower parity relationship:F t = S0 × [1 + (h FC– h US)]TUsing this relationship, we find the exchange rate in one year should be:F1 = 215[1 + (.086 – .035)]1F1 = HUF 225.97The exchange rate in two years should be:F2 = 215[1 + (.086 – .035)]2F2 = HUF 237.49And the exchange rate in five years should be:F5 = 215[1 + (.086 – .035)]5F5 = HUF 275.71ing the interest-rate parity theorem:(1 + R US) / (1 + R FC) = F(0,1) / S0We can find the forward rate as:F(0,1) = [(1 + R US) / (1 + R FC)] S0F(0,1) = (1.13 / 1.08)$1.50/£F(0,1) = $1.57/£Intermediate15.First, we need to forecast the future spot rate for each of the next three years. From interest rate andpurchasing power parity, the expected exchange rate is:E(S T) = [(1 + R US) / (1 + R FC)]T S0So:E(S1) = (1.0480 / 1.0410)1 $1.22/€ = $1.2282/€E(S2) = (1.0480 / 1.0410)2 $1.22/€ = $1.2365/€E(S3) = (1.0480 / 1.0410)3 $1.22/€ = $1.2448/€Now we can use these future spot rates to find the dollar cash flows. The dollar cash flow each year will be:Year 0 cash flow = –€$12,000,000($1.22/€) = –$14,640,000.00Year 1 cash flow = €$2,700,000($1.2282/€) = $3,316,149.86Year 2 cash flow = €$3,500,000($1.2365/€) = $4,327,618.63Year 3 cash flow = (€3,300,000 + 7,400,000)($1.2448/€) = $13,319,111.90And the NPV of the project will be:NPV = –$14,640,000 + $3,316,149.86/1.13 + $4,4327,618.63/1.132 + $13,319,111.90/1.133NPV = $914,618.7316. a.Implicitly, it is assumed that interest rates won’t change over the life of the project, but theexchange rate is projected to decline because the Euroswiss rate is lower than the Eurodollar rate.b.We can use relative purchasing power parity to calculate the dollar cash flows at each time. Theequation is:E[S T] = (SFr 1.72)[1 + (.07 – .08)]TE[S T] = 1.72(.99)TSo, the cash flows each year in U.S. dollar terms will be:t SFr E[S T] US$0 –27.0M –$15,697,674.421 +7.5M 1.7028 $4,404,510.222 +7.5M 1.6858 $4,449,000.223 +7.5M 1.6689 $4,493,939.624 +7.5M 1.6522 $4,539,332.955 +7.5M 1.6357 $4,585,184.79And the NPV is:NPV = –$15,697,674.42 + $4,404,510.22/1.13 + $4,449,000.22/1.132 + $4,493,939.62/1.133 + $4,539,332.95/1.134 + $4,585,184.79/1.135NPV = $71,580.10c.Rearranging the relative purchasing power parity equation to find the required return in Swissfrancs, we get:R SFr = 1.13[1 + (.07 – .08)] – 1R SFr = 11.87%So, the NPV in Swiss francs is:NPV = –SFr 27.0M + SFr 7.5M(PVIFA11.87%,5)NPV = SFr 123,117.76Converting the NPV to dollars at the spot rate, we get the NPV in U.S. dollars as:NPV = (SFr 123,117.76)($1/SFr 1.72)NPV = $71,580.10Challenge17. a.The domestic Fisher effect is:1 + R US = (1 + r US)(1 + h US)1 + r US = (1 + R US)/(1 + h US)This relationship must hold for any country, that is:1 + r FC = (1 + R FC)/(1 + h FC)The international Fisher effect states that real rates are equal across countries, so:1 + r US = (1 + R US)/(1 + h US) = (1 + R FC)/(1 + h FC) = 1 + r FCb.The exact form of unbiased interest rate parity is:E[S t] = F t = S0 [(1 + R FC)/(1 + R US)]tc.The exact form for relative PPP is:E[S t] = S0 [(1 + h FC)/(1 + h US)]td.For the home currency approach, we calculate the expected currency spot rate at time t as:E[S t] = (€0.5)[1.07/1.05]t= (€0.5)(1.019)tWe then convert the euro cash flows using this equation at every time, and find the present value. Doing so, we find:NPV = –[€2M/(€0.5)] + {€0.9M/[1.019(€0.5)]}/1.1 + {€0.9M/[1.0192(€0.5)]}/1.12 + {€0.9M/[1.0193(€0.5/$1)]}/1.13NPV = $316,230.72For the foreign currency approach, we first find the return in the euros as:R FC = 1.10(1.07/1.05) – 1 = 0.121Next, we find the NPV in euros as:NPV = –€2M + (€0.9M)/1.121 + (€0.9M)/1.1212+ (€0.9M)/1.1213= €158,115.36And finally, we convert the euros to dollars at the current exchange rate, which is:NPV ($) = €158,115.36 /(€0.5/$1) = $316,230.72。
罗斯公司理财第六版习题答案第5章
Concept Questions◆Define pure discount bonds, level-coupon bonds, and consols.A pure discount bond is one that makes no intervening interest payments. One receives a single lump sum payment at maturity. A level-coupon bond is a combination of an annuity and a lump sum at maturity. A consol is a bond that makes interest payments forever.◆Contrast the state interest rate and the effective annual interest rate for bonds paying semi-annual interest. Effective annual interest rate on a bond takes into account two periods of compounding per year received on the coupon payments. The state rate does not take this into account.◆What is the relationship between interest rates and bond prices?There is an inverse relationship. When one goes up, the other goes down.◆How does one calculate the yield to maturity on a bond?One finds the discount rate that equates the promised future cash flows with the price of the bond.◆What are the three factors determining a firm's P/E ratio?Today's expectations of future growth opportunities.The discount rate.The accounting method.◆What is the closing price of General Data?The closing price of General Data is 6 3/16.◆What is the PE of General House?The PE of General House is 29.◆What is the annual dividend of General Host?The annual dividend of General Host is zero.Concept Questions - Appendix To Chapter 5◆What is the difference between a spot interest rate and the yield to maturity?The yield to maturity is the geometric average of the spot rates during the life of the bond.◆Define the forward rate.Given a one-year bond and a two-year bond, one knows the spot rates for both. The forward rate is the rate of return implicit on a one-year bond purchased in the second year that would equate the terminal wealth of purchasing the one-year bond today and another in one year with that of the two-year bond.◆What is the relationship between the one-year spot rate, the two-year spot rate and the forward rate over the second year?The forward rate f2 = [(1+r2)2 /(1+r1 )] - 1◆What is the expectation hypothesis?Investors set interest rates such that the forward rate over a given period equals the spot rate for that period.◆What is the liquidity-preference hypothesis?This hypothesis maintains that investors require a risk premium for holding longer-term bonds (i.e. they prefer to be liquid or short-term investors). This implies that the market sets the forward rate for a given period above the expected spot rate for that period.Questions And ProblemsHow to Value Bonds5.1 What is the present value of a 10-year, pure discount bond that pays $1,000 at maturity and is priced to yield the following rates?a. 5 percentb. 10 percentc. 15 percentSolutions a. $1,000 / 1.0510 = $613.91b. $1,000 / 1.1010 = $385.54c. $1,000 / 1.1510 = $247.185.2 Microhard has issued a bond with the following characteristics:Principal: $1,000Term to maturity: 20 yearsCoupon rate: 8 percentSemiannual paymentsCalculate the price of the Microhard bond if the stated annual interest rate is:a. 8 percentb. 10 percentc. 6 percentSolutions The amount of the semi-annual interest payment is $40 (=$1,000 ⨯ 0.08 / 2). There are a total of 40 periods; i.e., two half years in each of the twenty years in the term to maturity.The annuity factor tables can be used to price these bonds. The appropriate discount rate touse is the semi-annual rate. That rate is simply the annual rate divided by two. Thus, for part b the rate to be used is 5% and for part c is it 3%.a. $40 (19.7928) + $1,000 / 1.0440 = $1,000Notice that whenever the coupon rate and the market rate are the same, the bond ispriced at par.b. $40 (17.1591) + $1,000 / 1.0540 = $828.41Notice that whenever the coupon rate is below the market rate, the bond is pricedbelow par.c. $40 (23.1148) + $1,000 / 1.0340 = $1,231.15Notice that whenever the coupon rate is above the market rate, the bond is pricedabove par.5.3 Consider a bond with a face value of $1,000. The coupon is paid semiannually and the market interest rate (effective annual interest rate) is 12 percent. How much would you pay for the bond if a. the coupon rate is 8 percent and the remaining time to maturity is 20 years?b. the coupon rate is 10 percent and the remaining time to maturity is 15 years?Solutions Semi-annual discount factor = (1.12)1/2 - 1 = 0.05830 = 5.83%a. Price = $40400583.0A+ $1,000 / 1.058340= $614.98 + $103.67= $718.65b. Price = $50300583.0A+ $1,000 / 1.058330= $700.94 + $182.70 = $883.645.4 Pettit Trucking has issued an 8-percent, 20-year bond that pays interest semiannually. If the market prices the bond to yield an effective annual rate of 10 percent, what is the price of the bond? Solutions Effective annual rate of 10%:Semi-annual discount factor = (1.1)0.5 - 1 = 0.04881 = 4.881%Price = $404004881.0A+ $1,000 / 1.0488140= $846.335.5 A bond is sold at $923.14 (below its par value of $1,000). The bond has 15 years to maturity and investors require a 10-percent yield on the bond. What is the coupon rate for the bond if the coupon is paid semiannually?Solutions $923.14 = C3005.0A+ $1,000 / 1.0530= (15.37245) C + $231.38C = $45The annual coupon rate = $45 ⨯ 2 / $1,000 = 0.09 = 9%5.6 You have just purchased a newly issued $1,000 five-year Vanguard Company bond at par. This five-year bond pays $60 in interest semiannually. You are also considering the purchase of another Vanguard Company bond that returns $30 in semiannual interest payments and has six years remaining before it matures. This bond has a face value of $1,000.a. What is effective annual return on the five-year bond?b. Assume that the rate you calculated in part (a) is the correct rate for the bond with six years remaining before it matures. What should you be willing to pay for that bond?c. How will your answer to part (b) change if the five-year bond pays $40 in semiannual interest? Solutionsa. The semi-annual interest rate is $60 / $1,000 = 0.06. Thus, the effective annual rate is 1.062 - 1 =0.1236 = 12.36%.b. Price = $301206.0A+ $1,000 / 1.0612= $748.48c. Price = $301204.0A+ $1,000 / 1.0412= $906.15Note: In parts b and c we are implicitly assuming that the yield curve is flat. That is, the yield in year 5 applies for year 6 as well.Bond Concepts5.7 Consider two bonds, bond A and bond B, with equal rates of 10 percent and the same face values of $1,000. The coupons are paid annually for both bonds. Bond A has 20 years to maturity while bond B has10 years to maturity.a. What are the prices of the two bonds if the relevant market interest rate is 10 percent?b. If the market interest rate increases to 12 percent, what will be the prices of the two bonds?c. If the market interest rate decreases to 8 percent, what will be the prices of the two bonds?Solutionsa. PA = $1002010.0A+ $1,000 / 1.1020 = $1,000PB = $1001010.0A+ $1,000 / 1.1010 = $1,000b. PA = $1002012.0A+ $1,000 / 1.1220 = $850.61PB = $1001012.0A+ $1,000 / 1.1210 = $887.00c. PA = $1002008.0A+ $1,000 / 1.0820 = $1,196.36PB = $1001008.0A+ $1,000 / 1.0810 = $1,134.205.8 a. If the market interest rate (the required rate of return that investors demand) unexpectedly increases, what effect would you expect this increase to have on the prices of long-term bonds? Why?b. What would be the effect of the rise in the interest rate on the general level of stock prices? Why? Solutionsa. The price of long-term bonds should fall. The price is the PV of the cash flowsassociated with the bond. As the interest rate rises, the PV of those flows falls.This can be easily seen by looking at a one-year, pure discount bond.Price = $1,000 / (1 + i)As i. increases, the denominator rises. This increase causes the price to fall.b. The effect upon stocks is not as certain as that upon the bonds. The nominalinterest rate is a function of both the real interest rate and the inflation rate; i.e.,(1 + i) = (1 + r) (1 + inflation)From this relationship it is easy to conclude that as inflation rises, the nominalinterest rate rises. Stock prices are a function of dividends and future prices aswell as the interest rate. Those dividends and future prices are determined by theearning power of the firm. When inflation occurs, it may increase or decreasefirm earnings. Thus, the effect of a rise in the level of general prices upon thelevel of stock prices is uncertain.5.9 Consider a bond that pays an $80 coupon annually and has a face value of $1,000. Calculate the yield to maturity if the bond hasa. 20 years remaining to maturity and it is sold at $1,200.b. 10 years remaining to maturity and it is sold at $950.Solutions a. $1,200 = $8020rA+ $1,000 / (1 + r)20r = 0.0622 = 6.22%b. $950 = $8010rA+ $1,000 / (1 + r)10r = 0.0877 = 8.77%5.10 The Sue Fleming Corporation has two different bonds currently outstanding. Bond A has a face value of $40,000 and matures in 20 years. The bond makes no payments for the first six years and then pays $2,000 semiannually for the subsequent eight years, and finally pays $2,500 semiannually for the last six years. Bond B also has a face value of $40,000 and a maturity of 20 years; it makes no coupon payments over the life of the bond. If the required rate of return is 12 percent compounded semiannually, what is the current price of Bond A? of Bond B?Solutions PA = ($2,0001606.0A) / (1.06)12 + ($2,5001206.0A) / (1.06)28 + $40,000 / (1.06)40= $18,033.86PB = $ 40,000 / (1.06)40 = $3,888.89The Present Value of Common Stocks5.11 Use the following February 11, 2000, WSJ quotation for AT&T Corp. Which of the following statements is false?a. The closing price of the bond with the shortest time to maturity was $1,000.b. The annual coupon for the bond maturing in year 2016 is $90.00.c. The price on the day before this quotation (i.e., February 9) for the ATT bond maturing in year 2022 was $1.075 per bond contract.d. The current yield on the ATT bond maturing in year 2002 was 7.125%e. The ATT bond maturing in year 2002 has a yield to maturity less than 7.125%.Bonds Cur Yld Vol Close Net ChgATT 9s 16 ? 10 117 _ 1/4ATT 5 1/8 01 ? 5 100 _ 3/4ATT 7 1/8 02 ? 193 104 1/8 _ 1/4ATT 8 1/8 22 ? 39 107 3/8 _ 1/8Solutions a. TrueTrueFalseFalseTrue5.12 Following are selected quotations for New York Exchange Bonds from the Wall Street Journal. Which of the following statements about Wilson’s bond is false?a. The bond maturing in year 2000 has a yield to maturity greater th an 63⁄8%.b. The closing price of the bond with the shortest time to maturity on the day before this quotation was $1,003.25.c. This annual coupon for the bond maturing in year 2013 is $75.00.d. The current yield on the Wilson’s bond with the longest time to maturity was 7.29%.e. None of the above.Quotations as of 4 P.M. Eastern TimeFriday, April 23, 1999Bonds Current Yield Vol Close NetWILSON 6 3/8 99 ? 76 100 3/8 _ 1/8WILSON 6 3/8 00 ? 9 98 1/2WILSON 7 1/4 02 ? 39 103 5/8 1/8WILSON 7 1/2 13 ? 225 102 7/8 _ 1/8Solutions a. TrueFalseTrueTrueFalse5.13 A common stock pays a current dividend of $2. The dividend is expected to grow at an 8-percent annual rate for the next three years; then it will grow at 4 percent in perpetuity.The appropriate discount rate is 12 percent. What is the price of this stock?Solutions Price = $2 (1.08) / 1.12 + $2 (1.082) / 1.122 + $2 (1.083) / 1.123+ {$2 (1.083) (1.04) / (0.12 - 0.04)} / 1.123= $28.895.14 Use the following February 12, 1998, WSJ quotation for Merck & Co. to answer the next question. 52 Weeks Yld Vol NetHi Lo Stock Sym Div % PE 100s Hi Lo Close Chg120. 80.19 Merck MRK 1.80 ? 30 195111 115.9 114.5 115 _1.25Which of the following statements is false?a. The dividend yield was about 1.6%.b. The 52 weeks’ trading range was $39.81.c. The closing price per share on February 10, 1998, was $113.75.d. The closing price per share on February 11, 1998, was $115.e. The earnings per share were about $3.83.Solutions a. FalseTrueFalseFalseTrue5.15 Use the following stock quote.52 Weeks Yld Vol NetHi Lo Stock Sym Div % PE 100s Hi Lo Close Chg126.25 72.50 Citigroup CCI 1.30 1.32 16 20925 98.4 97.8 98.13 _.13The expected growth rate in Citigroup’s dividends is 7% a year. Suppose you use the discounted dividend model to price Citigroup’s shares. The constant growth dividend model would suggest that the required return on the Citigroup’s stock is what?98.125 = 1.30 ( 1.07) / r - 0.07r = 8.4175 %5.16 You own $100,000 worth of Smart Money stock. At the end of the first year you receive a dividend of $2 per share; at the end of year 2 you receive a $4 dividend. At the end of year 3 you sell the stock for $50 per share. Only ordinary (dividend) income is taxed at the rate of 28 percent. Taxes are paid at the time dividends are received. The required rate of return is 15 percent. How many shares of stock do you own? Solutions Price = $2 (0.72) / 1.15 + $4 (0.72) / 1.152 + $50 / 1.153= $36.31The number of shares you own = $100,000 / $36.31 = 2,754 shares5.17 Consider the stock of Davidson Company that will pay an annual dividend of $2 in the coming year. The dividend is expected to grow at a constant rate of 5 percent permanently.The market requires a 12-percent return on the company.a. What is the current price of a share of the stock?b. What will the stock price be 10 years from today?Solutionsa. P = $2 / (0.12 - 0.05) = $28.57b. P10 = D11 / (r - g)= $2 (1.0510) / (0.12 - 0.05) = $46.545.18 Easy Type, Inc., is one of a myriad of companies selling word processor programs. Their newest program will cost $5 million to develop. First-year net cash flows will be $2 million. As a result of competition, profits will fall by 2 percent each year thereafter.All cash inflows will occur at year-end. If the market discount rate is 14 percent, what is the value of this new program?SolutionsValue = -$5,000,000 + $2,000,000 / {0.14 - (-0.02)}= $7,500,0005.19 Whizzkids, Inc., is experiencing a period of rapid growth. Earnings and dividends per share are expected to grow at a rate of 18 percent during the next two years, 15 percent in the third year, and at a constant rate of 6 percent thereafter. Whizzkids’ last dividend, which has just been paid, was $1.15. If the required rate of return on the stock is 12 percent, what is the price of a share of the stock today? SolutionsPrice = $1.15 (1.18) / 1.12 + $1.15 (1.182) / 1.122 + $1.152 (1.182) / 1.123+ {$1.152 (1.182) (1.06) / (0.12 - 0.06)} / 1.123= $26.955.20 Allen, Inc., is expected to pay an equal amount of dividends at the end of the first two years. Thereafter, the dividend will grow at a constant rate of 4 percent indefinitely. The stock is currently traded at $30. What is the expected dividend per share for the next year if the required rate of return is 12 percent? Solutions$30 = D / 1.12 + D / 1.122 + {D (1 + 0.04) / (0.12 - 0.04)} / 1.122= 12.053571 DD = $2.495.21 Calamity Mining Company’s reserves of ore are being depleted, and its costs of recovering a declining quantity of ore are rising each year. As a result, the company’s earnings are declining at the rate of 10 percent per year. If the dividend per share that is about to be paid is $5 and the required rate of return is 14 percent, what is the value of the firm’s stock?SolutionsDividend one year from now = $5 (1 - 0.10) = $4.50Price = $5 + $4.50 / {0.14 - (-0.10)} = $23.75Since the current $5 dividend has not yet been paid, it is still included in the stock price.5.22 The Highest Potential, Inc., will pay a quarterly dividend per share of $1 at the end of each of the next 12 quarters. Subsequently, the dividend will grow at a quarterly rate of 0.5 percent indefinitely. The appropriate rate of return on the stock is 10 percent. What is the current stock