罗斯 公司理财 英文第九版Chap005
《公司理财》斯蒂芬A罗斯英文》PPT课件讲义
5.1 Definition and Example of a Bond
• A bond is a legally binding agreement between a borrower and a lender: – Specifies the principal amount of the loan. – Specifies the size and timing of the cash flows:
• In dollar terms (fixed-rate borrowing) • As a formula (adjustable-rate borrowing)
5.1 Definition and Example of a Bond
• Consider a U.S. government bond listed as 6 3/8 of December 2009.
N I/Y PV PMT FV
12
5
– 1,070.52
31.875 = 1,000
1,000×0.06375 2
5.3 Bond Concepts
1. Bond prices and market interest rates move in opposite directions.
2. When coupon rate = YTM, price = par value. When coupon rate > YTM, price > par value (premium bond) When coupon rate < YTM, price < par value (discount bond)
英文版罗斯公司理财习题答案Chap005
CHAPTER 5INTEREST RATES AND BOND VALUATIONAnswers to Concepts Review and Critical Thinking Questions1.No. As interest rates fluctuate, the value of a Treasury security will fluctuate. Long-term Treasurysecurities have substantial interest rate risk.2.All else the same, the Treasury security will have lower coupons because of its lower default risk,so it will have greater interest rate risk.3. No. If the bid were higher than the ask, the implication would be that a dealer was willing to sell abond and immediately buy it back at a higher price. How many such transactions would you like to do?4.Prices and yields move in opposite directions. Since the bid price must be lower, the bid yieldmust be higher.5.There are two benefits. First, the company can take advantage of interest rate declines by callingin an issue and replacing it with a lower coupon issue. Second, a company might wish toeliminate a covenant for some reason. Calling the issue does this. The cost to the company is ahigher coupon. A put provision is desirable from an investor’s standpoint, so it helps the company by reducing the coupon rate on the bond. The cost to the company is that it may have to buy back the bond at an unattractive price.6. Bond issuers look at outstanding bonds of similar maturity and risk. The yields on such bonds areused to establish the coupon rate necessary for a particular issue to initially sell for par value.Bond issuers also simply ask potential purchasers what coupon rate would be necessary to attract them. The coupon rate is fixed and simply determines what the bond’s coupon payments will be.The required return is what investors actually demand on the issue, and it will fluctuate throughtime. The coupon rate and required return are equal only if the bond sells for exactly at par.7.Yes. Some investors have obligations that are denominated in dollars; i.e., they are nominal.Their primary concern is that an investment provides the needed nominal dollar amounts. Pension funds, for example, often must plan for pension payments many years in the future. If thosepayments are fixed in dollar terms, then it is the nominal return on an investment that is important.8. Companies pay to have their bonds rated simply because unrated bonds can be difficult to sell;many large investors are prohibited from investing in unrated issues.9.Treasury bonds have no credit risk since it is backed by the U.S. government, so a rating is notnecessary. Junk bonds often are not rated because there would be no point in an issuer paying arating agency to assign its bonds a low rating (it’s like paying someone to kick you!).10.The term structure is based on pure discount bonds. The yield curve is based on coupon-bearingissues.11.Bond ratings have a subjective factor to them. Split ratings reflect a difference of opinion amongcredit agencies.12.As a general constitutional principle, the federal government cannot tax the states without theirconsent if doing so would interfere with state government functions. At one time, this principlewas thought to provide for the tax-exempt status of municipal interest payments. However,modern court rulings make it clear that Congress can revoke the municipal exemption, so the only basis now appears to be historical precedent. The fact that the states and the federal government do not tax each other’s securities is referred to as “reciprocal immunity.”13. Lack of transparency means that a buyer or seller can’t see recent transactions, so it is muchharder to determine what the best bid and ask prices are at any point in time.14.One measure of liquidity is the bid-ask spread. Liquid instruments have relatively small spreads.Looking at Figure 7.4, the bellwether bond has a spread of one tick; it is one of the most liquid of all investments. Generally, liquidity declines after a bond is issued. Some older bonds, including some of the callable issues, have spreads as wide as six ticks.panies charge that bond rating agencies are pressuring them to pay for bond ratings. When acompany pays for a rating, it has the opportunity to make its case for a particular rating. With an unsolicited rating, the company has no input.16. A 100-year bond looks like a share of preferred stock. In particular, it is a loan with a life thatalmost certainly exceeds the life of the lender, assuming that the lender is an individual. With ajunk bond, the credit risk can be so high that the borrower is almost certain to default, meaningthat the creditors are very likely to end up as part owners of the business. In both cases, the“equity in disguise” has a significant tax advantage.17.a. The bond price is the present value of the cash flows from a bond. The YTM is the interest rate used in valuing the cash flows from a bond.b. If the coupon rate is higher than the required return on a bond, the bond will sell at a premium, since it provides periodic income in the form of coupon payments in excess of that required by investors on other similar bonds. If the coupon rate is lower than the required return on a bond, the