price?Estimates of Parameters in the Dividend-Discount ModelSolutionsPrice = $112025.0A+ {$1 (1 + 0.005) / (0.025 - 0.005)} / 1.02512= $10.26 + $37.36= $47.625.23 The newspaper reported last week that Bradley Enterprises earned $20 million. The report also stated that the firm’s return on equity remains on its historical trend of 14 percent. Bradley retains 60 percent of its earnings. What is the firm’s growth rate of earnings? What will next year’s earnings be? SolutionsGrowth rate g = 0.6 ⨯ 0.14 = 0.084 = 8.4%Next year earnings = $20 million ⨯ 1.084 = $21.68 million5.24 Von Neumann Enterprises has just reported earnings of $10 million, and it plans to retain 75 percent of its earnings. The company has 1.25 million shares of common stock outstanding. The stock is selling at $30. The historical return on equity (ROE) of 12 percent is expected to continue in the future. What is the required rate of return on the stock?Growth Opportunitiesg = retention ratio ⨯ ROE = 0.75 ⨯ 0.12= 0.09 = 9%Dividend per share = $10 million ⨯ (1 - 0.75) / 1.25 million= $2The required rate of return = $2 (1.09) / $30 + 0.09= 0.1627 = 16.27%5.25 Rite Bite Enterprises sells toothpicks. Gross revenues last year were $3 million, and total costs were $1.5 million. Rite Bite has 1 million shares of common stock outstanding. Gross revenues and costs are expected to grow at 5 percent per year. Rite Bite pays no income taxes, and all earnings are paid out as dividends.a. If the appropriate discount rate is 15 percent and all cash flows are received at year’s end, what is the price per share of Rite Bite stock?b. The president of Rite Bite decided to begin a program to produce toothbrushes. The project requires an immediate outlay of $15 million. In one year, another outlay of $5 million will be needed. The year after that, net cash inflows will be $6 million. This profit level will be maintained in perpetuity. What effect will undertaking this project have on the price per share of the stock?Solutionsa. Price = ($3 - $1.5) ⨯ 1.05 / (0.15 - 0.05)= $15.75b. NPVGO = -$15,000,000 - $5,000,000 / 1.15 + ($6,000,000 / 0.15) / 1.15= $15,434,783The price increases by $15.43 per share.5.26 California Electronics, Inc., expects to earn $100 million per year in perpetuity if it does not undertake any new projects. The firm has an opportunity that requires an investment of $15 million today and $5 million in one year. The new investment will begin to generate additional annual earnings of $10 million two years from today in perpetuity. The firm has 20 million shares of common stock outstanding, and the required rate of return on the stock is 15 percent.a. What is the price of a share of the stock if the firm does not undertake the new project?b. What is the value of the growth opportunities resulting from the new project?c. What is the price of a share of the stock if the firm undertakes the new project?Solutionsa. Price = EPS / r = {$100 million / 20 million} / 0.15= $33.33b. NPV = -$15 million - $5 million / 1.15 + ($10 million / 0.15) / 1.15= $38,623,188c. Price = $33.33 + $38,623,188 / 20,000,000= $35.265.27 Suppose Smithfield Foods, Inc., has just paid a dividend of $1.40 per share. Sales and profits for Smithfield Foods are expected to grow at a rate of 5% per year. Its dividend is expected to grow by the same rate. If the required return is 10%, what is the value of a share of Smithfield Foods?SolutionsPrice = 1.40 (1.05) / 0.10 - 0.05Price = $29.405.28 In order to buy back its own shares, Pennzoil Co. has decided to suspend its dividends for the next two years. It will resume its annual cash dividend of $2.00 a share 3 years from now. This level of dividends will be maintained for one more year. Thereafter, Pennzoil is expected to increase its cash dividend payments by an annual growth rate of 6% per year forever. The required rate of return on Pennzoil’s stock is 16%. According to the discounted dividend model, what should Pennzoil’s current share price be? SolutionsPrice = 2 / (1.16) 3 + 2 / (1.16)4 + 2.12 / 0.16 - 0.06= 1.28 + 1.10 + 21.20= $23.585.29 Four years ago, Ultramar Diamond Inc. paid a dividend of $0.80 per share. This year Ultramar paid a dividend of $1.66 per share. It is expected that the company will pay dividends growing at the same rate for the next 5 years. Thereafter, the growth rate will level at 8% per year. The required return on this stock is 18%. According to the discounted dividend model, what would Ultramar’s cash dividend be in 7 years? a. $2.86c. $3.68d. $4.30e. $4.82Solutionsa. g = 0.4 ⨯ 0.15 = 0.06 = 6%b. Dividend per share = $1.5 million ⨯ 0.6 / 300,000= $3Price = $3 (1.06) / (0.13 - 0.06)= $45.43c. Assuming the additional earnings generated are all paid out as cash dividends.NPV = -$1.2 million + $0.3 million {1 / (0.13 - 0.10)} {1 - (1.10 / 1.13)10}= $1,159,136.93d. Price = $45.43 + $1,159,136.93 / 300,000= $49.295.30 The Webster Co. has just paid a dividend of $5.25 per share. The company will increase its dividendby 15 percent next year and will then reduce its dividend growth by 3 percent each year until it reaches the industry average of 5 percent growth, after which the company will keep a constant growth, forever. The required rate of return for the Webster Co. is 14 percent. What will a share of stock sell for?SolutionsPrice = 3 / 1.15 + 4.5 / ( 1.15)2 + 4.725 / 0.15- 0.05= 2.61 + 3.40 + 47.52= $53.535.31 Consider Pacific Energy Company and U.S. Bluechips, Inc., both of which reported recent earnings of $800,000 and have 500,000 shares of common stock outstanding. Assume both firms have the same required rate of return of 15 percent a year.a. Pacific Energy Company has a new project that will generate cash flows of $100,000 each year in perpetuity. Calculate the P/E ratio of the company.Chapter 5 How to Value Bonds and Stocks 129b. U.S. Bluechips has a new project that will increase earnings by $200,000 in the coming year. The increased earnings will grow at 10 percent a year in perpetuity. Calculate the P/E ratio of the firm. Solutionsa. P/E of Pacific Energy Company:EPS = ($800,000 / 500,000) = $1.6NPVGO = {$100,000 / 500,000} / 0.15 = $1.33P/E = 1 / 0.15 + 1.33 / 1.6 = 7.50b. P/E of U. S. Bluechips, Inc.:NPVGO = {$200,000 / 500,000} / (0.15 - 0.10) = $8P/E = 1 / 0.15 + 8 / 1.6 = 11.675.32 (Challenge Question) Lewin Skis Inc. (today) expects to earn $4.00 per share for each of the future operating periods (beginning at time 1) if the firm makes no new investments (and returns the earnings as dividends to the shareholders). However, Clint Williams, President and CEO, has discovered an opportunity to retain (and invest) 25% of the earnings beginning three years from today (starting at time 3). This opportunity to invest will continue (for each period) indefinitely. He expects to earn 40% (per year) on this new equity investment (ROE of 40), the return beginning one year after each investment is made. The firm’s equity discount rate is 14% throughout.a. What is the price per share (now at time 0) of Lewin Skis Inc. stock without making the new investment?b. If the new investment is expected to be made, per the preceding information, what would the value of the stock (per share) be now (at time 0)?c. What is the expected capital gain yield for the second period, assuming the proposed investment is made? What is the expected capital gain yield for the second period if the proposed investment is not made?d. What is the expected dividend yield for the second period if the new investment is made? What is the expected dividend yield for the second period if the new investment is not made?Solutionsa. Price = $4 / 0.14 = $28.57Price = 28.57 + (-1 + 0.40 / 0.14) / 0.04(1.14) 3= 28.57 + 31.33The expected return of 14% less the dividend yield of 5% providesa capital gain yield of 9%. If there is no investment the yield is 14%.$3 / $59.90 = .05 and $4 / $28.57 = .14 without the investment.Appendix to Chapter 5 Questions And ProblemsA.1 The appropriate discount rate for cash flows received one year from today is 10 percent. The appropriate annual discount rate for cash flows received two years from today is 11 percent.a. What is the price of a two-year bond that pays an annual coupon of 6 percent?b. What is the yield to maturity of this bond?Solutionsa. P = $60 / 1.10 + $1,060 / (1.11)2= $54.55 + $ 860.32= $914.87$914.87 = $60 / ( 1 + y ) + $1,060 / ( 1 + y )2y = YTM = 10.97%A.2 The one-year spot rate equals 10 percent and the two-year spot rate equals 8 percent. What should a 5-percent coupon two-year bond cost?SolutionsP = $50 / 1.10 + $1,050 / (1.08)2= $45.45 + $900.21= $945.66A.3 If the one-year spot rate is 9 percent and the two-year spot rate is 10 percent, what is the forward rate? Solutions ( 1 + r1 )( 1 + ƒ2 ) = ( 1 + r2 )2( 1.09 ) ( 1 + ƒ2 ) = ( 1.10 )2ƒ2 = .1101A.4 Assume the following spot rates:Maturity Spot Rates (%)1 52 73 10What are the forward rates over each of the three years?Solutions( 1 + r2 )2 = ( 1+ r1 ) ( 1 + ƒ2 )( 1.07 )2 = ( 1.05 )( 1 + ƒ2 )ƒ2 = .0904, one-year forward rate over the 2nd year is 9.04%.( 1 + r3 )3 = ( 1 + r2 )2 ( 1 + ƒ3 )( 1.10 )3 = ( 1.07 )2 ( 1 + ƒ3 )ƒ3 = .1625, one-year forward rate over the 3rd year is 16.25%.。
《corporate finance》罗斯版英文版 Chapter 06书本课后习题及答案
Chapter 061.The changes in a firm's future cash flows that are a direct consequence of accepting a project arecalled _____ cash flows.A. i ncrementalB. s tand-aloneC. o pportunityD. n et present valueE. e rosion2.The annual annuity stream of payments with the same present value as a project's costs is calledthe project's _____ cost.A. i ncrementalB. s unkC. o pportunityD. e rosionE. e quivalent annual3. A cost that has already been paid, or the liability to pay has already been incurred, is a(n):A. s alvage value expense.B. n et working capital expense.C. s unk cost.D. o pportunity cost.E. e rosion cost.4.The most valuable investment given up if an alternative investment is chosen is a(n):A. s alvage value expense.B. n et working capital expense.C. s unk cost.D. o pportunity cost.E. e rosion cost.5. A decrease in a firm’s current cash flows resulting from the implementation of a new project isreferred to as:A. s alvage value expenses.B. n et working capital expenses.C. s unk costs.D. o pportunity costs.E. e rosion costs.6.The depreciation method currently allowed under U.S. tax law governing the accelerated write-offof property under various lifetime classifications is called _____ depreciation.A. F IFOB. M ACRSC. s traight-lineD. s um-of-years digitsE. c urvilinear7.The cash flow tax savings generated as a result of a firm's tax-deductible depreciation expense iscalled the:A. a ftertax depreciation savings.B. d epreciable basis.C. d epreciation tax shield.D. o perating cash flow.E. a ftertax salvage value.8.The cash flow from a project is computed as the:A. n et operating cash flow generated by the project, less any sunk costs and erosion costs.B. s um of the incremental operating cash flow and aftertax salvage value of the project.C. n et income generated by the project, plus the annual depreciation expense.D. s um of the incremental operating cash flow, capital spending, and net working capital cashflows incurred by the project.E. s um of the sunk costs, opportunity costs, and erosion costs of the project.9.Interest rates or rates of return on investments that have been adjusted for the effects of inflationare called _____ rates.A. r ealB. n ominalC. e ffectiveD. s trippedE. c oupon10.The increase you realize in buying power as a result of owning an investment is referred to as the_____ rate of return.A. i nflatedB. r ealizedC. n ominalD. r ealE. r isk-free11.The pro forma income statement for a cost reduction project:A. w ill reflect a reduction in the sales of the firm.B. w ill generally reflect no incremental sales.C. h as to be prepared reflecting the total sales and expenses of the entire firm.D. c annot be prepared due to the lack of any project related sales.E. w ill always reflect a negative project operating cash flow.12.One purpose of identifying all of the incremental cash flows related to a proposed project is to:A. i solate the total sunk costs so they can be evaluated to determine if the project will add valueto the firm.B. e liminate any cost which has previously been incurred so that it can be omitted from theanalysis of the project.C. m ake each project appear as profitable as possible for the firm.D. i nclude both the proposed and the current operations of a firm in the analysis of the project.E. i dentify any and all changes in the cash flows of the firm for the past year so they can beincluded in the analysis.13.Sunk costs include any cost that:A. w ill change if a project is undertaken.B. w ill be incurred if a project is accepted.C. h as previously been incurred and cannot be changed.D. w ill be paid to a third party and cannot be refunded for any reason whatsoever.E. w ill occur if a project is accepted and once incurred, cannot be recouped.14.You spent $500 last week fixing the transmission in your car. Now, the brakes are acting up andyou are trying to decide whether to fix them or trade the car in for a newer model. In analyzing the brake situation, the $500 you spent fixing the transmission is a(n) _____ cost.A. o pportunityB. f ixedC. i ncrementalD. s unkE. r elevant15.Erosion can be explained as the:A. a dditional income generated from the sales of a newly added product.B. l oss of current sales due to a new project being implemented.C. l oss of revenue due to employee theft.D. l oss of revenue due to customer theft.E. l oss of cash due to the expenses required to fix a parking lot after a heavy rain storm.16.Which one of these is an example of erosion that should be included in project analysis?A. T he anticipated loss of current sales when a new product is launched.B. T he expected decline in sales as a new product ages.C. T he reduction in your sales that occurs when a competitor introduces a new product.D. T he sudden loss of sales due to a major employer in your community implementing massivelayoffs.E. T he reduction in sales price that will most likely be required to sell inventory that has aged.17.Which one of the following should be excluded from the analysis of a project?A. e rosion costsB. i ncremental fixed costsC. i ncremental variable costsD. s unk costsE. o pportunity costs18.All of the following are anticipated effects of a proposed project. Which of these should be considered when computing the cash flow for the final year of a project?A. o perating cash flow and salvage valuesB. s alvage values and net working capital recoveryC.operating cash flow, net working capital recovery, salvage valuesD. n et working capital recovery and operating cash flowE.operating cash flow only19.Changes in the net working capital:A. c an affect the cash flows of a project every year of the project's life.B. o nly affect the initial cash flows of a project.C. a re included in project analysis only if they represent cash outflows.D. a re generally excluded from project analysis due to their irrelevance to the total project.E. a ffect the initial and the final cash flows of a project but not the cash flows of the middle years.20.The net working capital of a firm will decrease if there is:A. a decrease in accounts payable.B. a n increase in inventory.C. a decrease in accounts receivable.D. a n increase in the firm's checking account balance.E. a decrease in fixed assets. working capital:A. c an be ignored in project analysis because any expenditure is normally recouped by the end ofthe project.B. r equirements generally, but not always, create a cash inflow at the beginning of a project.C. e xpenditures commonly occur at the end of a project.D. i s frequently affected by the additional sales generated by a new project.E. i s the only expenditure where at least a partial recovery can be made at the end of a project.22.A company which uses the MACRS system of depreciation:A. w ill have equal depreciation costs each year of an asset's life.B. w ill expense the largest percentage of the cost during an asset’s first year of life.C. c an depreciate the cost of land, if it so desires.D. w ill write off the entire cost of an asset over the asset's class life.E. c annot expense any of the cost of a new asset during the first year of the asset's life.23.Champion Toys just purchased some MACRS 5-year property at a cost of $230,000. TheMACRS rates are 20 percent, 32 percent, 19.2 percent, 11.52 percent, 11.52 percent, and 5.76 percent for Years 1 to 6, respectively. The book value of the asset as of the end of Year 2 can be calculated as:A. $230,000 × (1 −.20 −.32).B. $230,000 × ([1 - (.20 × .32)].B. $230,000 × (1 - .20) × (1 - .32).C. $230,000 / (1 - .20 - .32).D. $230,000 - ($230,000 × .20 × .32).24.Pete’s Garage just purchased some equipment at a cost of $650,000. What is the propermethodology for computing the depreciation expense for Year 3 if the equipment is classified as 5-year property for MACRS? The MACRS rates are 20 percent, 32 percent, 19.2 percent, 11.52 percent, 11.52 percent, and 5.76 percent for Years 1 to 6, respectively.A. $650,000 ×(1 − .20) ×(1 −.32) ×(1 −.192)B. $650,000 ×(1 − .20) ×(1 −.32)C. $650,000 ×(1 − .20) ×(1 − .32) × .192)D. $650,000 ×(1 −.192)E. $650,000 ×.19225.The book value of an asset is primarily used to compute the:A. a nnual depreciation tax shield.B. a mount of cash received from the sale of an asset.C. a mount of tax saved annually due to the depreciation expense.D. a mount of tax due on the sale of an asset.E. c hange in depreciation needed to reflect the market value of the asset.26.The salvage value of an asset creates an aftertax cash flow in an amount equal to the:A. s ales price of the asset.B. s ales price minus the book value.C. s ales price minus the tax due based on the sales price minus the book value.D. s ales price plus the tax due based on the sales price minus the book value.E. s ales price plus the tax due based on the book value minus the sales price.27.The pretax salvage value of an asset is equal to the:A. b ook value if straight-line depreciation is used.B. b ook value if MACRS depreciation is used.C. m arket value minus the book value.D. b ook value minus the market value.E. m arket value.28.A project's operating cash flow will increase when the:A. d epreciation expense increases.B. s ales projections are lowered.C. i nterest expense is lowered.D. n et working capital requirement increases.E. e arnings before interest and taxes decreases.29.The cash flows of a project should:A. b e computed on a pretax basis.B. i nclude all sunk costs and opportunity costs.C. i nclude all incremental and opportunity costs.D. b e applied to the year when the related expense or income is recognized by GAAP.E. i nclude all financing costs related to new debt acquired to finance the project.30.Assume a firm has no interest expense or extraordinary items. Given this, the operating cash flow can be computed as:A. E BIT - Taxes.B. E BIT × (1 - Tax rate) + Depreciation × Tax rate.C. (Sales - Costs) × (1 - Tax rate).D. E BIT - Depreciation + Taxes.E.Net income + Depreciation.31.The bottom-up approach to computing the operating cash flow applies only when:A. b oth the depreciation expense and the interest expense are equal to zero.B. t he interest expense is equal to zero.C. t he project is a cost-cutting project.D. n o fixed assets are required for the project.E. t axes are ignored and the interest expense is equal to zero.32.The top-down approach to computing the operating cash flow:A. i gnores all noncash items.B. a pplies only if a project produces sales.C. c an only be used if the entire cash flows of a firm are included.D. i s equal to Sales −Costs −Taxes + Depreciation.E. i ncludes the interest expense related to a project.33.For a profitable firm, an increase in which one of the following will increase the operating cashflow?A. e mployee salariesB. o ffice rentC. b uilding maintenanceD. d epreciationE. e quipment rental34.Tax shield refers to a reduction in taxes created by:A. a reduction in sales.B. a n increase in interest expense.C. n oncash expenses.D. a project's incremental expenses.E. o pportunity costs.35.A project which is designed to improve the manufacturing efficiency of a firm but will generate noadditional sales revenue is referred to as a(n) _____ project.A. s unk costB. o pportunityC. c ost-cuttingD. r evenue-cuttingE. r evenue-generating36.Toni's Tools is comparing machines to determine which one to purchase. The machines sell fordiffering prices, have differing operating costs, differing machine lives, and will be replaced when worn out. These machines should be compared using:A. n et present value only.B. b oth net present value and the internal rate of return.C. t heir equivalent annual costs.D. t he depreciation tax shield approach.E. t he replacement parts approach.37.The equivalent annual cost method is useful in determining:A. t he annual operating cost of a machine if the annual maintenance is performed versus whenthe maintenance is not performed as recommended.B. t he tax shield benefits of depreciation given the purchase of new assets for a project.C. o perating cash flows for cost-cutting projects of equal duration.D. w hich one of two machines to acquire given equal machine lives but unequal machine costs.E. w hich one of two machines to purchase when the machines are mutually exclusive, havedifferent machine lives, and will be replaced once they are worn out.38.Marshall's purchased a corner lot five years ago at a cost of $498,000 and then spent $63,500 ongrading and drainage so the lot could be used for storing outdoor inventory. The lot was recently appraised at $610,000. The company now wants to build a new retail store on the site. Thebuilding cost is estimated at $1.1 million. What amount should be used as the initial cash flow for this building project?A. $1,661,500B. $1,100,000C. $1,208,635D. $1,710,000E. $1,498,00039.Samson's purchased a lot four years ago at a cost of $398,000. At that time, the firm spent$289,000 to build a small retail outlet on the site. The most recent appraisal on the propertyplaced a value of $629,000 on the property and building. Samson’s now wants to tear down the original structure and build a new strip mall on the site at an estimated cost of $2.3 million. What amount should be used as the initial cash flow for new project?A. $2,987,000B. $2,242,000C. $2,058,000D. $2,300,000E. $2,929,00040.Jamestown Ltd. currently produces boat sails and is considering expanding its operations toinclude awnings. The expansion would require the use of land the firm purchased three years ago at a cost of $142,000 that is currently valued at $137,500. The expansion could use someequipment that is currently sitting idle if $6,700 of modifications were made to it. The equipment originally cost $139,500 six years ago, has a current book value of $24,700, and a current market value of $39,000. Other capital purchases costing $780,000 will also be required. What is the amount of the initial cash flow for this expansion project?A. $953,400B. $962,300C. $948,900D. $927,800E. $963,20041.The Boat Works currently produces boat sails and is considering expanding its operations toinclude awnings. The expansion would require the use of land the firm purchased three years ago at a cost of $197,000 that is currently valued at $209,500. The expansion could use someequipment that is currently sitting idle if $7,500 of modifications were made to it. The equipment originally cost $387,500 five years ago, has a current book value of $132,700, and a current market value of $139,000. Other capital purchases costing $520,000 will also be required. What is the value of the opportunity costs that should be included in the initial cash flow for theexpansion project?A. $425,000B. $485,000C. $329,700D. $348,500E. $537,20042.Walks Softly sells customized shoes. Currently, it sells 14,800 pairs of shoes annually at anaverage price of $59 a pair. It is considering adding a lower-priced line of shoes that will be priced at $39 a pair. Walks Softly estimates it can sell 6,000 pairs of the lower-priced shoes but will sell 3,500 less pairs of the higher-priced shoes by doing so. What annual sales revenue should be used when evaluating the addition of the lower-priced shoes?A. $27,500B. $24,000C. $31,300D. $789,100E. $900,70043.Foamsoft sells customized boat shoes. Currently, it sells 16,850 pairs of shoes annually at anaverage price of $79 a pair. It is considering adding a lower-priced line of shoes which sell for $49a pair. Foamsoft estimates it can sell 5,000 pairs of the lower-priced shoes but will sell 1,250 lesspairs of the higher-priced shoes by doing so. What is the estimated value of the erosion cost that should be charged to the lower-priced shoe project?A. $138,750B. $146,250C. $98,750D. $52,000E. $123,24044.Sue purchased a house for $89,000, spent $56,000 upgrading it, and currently had it appraised at$212,900. The house is being rented to a family for $1,200 a month, the maintenance expenses average $200 a month, and the property taxes are $4,800 a year. If she sells the house she will incur $20,000 in expenses. She is considering converting the house into professional officespace. What opportunity cost, if any, should she assign to this property if she has been renting it for the past two years? A. $178,500A. $120,000B. $185,000C. A NSD. $192,900D. $232,90045.Jamie's Motor Home Sales currently sells 1,100 Class A motor homes, 2,200 Class C motorhomes, and 2,800 pop-up trailers each year. Jamie is considering adding a mid-range camper and expects that if she does so she can sell 1,500 of them. However, if the new camper is added, Jamie expects that her Class A sales will decline to 850 units while the Class C camper sales decline to 2,000. The sales of pop-ups will not be affected. Class A motor homes sell for anaverage of $140,000 each. Class C homes are priced at $59,500 and the pop-ups sell for $5,000 each. The new mid-range camper will sell for $42,900. What is the erosion cost of adding the mid-range camper?A. $54,250,000B. $46,900,000C. $53,750,000D. $63,150,000E. $78,750,00046.Ernie's Electrical is evaluating a project which will increase sales by $50,000 and costs by$30,000. The project will cost $150,000 and will be depreciated straight-line to a zero book value over the 10-year life of the project. The applicable tax rate is 34 percent. What is the operating cash flow for this project?A. $19,200B. $15,000C. $21,300D. $17,900E. $18,30047.Kurt's Cabinets is looking at a project that will require $80,000 in fixed assets and another$20,000 in net working capital. The project is expected to produce sales of $110,000 withassociated costs of $70,000. The project has a 4-year life. The company uses straight-line depreciation to a zero book value over the life of the project. The tax rate is 35 percent. What is the operating cash flow for this project?A. $7,000B. $13,000C. $27,000D. $33,000E. $40,00048.Peter's Boats has sales of $760,000 and a profit margin of 5 percent. The annual depreciationexpense is $80,000. What is the amount of the operating cash flow if the company has no long-term debt?A. $34,000B. $86,400C. $118,000D. $120,400E. $123,90049.Samoa's Tools has sales of $760,000 and a profit margin of 8 percent. The annual depreciationexpense is $50,000. What is the amount of the operating cash flow if the company has no long-term debt?A. $50,000B. $60,800C. $110,800D. $810,000E. $930,00050.Le Place has sales of $439,000, depreciation of $32,000, and net working capital of $56,000. Thefirm has a tax rate of 34 percent and a profit margin of 6 percent. The firm has no interestexpense. What is the amount of the operating cash flow?A. $49,384B. $52,616C. $54,980D. $58,340E. $114,34051.The By-Way has sales of $435,000, costs of $254,000, depreciation of $35,000, interest expenseof $22,000, and taxes of $43,400. What is the amount of the operating cash flow?A. $115,600B. $157,900C. $137,600D. $322,100E. $114,34052.Ben's Border Café is considering a project that will produce sales of $16,000 and increase cashexpenses by $10,000. If the project is implemented, taxes will increase from $23,000 to $24,500 and depreciation will increase from $4,000 to $5,500. What is the amount of the operating cash flow using the top-down approach?A. $4,000B. $4,500C. $6,000D. $7,500E. $8,50053.Camille's Café is considering a project that will not produce any sales but will decrease cashexpenses by $12,000. If the project is implemented, taxes will increase from $23,000 to $24,500 and depreciation will increase from $4,000 to $5,500. What is the amount of the operating cash flow using the top-down approach?A. $15,000B. $10,500C. $5,500D. $17,500E. $13,50054.Ronnie's Coffee House is considering a project which will produce sales of $6,000 and increasecash expenses by $2,500. If the project is implemented, taxes will increase by $1,300. The additional depreciation expense will be $1,000. An initial cash outlay of $2,000 is required for net working capital. What is the amount of the operating cash flow using the top-down approach?A. $200B. $1,500C. $2,200D. $3,500E. $4,20055.A project will increase sales by $60,000 and cash expenses by $51,000. The project will cost$40,000 and will be depreciated using straight-line depreciation to a zero book value over the 4-year life of the project. The company has a marginal tax rate of 35 percent. What is the operating cash flow of the project using the tax shield approach?A. $5,850B. $8,650C. $9,350D. $9,700E. $10,35056.A project will increase sales by $140,000 and cash expenses by $95,000. The project will cost$100,000 and will be depreciated using the straight-line method to a zero book value over the 4-year life of the project. The company has a marginal tax rate of 34 percent. What is the value of the depreciation tax shield?A. $8,500B. $17,000C. $22,500D. $25,000E. $37,75057.Lee's Furniture just purchased $24,000 of fixed assets that are classified as 5-year MACRSproperty. The MACRS rates are 20 percent, 32 percent, 19.2 percent, 11.52 percent, 11.52 percent, and 5.76 percent for Years 1 to 6, respectively. What is the amount of the depreciation expense for the third year?A. $2,304B. $2,507C. $2,765D. $4,608E. $4,80058.Lew just purchased $67,600 of equipment that is classified as 5-year MACRS property. TheMACRS rates are 20 percent, 32 percent, 19.2 percent, 11.52 percent, 11.52 percent, and 5.76 percent for Years 1 to 6, respectively. What will the book value of this equipment be at the end of four years should he decide to resell the equipment at that point in time?A. $11,681.28B. $18,280.20C. $17,040.00D. $19,468.80E. $22,672.0059.Northern Enterprises just purchased $1,900 of fixed assets that are classified as 3-year MACRSproperty. The MACRS rates are 33.33 percent, 44.44 percent, 14.82 percent, and 7.41 percent for Years 1 to 4, respectively. What is the amount of the depreciation expense for Year 2?A. $562.93B. $633.27C. $719.67D. $844.36E. $1,477.6360.The Galley purchased some 3-year MACRS property two years ago at a cost of $19,800. TheMACRS rates are 33.33 percent, 44.44 percent, 14.82 percent, and 7.41 percent. The firm no longer uses this property so is selling it today at a price of $13,500. What is the amount of the pretax profit on the sale?A. $11,140.48B. $9,098.46C. $10,500.00D. $8,016.67E. $10,702.4061.Three years ago, you purchased some 5-year MACRS equipment at a cost of $135,000. TheMACRS rates are 20 percent, 32 percent, 19.2 percent, 11.52 percent, 11.52 percent, and 5.76 percent for Years 1 to 6, respectively. You sold the equipment today for $82,500. Which of these statements is correct if your tax rate is 34 percent?A. T he tax due on the sale is $14,830.80.B. T he book value today is $40,478.C. T he book value today is $37,320.D. T he taxable amount on the sale is $47,380.E. T he tax refund from the sale is $13,219.20.62.Custom Cars purchased some $39,000 of fixed assets two years ago that are classified as 5-yearMACRS property. The MACRS rates are 20 percent, 32 percent, 19.2 percent, 11.52 percent,11.52 percent, and 5.76 percent for Years 1 to 6, respectively. The tax rate is 34 percent. If theassets are sold today for $19,000, what will be the aftertax cash flow from the sale?A. $16,358.88B. $17,909.09C. $18,720.00D. $18,904.80E. $19,000.0063.Winslow Motors purchased $225,000 of MACRS 5-year property. The MACRS rates are 20percent, 32 percent, 19.2 percent, 11.52 percent, 11.52 percent, and 5.76 percent for Years 1 to 6, respectively. The tax rate is 34 percent. If the firm sells the asset after five years for $10,000, what will be the aftertax cash flow from the sale?A. $8,993.60B. $8,880.20C. $11,006.40D. $7,770.40E. $12,892.0064.A project is expected to create operating cash flows of $26,500 a year for four years. The initialcost of the fixed assets is $62,000. These assets will be worthless at the end of the project. An additional $3,000 of net working capital will be required throughout the life of the project. What is the project's net present value if the required rate of return is 12 percent?A. $19,208.11B. $14,028.18C. $15,306.09D. $17,396.31E. $21,954.1765.A project will produce operating cash flows of $45,000 a year for four years. During the life of theproject, inventory will be lowered by $30,000 and accounts receivable will increase by $15,000.Accounts payable will decrease by $10,000. The project requires the purchase of equipment at an initial cost of $120,000. The equipment will be depreciated straight-line to a zero book value over the life of the project. The equipment will be salvaged at the end of the project creating a $25,000 aftertax cash inflow. At the end of the project, net working capital will return to its normal level. What is the net present value of this project given a required return of 15 percent?A. $23,483.48B. $16,117.05C. $24,909.09D. $22,037.86E. $19,876.0266.A project will produce an operating cash flow of $7,300 a year for three years. The initialinvestment for fixed assets will be $11,600, which will be depreciated straight-line to zero over the asset’s 4-year life. The project will require an initial $500 in net working capital plus an additional $500 every year with all net working capital levels restored to their original levels when the project ends. The fixed assets can be sold for an estimated $2,500 at the end of the project, the tax rate is 34 percent, and the required rate of return is 12 percent. What is the net present value of the project?A. $7,532.27B. $9,896.87C. $7,072.72D. $6,353.41E. $8,398.2967.Matty's Place is considering the installation of a new computer system that will cut annualoperating costs by $12,000. The system will cost $42,000 to purchase and install. This system is expected to have a 5-year life and will be depreciated to zero using straight-line depreciation.What is the amount of the earnings before interest and taxes for each year of this project?A. −$20,400B. $5,400C. $3,600D. $12,000E. $8,400。
罗斯《公司理财》英文习题答案DOCchap
30.1 The new corporation issues $300,000 in new debt. The merger creates $100,000 ofgoodwill because the merger is a purchase.Balance SheetLager Brewing(in $ thousands)Current assets $480 Current liabilities $200Other assets 140 Long-term debt 400Net fixed assets 580 Equity 700Goodwill 100Total assets $1,300 Total liabilities $1,300 30.2 If the balance sheet for Philadelphia Pretzel shows assets at book value instead of marketvalue, the goodwill will be only $60,000 (=$300,000 - $240,000). Thus, the net fixed assetsare $620,000 (=$1,300,000 - $480,000 - $140,000 - $60,000).Balance SheetLager Brewing(in $ thousands)Current assets $480 Current liabilities $200Other assets 140 Long-term debt 400Net fixed assets 620 Equity 700Goodwill 60Total assets $1,300 Total liabilities $1,300 30.3Balance SheetLager Brewing(in $ thousands)Current assets $480 Current liabilities $280Other assets 140 Long-term debt 100Net fixed assets 580 Equity 820Total assets $1,200 Total liabilities $1,200 30.4 a. False. Although the reasoning seems correct, the Stillman-Eckbo data do not supportthe monopoly power theory.b. True. When managers act in their own interest, acquisitions are an important controldevice for shareholders. It appears that some acquisitions and takeovers are theconsequence of underlying conflicts between managers and shareholders.c. False. Even if markets are efficient, the presence of synergy will make the value ofthe combined firm different from the sum of the values of the separate firms.Incremental cash flows provide the positive NPV of the transaction.d. False. In an efficient market, traders will value takeovers based on “Fundamentalfactors” regardless of the time horizon. Recall that the evidence as a whole suggestsefficiency in the markets. Mergers should be no different.e. False. The tax effect of an acquisition depends on whether the merger is taxable ornon-taxable. In a taxable merger, there are two opposing factors to consider, thecapital gains effect and the write-up effect. The net effect is the sum of these twoeffects.f. True. Because of the coinsurance effect, wealth might be transferred from thestockholders to the bondholders. Acquisition analysis usually disregards this effectand considers only the total value.30.530.6 a. The weather conditions are independent. Thus, the joint probabilities are theproducts of the individual probabilities.Possible states Joint probabilityRain Rain 0.1 x 0.1=0.01Rain Warm 0.1 x 0.4=0.04Rain Hot 0.1 x 0.5=0.05Warm Rain 0.4 x 0.1=0.04Warm Warm 0.4 x 0.4=0.16Warm Hot 0.4 x 0.5=0.20Hot Rain 0.5 x 0.1=0.05Hot Warm 0.5 x 0.4=0.20Hot Hot 0.5 x 0.5=0.25Since the state Rain Warm has the same outcome (revenue) as Warm Rain, theirprobabilities can be added. The same is true of Rain Hot, Hot Rain and Warm Hot,Hot Warm. Thus the joint probabilities arePossibleJoint probabilitystatesRain Rain 0.01Rain Warm 0.08Rain Hot 0.10Warm Warm 0.16Warm Hot 0.40Hot Hot 0.25The joint values are the sums of the values of the two companies for the particularstate.Possible states Joint valueRain Rain $200,000Rain Warm 300,000Warm Warm 400,000Rain Hot 500,000Warm Hot 600,000Hot Hot 800,000b. Recall, if a firm cannot service its debt, the bondholders receive the value of the assets.Thus, the value of the debt is the value of the company if the face value of the debt isgreater than the value of the company. If the value of the company is greater than the value of the debt, the value of the debt is its face value. Here the value of the common stock is always the residual value of the firm over the value of the debt.Joint Prob. Joint Value Debt Value Stock Value0.01 $200,000 $200,000 $00.08 300,000 300,000 00.16 400,000 400,000 00.10 500,000 400,000 100,0000.40 600,000 400,000 200,0000.25 800,000 400,000 400,000c. To show that the value of the combined firm is the sum of the individual values, youmust show that the expected joint value is equal to the sum of the separate expected values.Expected joint value= 0.01($200,000) + 0.08($300,000) + 0.16($400,000) + 0.10($500,000) +0.40($600,000) + 0.25($800,000)= $580,000Since the firms are identical, the sum of the expected values is twice the expectedvalue of either.Expected individual value = 0.1($100,000) + 0.4($200,000) + 0.5($400,000) = $290,000 Expected combined value = 2($290,000) = $580,000d. The bondholders are better off if the value of the debt after the merger is greater thanthe value of the debt before the merger.Value of the debt before the merger:The value of debt for either company= 0.1($100,000) + 0.4($200,000) + 0.5($200,000) = $190,000Total value of debt before the merger = 2($190,000) = $380,000Value of debt after the merger= 0.01($200,000) + 0.08($300,000) + 0.16($400,000) + 0.10($400,000) +0.40($400,000) +0.25($400,000)= $390,000The bondholders are $10,000 better off after the merger.30.7 The decision hinges upon the risk of surviving. The final decision should hinge on thewealth transfer from bondholders to stockholders when risky projects are undertaken.High-risk projects will reduce the expected value of the bondholders’ claims on the firm.The telecommunications business is riskier than the utilities business. If the total value of the firm does not change, the increase in risk should favor the stockholder. Hence,management should approve this transaction. Note, if the total value of the firm dropsbecause of the transaction and the wealth effect is lower than the reduction in total value, management should reject the project.30.8 If the market is “smart,” the P/E ratio will not be constant.a. Value = $2,500 + $1,000 = $3,500b. EPS = Post-merger earnings / Total number of shares=($100 + $100)/200 =$1c. Price per share = Value/Total number of shares=$3,500/200 =$17.50d. If the market is “fooled,” the P/E ratio will be constant at $25.Value = P/E * Total number of shares= 25 * 200 = $5,000EPS = Post-merger earnings / Total number of shares=$5,000/200 = $25.0030.9 a. After the merger, Arcadia Financial will have 130,000 [=10,000 + (50,000)(6/10)]shares outstanding. The earnings of the combined firm will be $325,000. The earningsper share of the combined firm will be $2.50 (=$325,000/130,000). The acquisition will increase the EPS for the stockholders from $2.25 to $2.50.b. There will be no effect on the original Arcadia stockholders. No synergies exist in thismerger since Arcadia is buying Coldran at its market price. Examining the relativevalues of the two firms sees the latter point.Share price of Arcadia = (16 * $225,000) / 100,000=$36Share price of Coldran = (10.8 * $100,000) / 50,000=$21.60The relative value of these prices is $21.6/$36 = 0.6. Since Coldran’s shareholdersreceive 0.6 shares of Arcadia for every share of Coldran, no synergies exist.30.10 a. The synergy will be the discounted incremental cash flows. Since the cash flows areperpetual, this amount isb. The value of Flash-in-the-Pan to Fly-by-Night is the synergy plus the current marketvalue of Flash-in-the-Pan.V = $7,500,000 + $20,000,000= $27,500,000c. Cash alternative = $15,000,000Stock alternative = 0.25($27,500,000 + $35,000,000)= $15,625,000d. NPV of cash alternative = V - Cost=$27,500,000 - $15,000,000=$12,500,000NPV of stock alternative = V - Cost=$27,500,000 - $15,625,000=$11,875,000e. Use the cash alternative, its NPV is greater.30.11 a. The value of Portland Industries before the merger is $9,000,000 (=750,000x12). Thisvalue is also the discounted value of the expected future dividends.$9,000,000 =r = 0.1025 = 10.25%r is the risk-adjusted discount rate for Portland’s expected future dividends.the value of Portland Industries after the merger isThis is the value of Portland Industries to Freeport.b. NPV = Gain - Cost= $14,815,385 - ($40x250, 000)= $4,815,385c. If Freeport offers stock, the value of Portland Industries to Freeport is the same, but thecost differs.Cost = (Fraction of combined firm owned by Portland’s stockholders)x(Value of the combined firm)Value of the combined firm = (Value of Freeport before merger)+ (Value of Portland to Freeport)= $15x1,000,000 + $14,815,385= $29,815,385Cost = 0.375x$29,815,385= $11,180,769NPV= $14,815,385 - $11,180,769=$3,634,616d. The acquisition should be attempted with a cash offer since it provides a higher NPV.e. The value of Portland Industries after the merger isThis is the value of Portland Industries to Freeport.NPV = Gain-Cost=$11,223,529 - ($40x250,000)=$1,223,529If Freeport offers stock, the value of Portland Industries to Freeport is the same, but the cost differs.Cost = (Fraction of combined firm owned by Portland’s stockholders)x(Value of the combined firm)Value of the combined firm = (Value of Freeport before merger)+ (Value of Portland to Freeport)= $15x1,000,000 + $11,223,529= $26,223,529Cost = 0.375 * $26,223,529=$9,833,823NPV = $11,223,529 - $9,833,823=$1,389,706The acquisition should be attempted with a stock offer since it provides a higher NPV.30.12 a. Number of shares after acquisition=30 + 15 = 45 milStock price of Harrods after acquisition = 1,000/45=22.22 poundsb. Value of Selfridge stockholders after merger:α * 1,000 = 300α = 30%New shares issued = 12.86 mil12.86:20 = 0.643:1The proper exchange ratio should be 0.643 to make the stock offer’s value to Selfridgeequivalent to the cash offer.30.13 To evaluate this proposal, look at the present value of the incremental cash flows.Cash Flows to Company A(in $ million)Year 0 1 2 3 4 5Acquisition of B -550Dividends from B 150 32 5 20 30 45Tax-loss carryforwards 25 25Terminal value 600Total -400 32 30 45 30 645 The additional cash flows from the tax-loss carry forwards and the proposed level of debt should be discounted at the cost of debt because they are determined with very littleuncertainty.The after-tax cash flows are subject to normal business risk and must be discounted at anormal rate.Beta coefficient for the bond = 0.25 = [(8%-6%)/8%].Beta coefficient for the company = 1 = [(0.25)2 + (1.25)(0.75)]Discount rate for normal operations:r = 6% + 8% (1) = 14%Discount rate for dividends:The new beta coefficient for the company, 1, must be the weighted average of the debtbeta and the stock beta.1 = 0.5(0.25) + 0.5(βs)βs = 1.75r = 6% + 8%(1.75) = 20%Because the NPV of the acquisition is negative, Company A should not acquireCompany B.30.14 The commonly used defensive tactics by target-firm managers include:i. corporate charter amendments like super-majority amendment or staggering theelection of board members.ii. repurchase standstill agreements.iii. exclusionary self-tenders.iv. going private and leveraged buyouts.v. other devices like golden parachutes, scorched earth strategy, poison pill, ..., etc.Mini Case: U.S.Steel’s case.You have 3 choices: tender, or do not tender or sell in the market. If you do sell your shares in the market, at some point, somebody else would need to make a decision in “tender” or “not tender” as well.It is important to recognize that the firm has about 60 million shares outstanding (since 30 million shares will give US Steel 50.1% of Marathon shares). Let’s consider the possible sellingthe market price.If you choose not to tender, and 30 million shares were tendered US Steel succeeds to gain50.1% control, you will only receive $85 a share. If you do tender, the price you will receive will be no worse than $85 a share and can be as high as $125 a share. Depending on the number of shares tendered, you will receive one of the following prices.If only 50.1% tendered, you will get $125 per share.If the shares tendered exceed 50.1% but less than 100%, you will get more than $105 ashare.If all 60 million shares were tendered, you will get $105 per share. (which is )It is clear that, in the above 3 cases, when you are not sure about whether US Steel will succeed or not, you will be better off to tender your shares than not tender. This is because at best, you will only receive $85 per share if you choose not to tender.版权申明本文部分内容，包括文字、图片、以及设计等在网上搜集整理。
罗斯公司理财第六版习题答案第5章
Concept Questions◆Define pure discount bonds, level-coupon bonds, and consols.A pure discount bond is one that makes no intervening interest payments. One receives a single lump sum payment at maturity. A level-coupon bond is a combination of an annuity and a lump sum at maturity. A consol is a bond that makes interest payments forever.◆Contrast the state interest rate and the effective annual interest rate for bonds paying semi-annual interest. Effective annual interest rate on a bond takes into account two periods of compounding per year received on the coupon payments. The state rate does not take this into account.◆What is the relationship between interest rates and bond prices?There is an inverse relationship. When one goes up, the other goes down.◆How does one calculate the yield to maturity on a bond?One finds the discount rate that equates the promised future cash flows with the price of the bond.◆What are the three factors determining a firm's P/E ratio?Today's expectations of future growth opportunities.The discount rate.The accounting method.◆What is the closing price of General Data?The closing price of General Data is 6 3/16.◆What is the PE of General House?The PE of General House is 29.◆What is the annual dividend of General Host?The annual dividend of General Host is zero.Concept Questions- Appendix To Chapter 5◆What is the difference between a spot interest rate and the yield to maturity?The yield to maturity is the geometric average of the spot rates during the life of the bond.◆Define the forward rate.Given a one-year bond and a two-year bond, one knows the spot rates for both. The forward rate is the rate of return implicit on a one-year bond purchased in the second year that would equate the terminal wealth of purchasing the one-year bond today and another in one year with that of the two-year bond.◆What is the relationship between the one-year spot rate, the two-year spot rate and the forward rate over the second year?The forward rate f2 = [(1+r2)2 /(1+r1 )] - 1◆What is the expectation hypothesis?Investors set interest rates such that the forward rate over a given period equals the spot rate for that period.◆What is the liquidity-preference hypothesis?This hypothesis maintains that investors require a risk premium for holding longer-term bonds (i.e. they prefer to be liquid or short-term investors). This implies that the market sets the forward rate for a given period above the expected spot rate for that period.Questions And ProblemsHow to Value Bonds5.1 What is the present value of a 10-year, pure discount bond that pays $1,000 at maturity andis priced to yield the following rates?a. 5 percentb. 10 percentc. 15 percentSolutions a. $1,000 / 1.0510 = $613.91b. $1,000 / 1.1010 = $385.54c. $1,000 / 1.1510 = $247.185.2 Microhard has issued a bond with the following characteristics:Principal: $1,000Term to maturity: 20 yearsCoupon rate: 8 percentSemiannual paymentsCalculate the price of the Microhard bond if the stated annual interest rate is:a. 8 percentb. 10 percentc. 6 percentSolutions The amount of the semi-annual interest payment is $40 (=$1,000 ⨯ 0.08 / 2). There are a total of 40 periods; i.e., two half years in each of the twenty years in the term to maturity.The annuity factor tables can be used to price these bonds. The appropriate discount rate touse is the semi-annual rate. That rate is simply the annual rate divided by two. Thus, for part b the rate to be used is 5% and for part c is it 3%.a. $40 (19.7928) + $1,000 / 1.0440 = $1,000Notice that whenever the coupon rate and the market rate are the same, the bond ispriced at par.b. $40 (17.1591) + $1,000 / 1.0540 = $828.41Notice that whenever the coupon rate is below the market rate, the bond is pricedbelow par.c. $40 (23.1148) + $1,000 / 1.0340 = $1,231.15Notice that whenever the coupon rate is above the market rate, the bond is pricedabove par.5.3 Consider a bond with a face value of $1,000. The coupon is paid semiannually and themarket interest rate (effective annual interest rate) is 12 percent. How much would you payfor the bond ifa. the coupon rate is 8 percent and the remaining time to maturity is 20 years?b. the coupon rate is 10 percent and the remaining time to maturity is 15 years?Solutions Semi-annual discount factor = (1.12)1/2 - 1 = 0.05830 = 5.83%a. Price = $40400583.0A+ $1,000 / 1.058340= $614.98 + $103.67= $718.65b. Price = $50300583.0A+ $1,000 / 1.058330= $700.94 + $182.70 = $883.645.4 Pettit Trucking has issued an 8-percent, 20-year bond that pays interest semiannually. If themarket prices the bond to yield an effective annual rate of 10 percent, what is the price ofthe bond? Solutions Effective annual rate of 10%:Semi-annual discount factor = (1.1)0.5 - 1 = 0.04881 = 4.881%Price = $404004881.0A+ $1,000 / 1.0488140= $846.335.5 A bond is sold at $923.14 (below its par value of $1,000). The bond has 15 years tomaturity and investors require a 10-percent yield on the bond. What is the coupon rate forthe bond if the coupon is paid semiannually?Solutions $923.14 = C3005.0A+ $1,000 / 1.0530= (15.37245) C + $231.38C = $45The annual coupon rate = $45 ⨯ 2 / $1,000 = 0.09 = 9%5.6 You have just purchased a newly issued $1,000 five-year Vanguard Company bond at par.This five-year bond pays $60 in interest semiannually. You are also considering the purchaseof another Vanguard Company bond that returns $30 in semiannual interest payments andhas six years remaining before it matures. This bond has a face value of $1,000.a. What is effective annual return on the five-year bond?b. Assume that the rate you calculated in part (a) is the correct rate for the bond with sixyears remaining before it matures. What should you be willing to pay for that bond?c. How will your answer to part (b) change if the five-year bond pays $40 in semiannualinterest? Solutionsa. The semi-annual interest rate is $60 / $1,000 = 0.06. Thus, the effective annual rate is 1.062 - 1 =0.1236 = 12.36%.b. Price = $301206.0A+ $1,000 / 1.0612= $748.48c. Price = $301204.0A+ $1,000 / 1.0412= $906.15Note: In parts b and c we are implicitly assuming that the yield curve is flat. That is, the yield in year 5 applies for year 6 as well.Bond Concepts5.7 Consider two bonds, bond A and bond B, with equal rates of 10 percent and the same facevalues of $1,000. The coupons are paid annually for both bonds. Bond A has 20 years tomaturity while bond B has10 years to maturity.a. What are the prices of the two bonds if the relevant market interest rate is 10 percent?b. If the market interest rate increases to 12 percent, what will be the prices of the two bonds?c. If the market interest rate decreases to 8 percent, what will be the prices of the two bonds? Solutionsa. PA = $1002010.0A+ $1,000 / 1.1020 = $1,000PB = $1001010.0A+ $1,000 / 1.1010 = $1,000b. PA = $1002012.0A+ $1,000 / 1.1220 = $850.61PB = $1001012.0A+ $1,000 / 1.1210 = $887.00c. PA = $1002008.0A+ $1,000 / 1.0820 = $1,196.36PB = $1001008.0A+ $1,000 / 1.0810 = $1,134.205.8 a. If the market interest rate (the required rate of return that investors demand)unexpectedly increases, what effect would you expect this increase to have on theprices of long-term bonds? Why?b. What would be the effect of the rise in the interest rate on the general level of stockprices? Why? Solutionsa. The price of long-term bonds should fall. The price is the PV of the cash flowsassociated with the bond. As the interest rate rises, the PV of those flows falls.This can be easily seen by looking at a one-year, pure discount bond.Price = $1,000 / (1 + i)As i. increases, the denominator rises. This increase causes the price to fall.b. The effect upon stocks is not as certain as that upon the bonds. The nominalinterest rate is a function of both the real interest rate and the inflation rate; i.e.,(1 + i) = (1 + r) (1 + inflation)From this relationship it is easy to conclude that as inflation rises, the nominal interest rate rises. Stock prices are a function of dividends and future prices as well as the interest rate. Those dividends and future prices are determined by the earning power of the firm. When inflation occurs, it may increase or decrease firm earnings. Thus, the effect of a rise in the level of general prices upon the level of stock prices is uncertain.5.9 Consider a bond that pays an $80 coupon annually and has a face value of $1,000.Calculate the yield to maturity if the bond hasa. 20 years remaining to maturity and it is sold at $1,200.b. 10 years remaining to maturity and it is sold at $950.Solutions a. $1,200 = $8020rA+ $1,000 / (1 + r)20r = 0.0622 = 6.22%b. $950 = $8010rA+ $1,000 / (1 + r)10r = 0.0877 = 8.77%5.10 The Sue Fleming Corporation has two different bonds currently outstanding. Bond A has aface value of $40,000 and matures in 20 years. The bond makes no payments for the firstsix years and then pays $2,000 semiannually for the subsequent eight years, and finallypays $2,500 semiannually for the last six years. Bond B also has a face value of $40,000and a maturity of 20 years; it makes no coupon payments over the life of the bond. If therequired rate of return is 12 percent compounded semiannually, what is the current price ofBond A? of Bond B?Solutions PA = ($2,0001606.0A) / (1.06)12 + ($2,5001206.0A) / (1.06)28 + $40,000 / (1.06)40= $18,033.86PB = $ 40,000 / (1.06)40 = $3,888.89The Present Value of Common Stocks5.11 Use the following February 11, 2000, WSJ quotation for AT&T Corp. Which of thefollowing statements is false?a. The closing price of the bond with the shortest time to maturity was $1,000.b. The annual coupon for the bond maturing in year 2016 is $90.00.c. The price on the day before this quotation (i.e., February 9) for the ATT bond maturingin year 2022 was $1.075 per bond contract.d. The current yield on the ATT bond maturing in year 2002 was 7.125%e. The ATT bond maturing in year 2002 has a yield to maturity less than 7.125%.Bonds Cur Yld Vol Close Net ChgATT 9s 16 ? 10 117 _ 1/4ATT 5 1/8 01 ? 5 100 _ 3/4ATT 7 1/8 02 ? 193 104 1/8 _ 1/4ATT 8 1/8 22 ? 39 107 3/8 _ 1/8Solutions a. TrueTrueFalseFalseTrue5.12 Following are selected quotations for New York Exchange Bonds from the Wall StreetJournal. Which of the following statements about Wilson’s bond is false?a. The bond maturing in year 2000 has a yield to maturity greater than 63⁄8%.b. The closing price of the bond with the shortest time to maturity on the day before thisquotation was $1,003.25.c. This annual coupon for the bond maturing in year 2013 is $75.00.d. The current yield on the Wilson’s bond with the longest time to maturity was 7.29%.e. None of the above.Quotations as of 4 P.M. Eastern TimeFriday, April 23, 1999Bonds Current Yield Vol Close NetWILSON 6 3/8 99 ? 76 100 3/8 _ 1/8WILSON 6 3/8 00 ? 9 98 1/2WILSON 7 1/4 02 ? 39 103 5/8 1/8WILSON 7 1/2 13 ? 225 102 7/8 _ 1/8Solutions a. TrueFalseTrueTrueFalse5.13 A common stock pays a current dividend of $2. The dividend is expected to grow at an8-percent annual rate for the next three years; then it will grow at 4 percent in perpetuity.The appropriate discount rate is 12 percent. What is the price of this stock?Solutions Price = $2 (1.08) / 1.12 + $2 (1.082) / 1.122 + $2 (1.083) / 1.123+ {$2 (1.083) (1.04) / (0.12 - 0.04)} / 1.123= $28.895.14 Use the following February 12, 1998, WSJ quotation for Merck & Co. to answer the nextquestion. 52 Weeks Yld Vol NetHi Lo Stock Sym Div % PE 100s Hi Lo Close Chg120. 80.19 Merck MRK 1.80 ? 30 195111 115.9 114.5 115 _1.25Which of the following statements is false?a. The dividend yield was about 1.6%.b. The 52 weeks’ trading range was $39.81.c. The closing price per share on February 10, 1998, was $113.75.d. The closing price per share on February 11, 1998, was $115.e. The earnings per share were about $3.83.Solutions a. FalseTrueFalseFalseTrue5.15 Use the following stock quote.52 Weeks Yld Vol NetHi Lo Stock Sym Div % PE 100s Hi Lo Close Chg126.25 72.50 Citigroup CCI 1.30 1.32 16 20925 98.4 97.8 98.13 _.13The expected growth rate in Citigroup’s dividends is 7% a year. Suppose you use thediscounted dividend model to price Citigroup’s shares. The constant growth dividendmodel would suggest that the required return on the Citigroup’s stock is what?98.125 = 1.30 ( 1.07) / r - 0.07r = 8.4175 %5.16 You own $100,000 worth of Smart Money stock. At the end of the first year you receive adividend of $2 per share; at the end of year 2 you receive a $4 dividend. At the end of year3 you sell the stock for $50 per share. Only ordinary (dividend) income is taxed at the rateof 28 percent. Taxes are paid at the time dividends are received. The required rate of returnis 15 percent. How many shares of stock do you own? Solutions Price = $2 (0.72) / 1.15 + $4 (0.72) / 1.152 + $50 / 1.153= $36.31The number of shares you own = $100,000 / $36.31 = 2,754 shares5.17 Consider the stock of Davidson Company that will pay an annual dividend of $2 in thecoming year. The dividend is expected to grow at a constant rate of 5 percent permanently.The market requires a 12-percent return on the company.a. What is the current price of a share of the stock?b. What will the stock price be 10 years from today?Solutionsa. P = $2 / (0.12 - 0.05) = $28.57b. P10 = D11 / (r - g)= $2 (1.0510) / (0.12 - 0.05) = $46.545.18 Easy Type, Inc., is one of a myriad of companies selling word processor programs.Their newest program will cost $5 million to develop. First-year net cash flows will be$2 million. As a result of competition, profits will fall by 2 percent each year thereafter.All cash inflows will occur at year-end. If the market discount rate is 14 percent, what isthe value of this new program?SolutionsValue = -$5,000,000 + $2,000,000 / {0.14 - (-0.02)}= $7,500,0005.19 Whizzkids, Inc., is experiencing a period of rapid growth. Earnings and dividends pershare are expected to grow at a rate of 18 percent during the next two years, 15 percent inthe third year, and at a constant rate of 6 percent thereafter. Whizzkids’ last dividend,which has just been paid, was $1.15. If the required rate of return on the stock is 12percent, what is the price of a share of the stock today?SolutionsPrice = $1.15 (1.18) / 1.12 + $1.15 (1.182) / 1.122 + $1.152 (1.182) / 1.123+ {$1.152 (1.182) (1.06) / (0.12 - 0.06)} / 1.123= $26.955.20 Allen, Inc., is expected to pay an equal amount of dividends at the end of the first twoyears. Thereafter, the dividend will grow at a constant rate of 4 percent indefinitely. Thestock is currently traded at $30. What is the expected dividend per share for the next yearif the required rate of return is 12 percent?Solutions$30 = D / 1.12 + D / 1.122 + {D (1 + 0.04) / (0.12 - 0.04)} / 1.122= 12.053571 DD = $2.495.21 Calamity Mining Company’s reserves of ore are being depleted, and its costs ofrecovering a declining quantity of ore are rising each year. As a result, the company’searnings are declining at the rate of 10 percent per year. If the dividend per share that isabout to be paid is $5 and the required rate of return is 14 percent, what is the value of thefirm’s stock?SolutionsDividend one year from now = $5 (1 - 0.10) = $4.50Price = $5 + $4.50 / {0.14 - (-0.10)} = $23.75Since the current $5 dividend has not yet been paid, it is still included in the stock price.5.22 The Highest Potential, Inc., will pay a quarterly dividend per share of $1 at the end of eachof the next 12 quarters. Subsequently, the dividend will grow at a quarterly rate of 0.5percent indefinitely. The appropriate rate of return on the stock is 10 percent. What is thecurrent stock price?Estimates of Parameters in the Dividend-Discount ModelSolutionsPrice = $112025.0A+ {$1 (1 + 0.005) / (0.025 - 0.005)} / 1.02512= $10.26 + $37.36= $47.625.23 The newspaper reported last week that Bradley Enterprises earned $20 million. The reportalso stated that the firm’s return on equity remains on its historical trend of 14 percent.Bradley retains 60 percent of its earnings. What is the firm’s growth rate of earnings?What will next year’s earnings be?SolutionsGrowth rate g = 0.6 ⨯ 0.14 = 0.084 = 8.4%Next year earnings = $20 million ⨯ 1.084 = $21.68 million5.24 Von Neumann Enterprises has just reported earnings of $10 million, and it plans to retain 75percent of its earnings. The company has 1.25 million shares of common stock outstanding.The stock is selling at $30. The historical return on equity (ROE) of 12 percent is expectedto continue in the future. What is the required rate of return on the stock?Growth Opportunitiesg = retention ratio ⨯ ROE = 0.75 ⨯ 0.12= 0.09 = 9%Dividend per share = $10 million ⨯ (1 - 0.75) / 1.25 million= $2The required rate of return = $2 (1.09) / $30 + 0.09= 0.1627 = 16.27%5.25 Rite Bite Enterprises sells toothpicks. Gross revenues last year were $3 million, and totalcosts were $1.5 million. Rite Bite has 1 million shares of common stock outstanding.Gross revenues and costs are expected to grow at 5 percent per year. Rite Bite pays noincome taxes, and all earnings are paid out as dividends.a. If the appropriate discount rate is 15 percent and all cash flows are received at year’send, what is the price per share of Rite Bite stock?b. The president of Rite Bite decided to begin a program to produce toothbrushes. Theproject requires an immediate outlay of $15 million. In one year, another outlay of$5 million will be needed. The year after that, net cash inflows will be $6 million. Thisprofit level will be maintained in perpetuity. What effect will undertaking this projecthave on the price per share of the stock?Solutionsa. Price = ($3 - $1.5) ⨯ 1.05 / (0.15 - 0.05)= $15.75b. NPVGO = -$15,000,000 - $5,000,000 / 1.15 + ($6,000,000 / 0.15) / 1.15= $15,434,783The price increases by $15.43 per share.5.26 California Electronics, Inc., expects to earn $100 million per year in perpetuity if it doesnot undertake any new projects. The firm has an opportunity that requires an investment of$15 million today and $5 million in one year. The new investment will begin to generateadditional annual earnings of $10 million two years from today in perpetuity. The firm has20 million shares of common stock outstanding, and the required rate of return on thestock is 15 percent.a. What is the price of a share of the stock if the firm does not undertake the new project?b. What is the value of the growth opportunities resulting from the new project?c. What is the price of a share of the stock if the firm undertakes the new project?Solutionsa. Price = EPS / r = {$100 million / 20 million} / 0.15= $33.33b. NPV = -$15 million - $5 million / 1.15 + ($10 million / 0.15) / 1.15= $38,623,188c. Price = $33.33 + $38,623,188 / 20,000,000= $35.265.27 Suppose Smithfield Foods, Inc., has just paid a dividend of $1.40 per share. Sales andprofits for Smithfield Foods are expected to grow at a rate of 5% per year. Its dividend isexpected to grow by the same rate. If the required return is 10%, what is the value of ashare of Smithfield Foods?SolutionsPrice = 1.40 (1.05) / 0.10 - 0.05Price = $29.405.28 In order to buy back its own shares, Pennzoil Co. has decided to suspend its dividends forthe next two years. It will resume its annual cash dividend of $2.00 a share 3 years fromnow. This level of dividendswill be maintained for one more year. Thereafter, Pennzoil isexpected to increase its cash dividend payments by an annual growth rate of 6% per yearforever. The required rate of return on Pennzoil’s stock is 16%. According to thediscounted dividend model, what should Pennzoil’s current share price be? SolutionsPrice = 2 / (1.16) 3 + 2 / (1.16)4 + 2.12 / 0.16 - 0.06= 1.28 + 1.10 + 21.20= $23.585.29 Four years ago, Ultramar Diamond Inc. paid a dividend of $0.80 per share. This yearUltramar paid a dividend of $1.66 per share. It is expected that the company will paydividends growing at the same rate for the next 5 years. Thereafter, the growth rate willlevel at 8% per year. The required return on this stock is 18%. According to the discounteddividend model, what would Ultramar’s cash dividend be in 7 years?a. $2.86c. $3.68d. $4.30e. $4.82Solutionsa. g = 0.4 ⨯ 0.15 = 0.06 = 6%b. Dividend per share = $1.5 million ⨯ 0.6 / 300,000= $3Price = $3 (1.06) / (0.13 - 0.06)= $45.43c. Assuming the additional earnings generated are all paid out as cash dividends.NPV = -$1.2 million + $0.3 million {1 / (0.13 - 0.10)} {1 - (1.10 / 1.13)10}= $1,159,136.93d. Price = $45.43 + $1,159,136.93 / 300,000= $49.295.30 The Webster Co. has just paid a dividend of $5.25 per share. The company will increase itsdividend by 15 percent next year and will then reduce its dividend growth by 3 percenteach year until it reaches the industry average of 5 percent growth, after which thecompany will keep a constant growth, forever. The required rate of return for the WebsterCo. is 14 percent. What will a share of stock sell for?SolutionsPrice = 3 / 1.15 + 4.5 / ( 1.15)2 + 4.725 / 0.15- 0.05= 2.61 + 3.40 + 47.52= $53.535.31 Consider Pacific Energy Company and U.S. Bluechips, Inc., both of which reported recentearnings of $800,000 and have 500,000 shares of common stock outstanding. Assume bothfirms have the same required rate of return of 15 percent a year.a. Pacific Energy Company has a new project that will generate cash flows of $100,000each year in perpetuity. Calculate the P/E ratio of the company.Chapter 5 How to Value Bonds and Stocks 129b. U.S. Bluechips has a new project that will increase earnings by $200,000 in the comingyear. The increased earnings will grow at 10 percent a year in perpetuity. Calculate theP/E ratio of the firm. Solutionsa. P/E of Pacific Energy Company:EPS = ($800,000 / 500,000) = $1.6NPVGO = {$100,000 / 500,000} / 0.15 = $1.33P/E = 1 / 0.15 + 1.33 / 1.6 = 7.50b. P/E of U. S. Bluechips, Inc.:NPVGO = {$200,000 / 500,000} / (0.15 - 0.10) = $8P/E = 1 / 0.15 + 8 / 1.6 = 11.675.32 (Challenge Question) Lewin Skis Inc. (today) expects to earn $4.00 per share for each ofthe future operating periods (beginning at time 1) if the firm makes no new investments(and returns the earnings as dividends to the shareholders). However, Clint Williams,President and CEO, has discovered an opportunity to retain (and invest) 25% of theearnings beginning three years from today (starting at time 3). This opportunity to investwill continue (for each period) indefinitely. He expects to earn 40% (per year) on this newequity investment (ROE of 40), the return beginning one year after each investment ismade. The firm’s equity discount rate is 14% throughout.a. What is the price per share (now at time 0) of Lewin Skis Inc. stock without making thenew investment?b. If the new investment is expected to be made, per the preceding information, whatwould the value of the stock (per share) be now (at time 0)?c. What is the expected capital gain yield for the second period, assuming the proposedinvestment is made? What is the expected capital gain yield for the second period if theproposed investment is not made?d. What is the expected dividend yield for the second period if the new investment ismade? What is the expected dividend yield for the second period if the new investmentis not made?Solutionsa. Price = $4 / 0.14 = $28.57Price = 28.57 + (-1 + 0.40 / 0.14) / 0.04(1.14) 3= 28.57 + 31.33The expected return of 14% less the dividend yield of 5% providesa capital gain yield of 9%. If there is no investment the yield is 14%.$3 / $59.90 = .05 and $4 / $28.57 = .14 without the investment.Appendix to Chapter 5Questions And ProblemsA.1 The appropriate discount rate for cash flows received one year from today is 10 percent. Theappropriate annual discount rate for cash flows received two years from today is 11 percent.a. What is the price of a two-year bond that pays an annual coupon of 6 percent?b. What is the yield to maturity of this bond?Solutionsa. P = $60 / 1.10 + $1,060 / (1.11)2= $54.55 + $ 860.32= $914.87$914.87 = $60 / ( 1 + y ) + $1,060 / ( 1 + y )2y = YTM = 10.97%A.2 The one-year spot rate equals 10 percent and the two-year spot rate equals 8 percent. Whatshould a 5-percent coupon two-year bond cost?SolutionsP = $50 / 1.10 + $1,050 / (1.08)2= $45.45 + $900.21= $945.66A.3 If the one-year spot rate is 9 percent and the two-year spot rate is 10 percent, what is theforward rate? Solutions ( 1 + r1 )( 1 + ƒ2 ) = ( 1 + r2 )2( 1.09 ) ( 1 + ƒ2 ) = ( 1.10 )2ƒ2 = .1101A.4 Assume the following spot rates:Maturity Spot Rates (%)1 52 73 10What are the forward rates over each of the three years?Solutions( 1 + r2 )2 = ( 1+ r1 ) ( 1 + ƒ2 )( 1.07 )2 = ( 1.05 )( 1 + ƒ2 )ƒ2 = .0904, one-year forward rate over the 2nd year is 9.04%.( 1 + r3 )3 = ( 1 + r2 )2 ( 1 + ƒ3 )( 1.10 )3 = ( 1.07 )2 ( 1 + ƒ3 )ƒ3 = .1625, one-year forward rate over the 3rd year is 16.25%.。
罗斯《公司理财》英文习题答案DOCchap019
公司理财习题答案第十九章Chapter 19: Issuing Equity Securities to the Public19.1 a. A general cash offer is a public issue of a security that is sold to all interestedinvestors. A general cash offer is not restricted to current stockholders.b. A rights offer is an issuance that gives the current stockholders the opportunity tomaintain a proportionate ownership of the company. The shares are offered to thecurrent shareholders before they are offered to the general public.c. A registration statement is the filing with the SEC, which discloses all pertinentinformation concerning the corporation that wants to make a public offering.d. A prospectus is the legal document that must be given to every investor whocontemplates purchasing registered securities in a public offering. The prospectusdescribes the details of the company and the particular issue.e. An initial public offering (IPO) is the original sale of a company’s securities to thepublic. An IPO is also called an unseasoned issue.f. A seasoned new issue is a new issue of stock after the company’s securities havepreviously been publicly traded.g. Shelf registration is an SEC procedure, which allows a firm to file a masterregistration statement summarizing the planned financing for a two year period.The firm files short forms whenever it wishes to sell any of the approved masterregistration securities during the two year period.19.2 a. The Securities Exchange Act of 1933 regulates the trading of new, unseasonedsecurities.b. The Securities Exchange Act of 1934 regulates the trading of seasoned securities.This act regulates trading in what is called the secondary market.19.3 Competitive offer and negotiated offer are two methods to select investment bankers forunderwriting. Under the competitive offers, the issuing firm can award its securities to the underwriter with the highest bid, which in turn implies the lowest cost. On the other hand, in negotiated deals, underwriter gains much information about the issuing firm throughnegotiation, which helps increase the possibility of a successful offering.19.4 a. Firm commitment underwriting is an underwriting in which an investment bankingfirm commits to buy the entire issue. It will then sell the shares to the public. Theinvestment banking firm assumes all financial responsibility for any unsold shares.b. A syndicate is a group of investment banking companies that agree to cooperate in ajoint venture to underwrite an offering of securities.c. The spread is the difference between the underwriter’s buying price and the offeringprice. The spread is a fee for the services of the underwriting syndicate.d. Best efforts underwriting is an offering in which the underwriter agrees to distributeas much of the offering as possible. Any unsold portions of the offering are returnedto the issuing firm.19.5 a. The risk in a firm commitment underwriting is borne by the underwriter(s). Thesyndicate agrees to purchase all of an offering. Then they sell as much of it aspossible. Any unsold shares remain the responsibility of the underwriter(s). Therisk that the security’s price may become unfavorable also lies with theunderwriter(s).b. The issuing firm bears the risk in a best efforts underwriting. The underwriter(s)agrees to make its best effort to sell the securities for the firm. Any unsoldsecurities are the responsibility of the firm.19.6 In general, the new price per share after the offering is:P = (market value + proceeds from offering) / total number of sharesi. At $40 P = ($400,000 + ($40 x 5,000)) / 15,000 =$40ii. At $20 P = ($400,000 + ($20 x 5,000)) / 15,000 = $33.33iii. At $10 P = ($400,000 + ($10 x 5,000)) / 15,000 = $3019.7 The poor performance result should not surprise the professor. Since he subscribed to everyinitial public offering, he was bound to get fewer superior performers and more poorperformers. Financial analysts studied the companies and separated the bad prospects from the good ones. The analysts invested in only the good prospects. These issues becameoversubscribed. Since these good prospects were oversubscribed, the professor received a limited amount of stock from them. The poor prospects were probably under-subscribed, so he received as much of their stock as he desired. The result was that his performance was below average because the weight on the poor performers in his portfolio was greater than the weight on the superio r performers. This result is called the winner’s curse. The professor “won” the shares, but his bane was that the shares he “won” were poorperformers.19.8 There are two possible reasons for stock price drops on the announcement of a new equityissue:i. M anagement may attempt to issue new shares of stock when the stock is over-valued, that is, the intrinsic value is lower than the market price. The price drop isthe result of the downward adjustment of the overvaluation.ii. W ith the increase of financial distress possibility, the firm is more likely to raise capital through equity than debt. The market price drops because it interprets theequity issue announcement as bad news.19.9 The costs of new issues include underwriter’s spread, direct and indirect expenses, negativeabnormal returns associated with the equity offer announcement, under-pricing, and green-shoe option.19.10 a. $12,000,000/$15 = 800,000b. 2,400,000/800,000 = 3c. The shareholders must remit $15 and three rights for each share of new stock theywish to purchase.19.11 a. In general, the ex-rights price isP = (Market value + Proceeds from offering) / Total number of sharesP = ($25 x 100,000 + $20 x 10,000) / (100,000 + 10,000) = $24.55b. The value of a right is the difference between the rights-on price of the stock andthe ex-rights price of the stock. The value of a right is $0.45 (=$25 - $24.55).Alternative solution:The value of a right can also be computed as:(Ex-rights price - Subscription price) / Number of rights required to buy a share ofstockValue of a right = ($24.55 - $20) / 10 = $0.45c. The market value of the firm after the issue is the number of shares times the ex-rights price.Value = 110,000 x $24.55 $2,700,000 (Note that the exact ex-rights price is$24.5454.)公司理财习题答案第十九章d. The most important reason to offer rights is to reduce issuance costs. Also, rightsofferings do not dilute ownership and they provide shareholders with moreflexibility. Shareholders can either exercise or sell their rights.19.12 The value of a right = $50 - $45 = $5The number of new shares = $5,000,000 / $25 = 200,000The number of rights / share = ($45 - $25) / $5 = 4The number of old shares = 200,000 x 4 = 800,00019.13 a. Assume you hold three shares of the company’s stock. The value of your holdingsbefore you exercise your rights is 3 x $45 = $135. When you exercise, you mustremit the three rights you receive for owning three shares, and ten dollars. You haveincreased your equity investment by $10. The value of your holdings is $135 + $10= $145. After exercise, you own four shares of stock. Thus, the price per share ofyour stock is $145 / 4 = $36.25.b. The value of a right is the difference between the rights-on price of the stock andthe ex-rights price of the stock. The value of a right is $8.75 (=$45 - $36.25).c. The price drop will occur on the ex-rights date. Although the ex-rights date isneither the expiration date nor the date on which the rights are first exercisable, it isthe day that the price will drop. If you purchase the stock before the ex-rights date,you will receive the rights. If you purchase the stock on or after the ex-rights date,you will not receive the rights. Since rights have value, the stockholder receivingthe rights must pay for them. The stock price drop on the ex-rights day is similar tothe stock price drop on an ex-dividend day.19.14 a. Stock price (ex-right) = (13+2) / (1+0.5) = $10Subscription price = 2 / 0.5 = $4Right’s price = 13-10 = $3= (10-4) / 2 = $3b. Stock price (ex-right) = (13+2) / (1+0.25) = $12Subscription price = 2 / 0.25 = $8Right’s price = 13-12 = $1= (12-8) / 4 = $1c. The stockholders’ wealth is the same between the two arrangements.19.15 If the interest of management is to increase the wealth of the current shareholders, a rightsoffering may be preferable because issuing costs as a percentage of capital raised is lower for rights offerings. Management does not have to worry about underpricing becauseshareholders get the rights, which are worth something. Rights offerings also preventexisting shareholders from losing proportionate ownership control. Finally, whether the shareholders exercise or sell their rights, they are the only beneficiaries.19.16 Reasons for shelf registration include:i. Flexibility in raising money only when necessary without incurring additional issuancecosts.ii. As Bhagat, Marr and Thompson showed, shelf registration is less costly than conventional underwritten issues.iii. Issuance of securities is greatly simplified.19.17 Suppliers of venture capital can include:i. Wealthy families / individuals.ii. Investment funds provided by a number of private partnerships and corporations.iii. Venture capital subsidiaries established by large industrial or financial corporations.iv. “Angels” in an informal venture capital market.19.18 The proceeds from IPO are used to:i. exchange inside equity ownership for outside equity ownershipii. finance the present and future operations of the IPO firms.19.19 Basic empirical regularities in IPOs include:i. underpricing of the offer price,ii. best-efforts offerings are generally used for small IPOs and firm-commitment offerings are generally used for large IPOs,iii. the underwriter price stabilization of the after market and,iv. that issuing costs are higher in negotiated deals than in competitive ones.。
英文版罗斯公司理财习题答案
CHAPTER 7NET PRESENT VALUE AND OTHER INVESTMENT CRITERIAAnswers to Concepts Review and Critical Thinking Questions1. A payback period less than the project’s life means that the NPV is positive for a zero discount rate,but nothing more definitive can be said. For discount rates greater than zero, the payback period will still be less than the project’s life, but the NPV may be positive, zero, or negative, depending on whether the discount rate is less than, equal to, or greater than the IRR. The discounted payback includes the effect of the relevant discount rate. If a project’s discounted payback period is less than the project’s life, it must be the case that NPV is positive.2.If a project has a positive NPV for a certain discount rate, then it will also have a positive NPV for azero discount rate; thus, the payback period must be less than the project life. Since discounted payback is calculated at the same discount rate as is NPV, if NPV is positive, the discounted payback period must be less than the project’s life. If NPV is positive, then the present value of future cash inflows is greater than the initial investment cost; thus PI must be greater than 1. If NPV is positive for a certain discount rate R, then it will be zero for some larger discount rate R*; thus, the IRR must be greater than the required return.3. a.Payback period is simply the accounting break-even point of a series of cash flows. To actuallycompute the payback period, it is assumed that any cash flow occurring during a given period isrealized continuously throughout the period, and not at a single point in time. The payback isthen the point in time for the series of cash flows when the initial cash outlays are fullyrecovered. Given some predetermined cutoff for the payback period, the decision rule is toaccept projects that payback before this cutoff, and reject projects that take longer to payback.The worst problem associated with payback period is that it ignores the time value of money. Inaddition, the selection of a hurdle point for payback period is an arbitrary exercise that lacksany steadfast rule or method. The payback period is biased towards short-term projects; it fullyignores any cash flows that occur after the cutoff point.b.The average accounting return is interpreted as an average measure of the accountingperformance of a project over time, computed as some average profit measure attributable tothe project divided by some average balance sheet value for the project. This text computesAAR as average net income with respect to average (total) book value. Given somepredetermined cutoff for AAR, the decision rule is to accept projects with an AAR in excess ofthe target measure, and reject all other projects. AAR is not a measure of cash flows and marketvalue, but a measure of financial statement accounts that often bear little resemblance to therelevant value of a project. In addition, the selection of a cutoff is arbitrary, and the time valueof money is ignored. For a financial manager, both the reliance on accounting numbers ratherthan relevant market data and the exclusion of time value of money considerations are troubling.Despite these problems, AAR continues to be used in practice because (1) the accountinginformation is usually available, (2) analysts often use accounting ratios to analyze firmperformance, and (3) managerial compensation is often tied to the attainment of targetaccounting ratio goals.c.The IRR is the discount rate that causes the NPV of a series of cash flows to be identically zero.IRR can thus be interpreted as a financial break-even rate of return; at the IRR discount rate,the net value of the project is zero. The acceptance and rejection criteria are:If C0 < 0 and all future cash flows are positive, accept the project if the internal rate ofreturn is greater than or equal to the discount rate.If C0 < 0 and all future cash flows are positive, reject the project if the internal rate ofreturn is less than the discount rate.If C0 > 0 and all future cash flows are negative, accept the project if the internal rate ofreturn is less than or equal to the discount rate.If C0 > 0 and all future cash flows are negative, reject the project if the internal rate ofreturn is greater than the discount rate.IRR is the interest rate that causes NPV for a series of cash flows to be zero. NPV is preferred in all situations to IRR; IRR can lead to ambiguous results if there are non-conventional cash flows, and it also ambiguously ranks some mutually exclusive projects. However, for stand-alone projects with conventional cash flows, IRR and NPV are interchangeable techniques. The IRR decision rule for projectsd.The profitability index is the present value of cash inflows relative to the project cost. As such,it is a benefit/cost ratio, providing a measure of the relative profitability of a project. The profitability index decision rule is to accept projects with a PI greater than one, and to reject projects with a PI less than one. The profitability index can be expressed as: PI = (NPV + cost)/cost = 1 + (NPV/cost). If a firm has a basket of positive NPV projects and is subject to capital rationing, PI may provide a good ranking measure of the projects, indicating the “bang for the buck” of each particu lar project.e.NPV is simply the present value of a project’s cash flows. NPV specifically measures, afterconsidering the time value of money, the net increase or decrease in firm wealth due to the project. The decision rule is to accept projects that have a positive NPV, and reject projects with a negative NPV. NPV is superior to the other methods of analysis presented in the text because it has no serious flaws. The method unambiguously ranks mutually exclusive projects, and can differentiate between projects of different scale and time horizon. The only drawback to NPV is that it relies on cash flow and discount rate values that are often estimates and not certain, but this is a problem shared by the other performance criteria as well. A project with NPV = $2,500 implies that the total shareholder wealth of the firm will increase by $2,500 if the project is accepted.4.For a project with future cash flows that are an annuity:Payback = I / CAnd the IRR is:0 = – I + C / IRRSolving the IRR equation for IRR, we get:IRR = C / INotice this is just the reciprocal of the payback. So:IRR = 1 / PBFor long-lived projects with relatively constant cash flows, the sooner the project pays back, the greater is the IRR.5.There are a number of reasons. Two of the most important have to do with transportation costs andexchange rates. Manufacturing in the U.S. places the finished product much closer to the point of sale, resulting in significant savings in transportation costs. It also reduces inventories because goods spend less time in transit. Higher labor costs tend to offset these savings to some degree, at least compared to other possible manufacturing locations. Of great importance is the fact that manufacturing in the U.S. means that a much higher proportion of the costs are paid in dollars. Since sales are in dollars, the net effect is to immunize profits to a large extent against fluctuations in exchange rates. This issue is discussed in greater detail in the chapter on international finance.6.The single biggest difficulty, by far, is coming up with reliable cash flow estimates. Determining anappropriate discount rate is also not a simple task. These issues are discussed in greater depth in the next several chapters. The payback approach is probably the simplest, followed by the AAR, but even these require revenue and cost projections. The discounted cash flow measures (discounted payback, NPV, IRR, and profitability index) are really only slightly more difficult in practice.7.Yes, they are. Such entities generally need to allocate available capital efficiently, just as for-profitsdo. However, it is frequently the case that the “revenues” from not-for-profit ventures are not tangible. For example, charitable giving has real opportunity costs, but the benefits are generally hard to measure. To the extent that benefits are measurable, the question of an appropriate required return remains. Payback rules are commonly used in such cases. Finally, realistic cost/benefit analysis along the lines indicated should definitely be used by the U.S. government and would go a long way toward balancing the budget!8.The statement is false. If the cash flows of Project B occur early and the cash flows of Project Aoccur late, then for a low discount rate the NPV of A can exceed the NPV of B. Observe the following example.C0C1C2IRR NPV @ 0% Project A –$1,000,000 $0 $1,440,000 20% $440,000 Project B –$2,000,000 $2,400,000 $0 20% 400,000However, in one particular case, the statement is true for equally risky Projects. If the lives of the two Projects are equal and the cash flows of Project B are twice the cash flows of Project A in every time period, the NPV of Project B will be twice the NPV of Project A.9. Although the profitability index (PI) is higher for Project B than for Project A, Project A should bechosen because it has the greater NPV. Confusion arises because Project B requires a smaller investment than Project A requires. Since the denominator of the PI ratio is lower for Project B than for Project A, B can have a higher PI yet have a lower NPV. Only in the case of capital rationing could the company’s decision have been incorrect.10. a.Project A would have a higher IRR since initial investment for Project A is less than that ofProject B, if the cash flows for the two projects are identical.b.Yes, since both the cash flows as well as the initial investment are twice that of Project B.11.Project B would have a more sensitive NPV to changes in the discount rate. The reason is the timevalue of money. Cash flows that occur further out in the future are always more sensitive to changes in the interest rate. This is similar to the interest rate risk of a bond.12.The MIRR is calculated by finding the present value of all cash outflows, the future value of all cashinflows to the end of the project, and then calculating the IRR of the two cash flows. As a result, the cash flows have been discounted or compounded by one interest rate (the required return), and then the interest rate between the two remaining cash flows is calculated. As such, the MIRR is not a true interest rate. In contrast, consider the IRR. If you take the initial investment, and calculate the future value at the IRR, you can replicate the future cash flows of the project exactly.13.The criticism is incorrect. It is true that if you calculate the future value of all intermediate cashflows to the end of the project at the required return, then calculate the NPV of this future value and the initial investment, you will get the same NPV. However, NPV says nothing about reinvestment of intermediate cash flows. The NPV is the present value of the project cash flows. The fact that the reinvestment works is an artifact of the time value of money.14.The criticism is incorrect for several reasons. It is true that if you calculate the future value of allintermediate cash flows to the end of the project at the IRR, then calculate the IRR of this future value and the initial investment, you will get the same IRR. This only occurs if the intermediate cash flows are reinvested at the IRR. However, similar to the previous question, IRR deals with the present value of the cash flows, not the future value. There is also another important point. This criticism deals with the reinvestment of the intermediate cash flows. As we will see in the next chapter, any reinvestment assumption concerning the intermediate cash flows is incorrect. The reason is that when we are calculating the cash flows for a project, we are concerned with the incremental cash flows from the project, that is, the cash flows the project creates. Reinvestment violates this principal. Consider the following example:C0C1C2IRR Project A –$100 $10 $110 10% Suppose this is a deposit into a bank account. The IRR of the cash flows is 10 percent. Does it the IRR change if the Year 1 cash flow is reinvested in the account, or if it is withdrawn and spent on pizza? No. Finally, think back to the yield to maturity calculation on a bond. The YTM is the IRR of the bond investment, but no mention of a reinvestment assumption of the bond coupons is inferred.The reason is that the reinvestment assumption is irrelevant to calculating the YTM on a bond; in the same way, the reinvestment assumption is irrelevant in the IRR calculation.Solutions to Questions and ProblemsNOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.Basic1. a.The payback period is the time that it takes for the cumulative undiscounted cash inflows toequal the initial investment.Project A:Cumulative cash flows Year 1 = €4,000 = €4,000Cumulative cash flows Year 2 = €4,000 +3,500 = €7,500 Payback period = 2 yearsProject B:Cumulative cash flows Year 1 = €2,500 = €2,500Cumulative cash flows Year 2 = €2,500 + 1,200 = €3,700Cumulative cash flows Year 3 = €2,500 + 1,200 + 3,000 = €6,700 Companies can calculate a more precise value using fractional years. To calculate the fractionalpayba ck period, find the fraction of year 3’s cash flows that is needed for the company to have cumulative undiscounted cash flows of €5,000. Divide the difference between the initial investment and the cumulative undiscounted cash flows as of year 2 by the undiscounted cashflow of year 3.Payback period = 2 + (€5,000 –€3,700) / €3,000Payback period = 2.43Since project A has a shorter payback period than project B has, the company should chooseproject A.b.Discount each project’s cash flows at 15 percent. Choose the project with the highest NPV.Project A:NPV = –€7,500 + €4,000 / 1.15 + €3,500 / 1.152 + €1,500 / 1.153NPV = –€388.96Project B:NPV = –€5,000 + €2,500 / 1.15 + €1,200 / 1.152 + €3,000 / 1.153NPV = €53.83The firm should choose Project B since it has a higher NPV than Project A has.2.To calculate the payback period, we need to find the time that the project has recovered its initialinvestment. The cash flows in this problem are an annuity, so the calculation is simpler. If the initial cost is £3,000, the payback period is:Payback = 3 + (£300 / £900) = 3.33 yearsThere is a shortcut to calculate the payback period if the future cash flows are an annuity. Just divide the initial cost by the annual cash flow. For the £3,000 cost, the payback period is:Payback = £3,000 / £900 = 3.33 yearsFor an initial cost of £5,000, the payback period is:Payback = 5 + (£500 / £900) = 5.55 yearsThe payback period for an initial cost of £10,000 is a little trickier. Notice that the total cash inflows after nine years will be:Total cash inflows = 8(£900) = £7,200If the initial cost is £10,000, the project never pays back. Notice that if you use the shortcut forannuity cash flows, you get:Payback = £10,000 / £900 = 11.11 years.This answer does not make sense since the cash flows stop after nine years, so the payback period is never.3.When we use discounted payback, we need to find the value of all cash flows today. The value todayof the project cash flows for the first four years is:Value today of Year 1 cash flow = $7,000/1.14 = $6,140.35Value today of Year 2 cash flow = $7,500/1.142 = $5,771.01Value today of Year 3 cash flow = $8,000/1.143 = $5,399.77Value today of Year 4 cash flow = $8,500/1.144 = $5,032.68To find the discounted payback, we use these values to find the payback period. The discounted first year cash flow is $6,140.35, so the discounted payback for an $8,000 initial cost is:Discounted payback = 1 + ($8,000 – 6,140.35)/$5,771.01 = 1.32 yearsFor an initial cost of $13,000, the discounted payback is:Discounted payback = 2 + ($13,000 – 6,140.35 – 5,771.01)/$5,399.77 = 2.20 yearsNotice the calculation of discounted payback. We know the payback period is between two and three years, so we subtract the discounted values of the Year 1 and Year 2 cash flows from the initial cost.This is the numerator, which is the discounted amount we still need to make to recover our initial investment. We divide this amount by the discounted amount we will earn in Year 3 to get the fractional portion of the discounted payback.If the initial cost is $18,000, the discounted payback is:Discounted payback = 3 + ($18,000 – 6,140.35 – 5,771.01 – 5,399.77) / $5,032.68 = 3.14 years4.To calculate the discounted payback, discount all future cash flows back to the present, and use thesediscounted cash flows to calculate the payback period. Doing so, we find:R = 0%: 4 + (£1,100 / £2,100) = 4.52 yearsDiscounted payback = Regular payback = 4.52 yearsR = 5%: £2,100/1.05 + £2,100/1.052 + £2,100/1.053 + £2,100/1.054 + £2,100/1.055 = £9,091.90 £2,100/1.056 = £1,567.05Discounted payback = 5 + (£9,500 – 9,091.90) / £1,567.05 = 5.26 years R = 15%: £2,100/1.15 + £2,100/1.152 + £2,100/1.153 + £2,100/1.154 + £2,100/1.155 + £2,100/1.156 = £7,947.41; The project never pays back.5. a.The average accounting return is the average project earnings after taxes, divided by theaverage book value, or average net investment, of the machine during its life. The book value of the machine is the gross investment minus the accumulated depreciation.Average book value = (Book Value0 + Book Value1 + Book Value2 + Book Value3 +Book Value4 + Book Value5) / (Economic Life)Average book value = ($16,000 + 12,000 + 8,000 + 4,000 + 0) / (5 years)Average book value = $8,000Average Project Earnings = $4,500To find the average accounting return, we divide the average project earnings by the average book value of the machine to calculate the average accounting return. Doing so, we find:Average Accounting Return = Average Project Earnings / Average Book ValueAverage Accounting Return = $4,500 / $8,000Average Accounting Return = 0.5625 or 56.25%6.First, we need to determine the average book value of the project. The book value is the grossinvestment minus accumulated depreciation.Purchase Date Year 1 Year 2 Year 3 Gross Investment €8,000 €8,000 €8,000 €8,000Less: Accumulated Depreciation 0 4,000 6,500 8,000Net Investment €8,000 €4,000 €1,500 €0 Now, we can calculate the average book value as:Average book value = (€8,000 + 4,000 + 1,500 + 0) / (4 years)Average book value = €3,375To calculate the average accounting return, we must remember to use the aftertax average netincome when calculating the average accounting return. So, the average aftertax net income is:Average aftertax net income = (1 – t c) Annual pretax net incomeAverage aftertax net income = (1 – 0.25) €2,000Average aftertax net income = €1,500The average accounting return is the average after-tax net income divided by the average book value, which is:Average accounting return = €1,500 / €3,375Average accounting return = 0.4444 or 44.44%7.The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that definesthe IRR for this project is:0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)30 = –¥8,000,000 + ¥4,000,000/(1 + IRR) + ¥3,000,000/(1 + IRR)2 + ¥2,000,000/(1 + IRR)3Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 6.93%Since the IRR is less than the required return we would reject the project.8.The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that definesthe IRR for this Project A is:0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)30 = – £2,000 + £1,000/(1 + IRR) + £1,500/(1 + IRR)2 + £2,000/(1 + IRR)3Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 47.15%And the IRR for Project B is:0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)30 = – £1,500 + £500/(1 + IRR) + £1,000/(1 + IRR)2 + £1,500/(1 + IRR)3Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 36.19%9.The profitability index is defined as the PV of the cash inflows divided by the PV of the cashoutflows. The cash flows from this project are an annuity, so the equation for the profitability index is:PI = C(PVIFA R,t) / C0PI = €41,000(PVIFA15%,7) / €160,000PI = 1.066110. a.The profitability index is the present value of the future cash flows divided by the initial cost.So, for Project Alpha, the profitability index is:PI Alpha = [$300 / 1.10 + $700 / 1.102 + $600 / 1.103] / $500 = 2.604And for Project Beta the profitability index is:PI Beta = [$300 / 1.10 + $1,800 / 1.102 + $1,700 / 1.103] / $2,000 = 1.519b.According to the profitability index, you would accept Project Alpha. However, remember theprofitability index rule can lead to incorrect decision when ranking mutually exclusive projects.Intermediate11. a.To have a payback equal to the project’s life, given C is a constant cash flow for N years:C = I/Nb.To have a positive NPV, I < C (PVIFA R%, N). Thus, C > I / (PVIFA R%, N).c.Benefits = C (PVIFA R%, N) = 2 × costs = 2IC = 2I / (PVIFA R%, N)12. a.The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equationthat defines the IRR for this project is:0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)3 + C4 / (1 + IRR)40 = ₩5,000 –₩2,500 / (1 + IRR) –₩2,000 / (1 + IRR)2–₩1,000 / (1 + IRR)3–₩1,000 / (1 +IRR)4Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:IRR = 13.99%b.This problem differs from previous ones because the initial cash flow is positive and all futurecash flows are negative. In other words, this is a financing-type project, while previous projects were investing-type projects. For financing situations, accept the project when the IRR is less than the discount rate. Reject the project when the IRR is greater than the discount rate.IRR = 13.99%Discount Rate = 12%IRR > Discount RateReject the offer when the discount rate is less than the IRR.ing the same reason as part b., we would accept the project if the discount rate is 20 percent.IRR = 13.99%Discount Rate = 19%IRR < Discount RateAccept the offer when the discount rate is greater than the IRR.d.The NPV is the sum of the present value of all cash flows, so the NPV of the project if thediscount rate is 10 percent will be:NPV = ₩5,000 –₩2,500 / 1.12 –₩2,000 / 1.122–₩1,000 / 1.123–₩1,000 / 1.124NPV = –₩173.83When the discount rate is 12 percent, the NPV of the offer is –₩359.95. Reject the offer.And the NPV of the project is the discount rate is 19 percent will be:NPV = ₩5,000 –₩2,500 / 1.19 –₩2,000 / 1.192–₩1,000 / 1.193–₩1,000 / 1.194NPV = ₩394.75When the discount rate is 19 percent, the NPV of the offer is ₩466.82. Accept the offer.e.Yes, the decisions under the NPV rule are consistent with the choices made under the IRR rulesince the signs of the cash flows change only once.13. a.The IRR is the interest rate that makes the NPV of the project equal to zero. So, the IRR foreach project is:Deepwater Fishing IRR:0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)30 = –$600,000 + $270,000 / (1 + IRR) + $350,000 / (1 + IRR)2 + $300,000 / (1 + IRR)3Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:IRR = 24.30%Submarine Ride IRR:0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)30 = –$1,800,000 + $1,000,000 / (1 + IRR) + $700,000 / (1 + IRR)2 + $900,000 / (1 + IRR)3Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:IRR = 21.46%Based on the IRR rule, the deepwater fishing project should be chosen because it has the higher IRR.b.To calculate the incremental IRR, we s ubtract the smaller project’s cash flows from the largerproject’s cash flows. In this case, we subtract the deepwater fishing cash flows from the submarine ride cash flows. The incremental IRR is the IRR of these incremental cash flows. So, the incremental cash flows of the submarine ride are:Year 0Year 1Year 2 Year 3 Submarine Ride –$1,800,000 $1,000,000 $700,000 $900,000Deepwater Fishing –600,000 270,000 350,000 300,000Submarine – Fishing –$1,200,000 $730,000 $350,000 $600,000 Setting the present value of these incremental cash flows equal to zero, we find the incremental IRR is:0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)30 = –$1,200,000 + $730,000 / (1 + IRR) + $350,000 / (1 + IRR)2 + $600,000 / (1 + IRR)3Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:Incremental IRR = 19.92%For investing-type projects, accept the larger project when the incremental IRR is greater than the discount rate. Since the incremental IRR, 19.92%, is greater than the required rate of return of 15 percent, choose the submarine ride project. Note that this is the choice when evaluating only the IRR of each project. The IRR decision rule is flawed because there is a scale problem.That is, the submarine ride has a greater initial investment than does the deepwater fishing project. This problem is corrected by calculating the IRR of the incremental cash flows, or by evaluating the NPV of each project.c.The NPV is the sum of the present value of the cash flows from the project, so the NPV of eachproject will be:Deepwater fishing:NPV = –$600,000 + $270,000 / 1.15 + $350,000 / 1.152 + $300,000 / 1.153NPV = $96,687.76Submarine ride:NPV = –$1,800,000 + $1,000,000 / 1.15 + $700,000 / 1.152 + $900,000 / 1.153NPV = $190,630.39Since the NPV of the submarine ride project is greater than the NPV of the deepwater fishingproject, choose the submarine ride project. The incremental IRR rule is always consistent withthe NPV rule.14. a.The profitability index is the PV of the future cash flows divided by the initial investment. Thecash flows for both projects are an annuity, so:PI I = 元15,000(PVIFA10%,3 ) / 元30,000 = 1.243PI II = 元2,800(PVIFA10%,3) / 元5,000 = 1.393The profitability index decision rule implies that we accept project II, since PI II is greater thanthe PI I.b.The NPV of each project is:NPV I = –元30,000 + 元15,000(PVIFA10%,3) = 元7,302.78NPV II = –元5,000 + 元2,800(PVIFA10%,3) = 元1,963.19The NPV decision rule implies accepting Project I, since the NPV I is greater than the NPV II.ing the profitability index to compare mutually exclusive projects can be ambiguous whenthe magnitudes of the cash flows for the two projects are of different scale. In this problem,project I is roughly 3 times as large as project II and produces a larger NPV, yet the profit-ability index criterion implies that project II is more acceptable.15. a.The equation for the NPV of the project is:NPV = –₦28,000,000 + ₦53,000,000/1.11 –₦8,000,000/1.112 = ₦13,254,768.28The NPV is greater than 0, so we would accept the project.b.The equation for the IRR of the project is:0 = –₦28,000,000 + ₦53,000,000/(1+IRR) –₦8,000,000/(1+IRR)2From Descartes rule of signs, we know there are two IRRs since the cash flows change signstwice. From trial and error, the two IRRs are:IRR = 72.75%, –83.46%。
英文版罗斯公司理财习题答案Chap006
CHAPTER 6STOCK VALUATIONAnswers to Concepts Review and Critical Thinking Questions1.The value of any investment depends on its cash flows; i.e., what investors will actually receive. Thecash flows from a share of stock are the dividends.2.Investors believe the company will eventually start paying dividends (or be sold to anothercompany).3.In general, companies that need the cash will often forgo dividends since dividends are a cashexpense. Young, growing companies with profitable investment opportunities are one example;another example is a company in financial distress. This question is examined in depth in a later chapter.4.The general method for valuing a share of stock is to find the present value of all expected futuredividends. The dividend growth model presented in the text is only valid (i) if dividends are expected to occur forever; that is, the stock provides dividends in perpetuity, and (ii) if a constant growth rate of dividends occurs forever. A violation of the first assumption might be a company that is expected to cease operations and dissolve itself some finite number of years from now. The stock of such a company would be valued by applying the general method of valuation explained in this chapter. A violation of the second assumption might be a start-up firm that isn’t currently paying any dividends, but is expected to eventually start making dividend payments some number of years from now. This stock would also be valued by the general dividend valuation method explained in this chapter.5.The common stock probably has a higher price because the dividend can grow, whereas it is fixed onthe preferred. However, the preferred is less risky because of the dividend and liquidation preference, so it is possible the preferred could be worth more, depending on the circumstances.6.The two components are the dividend yield and the capital gains yield. For most companies, thecapital gains yield is larger. This is easy to see for companies that pay no dividends. For companies that do pay dividends, the dividend yields are rarely over five percent and are often much less.7.Yes. If the dividend grows at a steady rate, so does the stock price. In other words, the dividendgrowth rate and the capital gains yield are the same.8.The three factors are: 1) The company’s future growth opportunities. 2) The company’s level of risk,which determines the interest rate used to discount cash flows. 3) The accounting method used.9.In a corporate election, you can buy votes (by buying shares), so money can be used to influence oreven determine the outcome. Many would argue the same is true in political elections, but, in principle at least, no one has more than one vote.10. It wouldn’t seem to be. Investors who don’t like the voting features of a particular class of stock areunder no obligation to buy it.11.Investors buy such stock because they want it, recognizing that the shares have no voting power.Presumably, investors pay a little less for such shares than they would otherwise.12.Presumably, the current stock value reflects the risk, timing and magnitude of all future cash flows,both short-term and long-term. If this is correct, then the statement is false.Solutions to Questions and ProblemsNOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.Basic1.The constant dividend growth model is:P t = D t × (1 + g) / (R–g)So, the price of the stock today is:P0 = D0(1 + g) / (R–g) = €1.40 (1.06) / (.12 – .06) = €24.73The dividend at year 4 is the dividend today times the FVIF for the growth rate in dividends and four years, so:P3 = D3(1 + g) / (R–g) = D0(1 + g)4/ (R– g) = €1.40 (1.06)4/ (.12 – .06) = €29.46We can do the same thing to find the dividend in Year 16, which gives us the price in Year 15, so: P15 = D15(1 + g) / (R–g) = D0(1 + g)16/ (R–g) = €1.40 (1.06)16/ (.12 – .06) = €59.27There is another feature of the constant dividend growth model: The stock price grows at the dividend growth rate. So, if we know the stock price today, we can find the future value for any time in the future we want to calculate the stock price. In this problem, we want to know the stock price in three years, and we have already calculated the stock price today. The stock price in three years will be:P3 = P0(1 + g)3 = €24.73(1 + .06)3 = €29.46And the stock price in 20 years will be:P15 = P0(1 + g)20 = €24.73(1 + .06)20 = €79.312.We need to find the required return of the stock. Using the constant growth model, we can solve theequation for R. Doing so, we find:R = (D1 / P0) + g = ($3.10 / $50.00) + .05 = 11.20%3.The dividend yield is the dividend next year divided by the current price, so the dividend yield is:Dividend yield = D1 / P0 = $3.10 / $50.00 = 6.20%The capital gains yield, or percentage increase in the stock price, is the same as the dividend growth rate, so:Capital gains yield = 5%ing the constant growth model, we find the price of the stock today is:P0 = D1 / (R– g) = £3.60 / (.13 – .062) = £52.945.The required return of a stock is made up of two parts: The dividend yield and the capital gains yield.So, the required return of this stock is:R = Dividend yield + Capital gains yield = .039 + .09 = 9.90%6.We know the stock has a required return of 14 percent, and the dividend and capital gains yield areequal, so:Dividend yield = 1/2(.14) = .07 = Capital gains yieldNow we know both the dividend yield and capital gains yield. The dividend is simply the stock price times the dividend yield, so:D1 = .07(元70) = 元4.90This is the dividend next year. The question asks for the dividend this year. Using the relationship between the dividend this year and the dividend next year:D1 = D0(1 + g)We can solve for the dividend that was just paid:元4.90 = D0 (1 + .07)D0 = 元4.90 / 1.07 = 元4.587.The price of any financial instrument is the PV of the future cash flows. The future dividends of thisstock are an annuity for eight years, so the price of the stock is the PVA, which will be:P0 = R12.00(PVIFA10%,8) = R64.028.The price a share of preferred stock is the dividend divided by the required return. This is the sameequation as the constant growth model, with a dividend growth rate of zero percent. Remember that most preferred stock pays a fixed dividend, so the growth rate is zero. Using this equation, we find the price per share of the preferred stock is:R = D/P0 = ¥820/¥11,350 = 7.22%9.The growth rate of earnings is the return on equity times the retention ratio, so:g = ROE ×bg = .14(.60)g = .084 or 8.40%To find next year’s earnings, we simply multiply the current earnings times one plus the growth rate, so:Next year’s earnings = Current earnings(1 + g)Next year’s earnings = Rs.20,000,000(1 + .084)Next year’s earnings = Rs.21,680,000Intermediate10.This stock has a constant growth rate of dividends, but the required return changes twice. To find thevalue of the stock today, we will begin by finding the price of the stock at Year 6, when both the dividend growth rate and the required return are stable forever. The price of the stock in Year 6 will be the dividend in Year 7, divided by the required return minus the growth rate in dividends. So:P6 = D6(1 + g) / (R–g) = D0(1 + g)7/ (R–g) = $3.00 (1.05)7/ (.11 – .05) = $70.36Now we can find the price of the stock in Year 3. We need to find the price here since the required return changes at that time. The price of the stock in Year 3 is the PV of the dividends in Years 4, 5, and 6, plus the PV of the stock price in Year 6. The price of the stock in Year 3 is:P3= $3.00(1.050)4/ 1.14 + $3.00(1.050)5/ 1.142 + $3.00(1.05)6/ 1.143 + $70.36 / 1.143P3= $56.35Finally, we can find the price of the stock today. The price today will be the PV of the dividends in Years 1, 2, and 3, plus the PV of the stock in Year 3. The price of the stock today is:P0 = $3.00(1.050) / 1.16 + $3.00(1.050)2 / (1.16)2 + $3.00(1.050)3 / (1.16)3 + $56.35 / (1.16)3 = $43.5011.Here we have a stock that pays no dividends for 10 years. Once the stock begins paying dividends, itwill have a constant growth rate of dividends. We can use the constant growth model at that point. It is important to remember that general constant dividend growth formula is:P t = [D t × (1 + g)] / (R–g)This means that since we will use the dividend in Year 10, we will be finding the stock price in Year9. The dividend growth model is similar to the PVA and the PV of a perpetuity: The equation givesyou the PV one period before the first payment. So, the price of the stock in Year 9 will be:P9 = D10/ (R–g) = €8.00 / (.13 – .06) = €114.29The price of the stock today is simply the PV of the stock price in the future. We simply discount the future stock price at the required return. The price of the stock today will be:P0 = €114.29 / 1.139 = €38.0412.The price of a stock is the PV of the future dividends. This stock is paying four dividends, so theprice of the stock is the PV of these dividends using the required return. The price of the stock is: P0 = $12 / 1.11 + $15 / 1.112 + $18 / 1.113 + $21 / 1.114 = $49.9813.With supernormal dividends, we find the price of the stock when the dividends level off at a constantgrowth rate, and then find the PV of the future stock price, plus the PV of all dividends during the supernormal growth period. The stock begins constant growth in Year 4, so we can find the price of the stock in Year 3, one year before the constant dividend growth begins, as:P4 = D4(1 + g) / (R–g) = £2.00(1.05) / (.13 – .05) = £26.25The price of the stock today is the PV of the first three dividends, plus the PV of the Year 3 stock price. So, the price of the stock today will be:P0 = £8.00 / 1.13 + £6.00 / 1.132 + £3.00 / 1.133 + £2.00 / 1.134 + £26.25 / 1.134 = £31.1814.With supernormal dividends, we find the price of the stock when the dividends level off at a constantgrowth rate, and then find the PV of the future stock price, plus the PV of all dividends during the supernormal growth period. The stock begins constant growth in Year 4, so we can find the price of the stock in Year 3, one year before the constant dividend growth begins as:P3 = D3(1 + g) / (R–g) = D0(1 + g1)3(1 + g2) / (R–g) = €2.80(1.25)3(1.07) / (.13 – .07) = €97.53 The price of the stock today is the PV of the first three dividends, plus the PV of the Year 3 stock price. The price of the stock today will be:P0 = 2.80(1.25) / 1.13 + €2.80(1.25)2/ 1.132 + €2.80(1.25)3/ 1.133 + €97.53 / 1.133P0= €77.9015.Here we need to find the dividend next year for a stock experiencing supernormal growth. We knowthe stock price, the dividend growth rates, and the required return, but not the dividend. First, we need to realize that the dividend in Year 3 is the current dividend times the FVIF. The dividend in Year 3 will be:D3 = D0(1.30)3And the dividend in Year 4 will be the dividend in Year 3 times one plus the growth rate, or:D4 = D0(1.30)3(1.18)The stock begins constant growth in Year 4, so we can find the price of the stock in Year 4 as the dividend in Year 5, divided by the required return minus the growth rate. The equation for the price of the stock in Year 4 is:P4 = D4(1 + g) / (R– g)Now we can substitute the previous dividend in Year 4 into this equation as follows:P4 = D0(1 + g1)3(1 + g2) (1 + g3) / (R–g)P4= D0(1.30)3(1.18) (1.08) / (.14 – .08) = 46.66D0When we solve this equation, we find that the stock price in Year 4 is 46.66 times as large as the dividend today. Now we need to find the equation for the stock price today. The stock price today is the PV of the dividends in Years 1, 2, 3, and 4, plus the PV of the Year 4 price. So:P0 = D0(1.30)/1.14 + D0(1.30)2/1.142 + D0(1.30)3/1.143+ D0(1.30)3(1.18)/1.144 + 46.66D0/1.144We can factor out D0 in the equation, and combine the last two terms. Doing so, we get:P0 = $70.00 = D0{1.30/1.14 + 1.302/1.142 + 1.303/1.143 + [(1.30)3(1.18) + 46.66] / 1.144}Reducing the equation even further by solving all of the terms in the braces, we get:$70 = $33.04D0D0 = $70.00 / $33.04 = $2.12This is the dividend today, so the projected dividend for the next year will be:D1 = $2.12(1.30) = $2.7516.The constant growth model can be applied even if the dividends are declining by a constantpercentage, just make sure to recognize the negative growth. So, the price of the stock today will be: P0 = D0(1 + g) / (R– g) = ZW$215(1 – .08) / [(.11 – (–.08)] = ZW$1,041.0517.We are given the stock price, the dividend growth rate, and the required return, and are asked to findthe dividend. Using the constant dividend growth model, we get:P0 = €50 = D0(1 + g) / (R–g)Solving this equation for the dividend gives us:D0 = €50(.14 – .08) / (1.08) = €2.7818.The price of a share of preferred stock is the dividend payment divided by the required return. Weknow the dividend payment in Year 6, so we can find the price of the stock in Year 5, one year before the first dividend payment. Doing so, we get:P5 = ¥295 / .07 = ¥4,214.28The price of the stock today is the PV of the stock price in the future, so the price today will be: P0 = ¥4,214.28 / (1.07)5 = ¥3,004.7219.The annual dividend paid to stockholders is $0.15, and the dividend yield is 0.2 percent. Using theequation for the dividend yield:Dividend yield = Dividend / Stock priceWe can plug the numbers in and solve for the stock price:.002 = $0.15 / P0P0 = $0.15/.002 = $75.00The “Net Chg” of the stock shows the stock increased by $2.20 on this day, so the closing stock price yesterday was:Y esterday’s closing price = $75.00 – 2.20 = $72.80To find the net income, we need to find the EPS. The stock quote tells us the P/E ratio for the stock is 14. Since we know the stock price as well, we can use the P/E ratio to solve for EPS as follows: P/E = 14 = Stock price / EPS = $75.00 / EPSEPS = $75.00 / 14 = $5.357We know that EPS is just the total net income divided by the number of shares outstanding, so:EPS = NI / Shares = $5.357 = NI / 25,000,000NI = $5.357(25,000,000) = $133,928,57120.To find the number of shares owned, we can divide the amount invested by the stock price. Theshare price of any financial asset is the present value of the cash flows, so, to find the price of the stock we need to find the cash flows. The cash flows are the two dividend payments plus the sale price. We also need to find the aftertax dividends since the assumption is all dividends are taxed at the same rate for all investors. The aftertax dividends are the dividends times one minus the tax rate, so:Year 1 aftertax dividend = $2.00(1 – .28)Year 1 aftertax dividend = $1.44Year 2 aftertax dividend = $4.00(1 – .28)Year 2 aftertax dividend = $2.88We can now discount all cash flows from the stock at the required return. Doing so, we find the price of the stock is:P = $1.44/1.15 + $2.88/(1.15)2 + $50/(1+.15)3P = $36.31The number of shares owned is the total investment divided by the stock price, which is:Shares owned = $100,000 / $36.31Shares owned = 2,75421.If the company’s earnings are declining at a constant rate, the dividends will decline at the same ratesince the dividends are assumed to be a constant percentage of income. The dividend next year will less tha n this year’s dividend, soP0 = D0(1 + g) / (R– g) = ₦5.00(1 – .08) / [(.14 – (–.08)] = ₦20.9122.Here we have a stock paying a constant dividend for a fixed period, and an increasing dividend after.We need to find the present value of the two different cash flows using the appropriate quarterly interest rate. The constant dividend is an annuity, so the present value of these dividends is:PVA = C(PVIFA R,t)PVA = ₪1(PVIFA2.5%,12)PVA = ₪10.26Now we can find the present value of the dividends beyond the constant dividend phase. Using the present value of a growing annuity equation, we find:P12 = D13/ (R–g)P12 = ₪1(1 + .005) / (.025 – .005)P12 = ₪50.25This is the price of the stock immediately after it has paid the last constant dividend. So, the present value of the future price is:PV = ₪50.25 / (1 + .025)12PV = ₪37.36The price today is the sum of the present value of the two cash flows, so:P0 = ₪10.26 + 37.36P0 = ₪47.6223. We can find the price of the stock in Year 4 when it begins a constant increase in dividends using thegrowing perpetuity equation. So, the price of the stock in Year 4, immediately after the dividend payment, is:P4 = D4(1 + g) / (R–g)P4 = 元2(1 + .07) / (.16 – .07)P4 = 元23.78The stock price today is the sum of the present value of the two fixed dividends plus the present value of the future price, so:P0 = 元2 / (1 + .16)3 + 元2 / (1 + .16)4 + 元23.78 / (1 + .16)4P0 = 元15.5124.Here we need to find the dividend next year for a stock with nonconstant growth. We know the stockprice, the dividend growth rates, and the required return, but not the dividend. First, we need to realize that the dividend in Year 3 is the constant dividend times the FVIF. The dividend in Year 3 will be:D3 = D(1.04)The equation for the stock price will be the present value of the constant dividends, plus the present value of the future stock price, or:P0 = D / 1.12 + D/1.122 + D(1.04)/(.12 – .04)]/1.122£30 = D / 1.12 + D/1.122 + D(1.04)/(.12 – .04)]/1.122We can factor out D0 in the equation, and combine the last two terms. Doing so, we get:£30 = D{1/1.12 + 1/1.122 + [(1.04)/(.12 – .04)] / 1.122}Reducing the equation even further by solving all of the terms in the braces, we get:£30 = D(12.0536)D = £30 / 12.0536 = £2.49This is the dividend today, so the projected dividend for the next year will be:D1 = £2.49(1.30) = £2.4925.The required return of a stock consists of two components, the capital gains yield and the dividendyield. In the constant dividend growth model (growing perpetuity equation), the capital gains yield is the same as the dividend growth rate, or algebraically:R = D1/P0 + gWe can find the dividend growth rate by the growth rate equation, or:g = ROE ×bg = .11 × .75g = .0825 or 8.25%This is also the growth rate in dividends. To find the current dividend, we can use the information provided about the net income, shares outstanding, and payout ratio. The total dividends paid is the net income times the payout ratio. To find the dividend per share, we can divide the total dividends paid by the number of shares outstanding. So:Dividend per share = (Net income × Payout ratio) / Shares outstandingDividend per share = ($10,000,000 × .25) / 1,250,000Dividend per share = $2.00Now we can use the initial equation for the required return. We must remember that the equation uses the dividend in one year, so:R = D1/P0 + gR = $2(1 + .0825)/$40 + .0825R = .1366 or 13.66%26.First, we need to find the annual dividend growth rate over the past four years. To do this, we canuse the future value of a lump sum equation, and solve for the interest rate. Doing so, we find the dividend growth rate over the past four years was:FV = PV(1 + R)t$1.66 = $0.90(1 + R)4R = .1654 or 16.54%We know the dividend will grow at this rate for five years before slowing to a constant rate indefinitely. So, the dividend amount in seven years will be:D7 = D0(1 + g1)5(1 + g2)2D7 = $1.66(1 + .1654)5(1 + .08)2D7 = $4.1627. a.We can find the price of the all the outstanding company stock by using the dividends the sameway we would value an individual share. Since earnings are equal to dividends, and there is no growth, the value of the company’s st ock today is the present value of a perpetuity, so:P = D / RP = £800,000 / .15P = £5,333,333.33The price-earnings ratio is the stock price divided by the current earnings, so the price-earnings ratio of each company with no growth is:P/E = Price / EarningsP/E = £5,333,333.33 / £800,000P/E = 6.67 timesb.Since the earnings have increased, the price of the stock will increase. The new price of the allthe outstanding company stock is:P = D / RP = (£800,000 + 100,000) / .15P = £6,000,000.00The price-earnings ratio is the stock price divided by the current earnings, so the price-earnings with the increased earnings is:P/E = Price / EarningsP/E = £6,000,000 / £800,000P/E = 7.50 timesc.Since the earnings have increased, the price of the stock will increase. The new price of the allthe outstanding company stock is:P = D / RP = (£800,000 + 200,000) / .15P = £6,666,666.67The price-earnings ratio is the stock price divided by the current earnings, so the price-earnings with the increased earnings is:P/E = Price / EarningsP/E = £6,666,666.67 / £800,000P/E = 8.33 times28. a.If the company does not make any new investments, the stock price will be the present value ofthe constant perpetual dividends. In this case, all earnings are paid dividends, so, applying the perpetuity equation, we get:P = Dividend / RP = €7 / .12P = €58.33b.The investment is a one-time investment that creates an increase in EPS for two years. Tocalculate the new stock price, we need the cash cow price plus the NPVGO. In this case, the NPVGO is simply the present value of the investment plus the present value of the increases in EPS. SO, the NPVGO will be:NPVGO = C1 / (1 + R) + C2 / (1 + R)2 + C3 / (1 + R)3NPVGO = –€1.75 / 1.12 + €1.90 / 1.122 + €2.10 / 1.123NPVGO = €1.45So, the price of the stock if the company undertakes the investment opportunity will be:P = €58.33 + 1.45P = €59.78c.After the project is over, and the earnings increase no longer exists, the price of the stock willrevert back to €58.33, the value of the company as a cash cow.29. a.The price of the stock is the present value of the dividends. Since earnings are equal todividends, we can find the present value of the earnings to calculate the stock price. Also, since we are excluding taxes, the earnings will be the revenues minus the costs. We simply need to find the present value of all future earnings to find the price of the stock. The present value of the revenues is:PV Revenue = C1 / (R–g)PV Revenue = $3,000,000(1 + .05) / (.15 – .05)PV Revenue = $31,500,000And the present value of the costs will be:PV Costs = C1 / (R–g)PV Costs = $1,500,000(1 + .05) / (.15 – .05)PV Costs = $15,750,000So, the prese nt value of the company’s earnings and dividends will be:PV Dividends = $31,500,000 – 15,750,000PV Dividends = $15,750,000Note that since revenues and costs increase at the same rate, we could have found the present value of future dividends as the present value of current dividends. Doing so, we find:D0 = Revenue0– Costs0D0 = $3,000,000 – 1,500,000D0 = $1,500,000Now, applying the growing perpetuity equation, we find:PV Dividends = C1 / (R–g)PV Dividends = $1,500,000(1 + .05) / (.15 – .05)PV Dividends = $15,750,000This is the same answer we found previously. The price per share of stock is the total value of the company’s stock divided by the shares outstanding, or:P = Value of all stock / Shares outstandingP = $15,750,000 / 1,000,000P = $15.75b.The value of a share of stock in a company is the present value of its current operations, plusthe present value of growth opportunities. To find the present value of the growth opportunities, we need to discount the cash outlay in Year 1 back to the present, and find the value today of the increase in earnings. The increase in earnings is a perpetuity, which we must discount back to today. So, the value of the growth opportunity is:NPVGO = C0 + C1 / (1 + R) + (C2 / R) / (1 + R)NPVGO = –$15,000,000 – $5,000,000 / (1 + .15) + ($6,000,000 / .15) / (1 + .15)NPVGO = $15,434,782.61To find the value of the growth opportunity on a per share basis, we must divide this amount by the number of shares outstanding, which gives us:NPVGO Per share = $15,434,782.61 / $1,000,000NPVGO Per share = $15.43The stock price will increase by $15.43 per share. The new stock price will be:New stock price = $15.75 + 15.43New stock price = $31.1830. a.If the company continues its current operations, it will not grow, so we can value the companyas a cash cow. The total value of the company as a cash cow is the present value of the future earnings, which are a perpetuity, so:Cash cow value of company = C / RCash cow value of company = ฿110,000,000 / .15Cash cow value of company = ฿733,333,333.33The value per share is the total value of the company divided by the shares outstanding, so:Share price = ฿733,333,333.33 / 20,000,000Share price = ฿36.67b.To find the value of the investment, we need to find the NPV of the growth opportunities. Theinitial cash flow occurs today, so it does not need to be discounted. The earnings growth is a perpetuity. Using the present value of a perpetuity equation will give us the value of the earnings growth one period from today, so we need to discount this back to today. The NPVGO of the investment opportunity is:NPVGO = C0 + C1 + (C2 / R) / (1 + R)NPVGO = –฿12,000,000 – 7,000,000 + (฿10,000,000 / .15) / (1 + .15)NPVGO = ฿39,884,057.97c.The price of a share of stock is the cash cow value plus the NPVGO. We have alreadycalculated the NPVGO for the entire project, so we need to find the NPVGO on a per share basis. The NPVGO on a per share basis is the NPVGO of the project divided by the shares outstanding, which is:NPVGO per share = ฿39,884,057.97 / 20,000,000NPVGO per share = ฿1.99This means the per share stock price if the company undertakes the project is:Share price = Cash cow price + NPVGO per shareShare price = ฿36.67 + 1.99Share price = ฿38.6631. a.If the company does not make any new investments, the stock price will be the present value ofthe constant perpetual dividends. In this case, all earnings are paid dividends, so, applying the perpetuity equation, we get:P = Dividend / RP = £5 / .14P = £35.71b.The investment occurs every year in the growth opportunity, so the opportunity is a growingperpetuity. So, we first need to find the growth rate. The growth rate is:g = Retention Ratio Return on Retained Earningsg = 0.25 × 0.40g = 0.10 or 10%Next, we need to calculate the NPV of the investment. During year 3, twenty-five percent ofthe earnings will be reinvested. Therefore, £1.25 is invested (£5 .25). One year later, theshareholders receive a 40 percent return on the investment, or £0.50 (£1.25 × .40), in perpetuity.The perpetuity formula values that stream as of year 3. Since the investment opportunity will continue indefinitely and grows at 10 percent, apply the growing perpetuity formula to calculate the NPV of the investment as of year 2. Discount that value back two years to today.NPVGO = [(Investment + Return / R) / (R– g)] / (1 + R)2NPVGO = [(–£1.25 + £0.50 / .14) / (0.14 – 0.1)] / (1.14)2NPVGO = £44.66The value of the stock is the PV of the firm without making the investment plus the NPV of theinvestment, or:P = PV(EPS) + NPVGOP = £35.71 + £44.66P = £80.37Challenge32.We are asked to find the dividend yield and capital gains yield for each of the stocks. All of thestocks have a 15 percent required return, which is the sum of the dividend yield and the capital gains yield. To find the components of the total return, we need to find the stock price for each stock.Using this stock price and the dividend, we can calculate the dividend yield. The capital gains yield for the stock will be the total return (required return) minus the dividend yield.W: P0 = D0(1 + g) / (R–g) = Au$4.50(1.10)/(.15 – .10) = Au$99.00Dividend yield = D1/P0 = 4.50(1.10)/99.00 = 5%Capital gains yield = .15 – .05 = 10%X: P0 = D0(1 + g) / (R–g) = Au$4.50/(.15 – 0) = Au$30.00Dividend yield = D1/P0 = 4.50/30.00 = 15%Capital gains yield = .15 – .15 = 0%Y: P0 = D0(1 + g) / (R–g) = Au$4.50(1 – .05)/(.15 + .05) = Au$21.38 Dividend yield = D1/P0 = 4.50(0.95)/21.38 = 20%Capital gains yield = .15 – .20 = – 5%。