bond will sell at a discount since it provides insufficient coupon payments compared to that required by investors on other similar bonds. For premium bonds, the coupon rate exceeds the YTM; for discount bonds, the YTM exceeds the coupon rate, and for bonds selling at par, the YTM is equal to the coupon rate.c. Current yield is defined as the annual coupon payment divided by the current bond price. For premium bonds, the current yield exceeds the YTM, for discount bonds the current yield is less than the YTM, and for bonds selling at par value, the current yield is equal to the YTM. In all cases, the current yield plus the expected one-period capital gains yield of the bond must be equal to the required return.18. A long-term bond has more interest rate risk compared to a short-term bond, all else the same. Alow coupon bond has more interest rate risk than a high coupon bond, all else the same. Whencomparing a high coupon, long-term bond to a low coupon, short-term bond, we are unsure which has more interest rate risk. Generally, the maturity of a bond is a more important determinant of the interest rate risk, so the long-term high coupon bond probably has more interest rate risk. The exception would be if the maturities are close, and the coupon rates are vastly different.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.NOTE: Most problems do not explicitly list a par value for bonds. Even though a bond can have any par value, in general, corporate bonds in the United States will have a par value of $1,000. We will use this par value in all problems unless a different par value is explicitly stated.Basic1.The price of a pure discount (zero coupon) bond is the present value of the par. Even though the bond makes no coupon payments, the present value is found using semiannual compounding periods, consistent with coupon bonds. This is a bond pricing convention. So, the price of the bond for each YTM is:a. P = €1,000/(1 + .03)20 = €553.68b. P = €1,000/(1 + .05)20 = €376.89c. P = €1,000/(1 + .07)20 = €258.422.The price of any bond is the PV of the interest payment, plus the PV of the par value. Notice this problem assumes an annual coupon. The price of the bond at each YTM will be:a.P = £40({1 – [1/(1 + .04)]40 } / .04) + £1,000[1 / (1 + .04)40]P = £1,000.00When the YTM and the coupon rate are equal, the bond will sell at par.b.P = £40({1 – [1/(1 + .05)]40 } / .05) + £1,000[1 / (1 + .05)40]P = £828.41When the YTM is greater than the coupon rate, the bond will sell at a discount.c.P = £40({1 – [1/(1 + .03)]40 } / .03) + £1,000[1 / (1 + .03)40]P = £1,231.15When the YTM is less than the coupon rate, the bond will sell at a premium.We would like to introduce shorthand notation here. Rather than write (or type, as the case may be) the entire equation for the PV of a lump sum, or the PVA equation, it is common to abbreviate the equations as:PVIF R,t = 1 / (1 + r)twhich stands for Present Value Interest FactorPVIFA R,t= ({1 – [1/(1 + r)]t } / r )which stands for Present Value Interest Factor of an AnnuityThese abbreviations are short hand notation for the equations in which the interest rate and the number of periods are substituted into the equation and solved. We will use this shorthand notation in remainder of the solutions key.3.Here we are finding the YTM of a semiannual coupon bond. The bond price equation is:P = 元970 = 元43(PVIFA R%,20) + 元1,000(PVIF R%,20)Since we cannot solve the equation directly for R, using a spreadsheet, a financial calculator, or trial and error, we find:R = 4.531%Since the coupon payments are semiannual, this is the semiannual interest rate. The YTM is the APR of the bond, so:YTM = 2 4.531% = 9.06%4.Here we need to find the coupon rate of the bond. All we need to do is to set up the bond pricing equation and solve for the coupon payment as follows:P = $1,145 = C(PVIFA3.75%,29) + $1,000(PVIF3.75%,29)Solving for the coupon payment, we get:C = $45.79Since this is the semiannual payment, the annual coupon payment is:2 × $45.79 = $91.58And the coupon rate is the coupon rate divided by par value, so:Coupon rate = $91.58 / $1,000 = 9.16%5.The approximate relationship between nominal interest rates (R), real interest rates (r), and inflation (h) is:R = r + hApproximate r = .06 –.045 =.015 or 1.50%The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation is:(1 + R) = (1 + r)(1 + h)(1 + .06) = (1 + r)(1 + .045)Exact r = [(1 + .06) / (1 + .045)] – 1 = .0144 or 1.44%6.The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation is:(1 + R) = (1 + r)(1 + h)R = (1 + .04)(1 + .025) – 1 = .0660 or 6.60%7. The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation is:(1 + R) = (1 + r)(1 + h)h = [(1 + .15) / (1 + .09)] – 1 = .0550 or 5.50%8.The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation is:(1 + R) = (1 + r)(1 + h)r = [(1 + .134) / (1.045)] – 1 = .0852 or 8.52%9.This is a bond since the maturity is greater than 10 years. The coupon rate, located in the first column of the quote is 6.125%. The bid price is:Bid price = 116:05 = 116 5/32 = 116.15625%⨯$1,000 = $1,161.5625The previous day’s ask price is found by:Previous day’s asked price = T oday’s asked price – Change = 116 5/32 – (–932) = 116 14/32 The previous day’s price in dollars was:Previous day’s dollar price = 116.4375%⨯$1,000 = $1,164.37510.This is a premium bond because it sells for more than 100% of face value. The current yield is:Current yield = Annual coupon payment / Price = $75/$1,320.9375 = 5.68%The YTM is located under the “ASK YLD” column, so the YTM is 4.93%.The bid-ask spread is the difference between the bid price and the ask price, so:Bid-Ask spread = 132:03 – 132:02 = 1/32Intermediate11.Here we are finding the YTM of semiannual coupon bonds for various maturity lengths. The bond price equation is:P = C(PVIFA R%,t) + £1,000(PVIF R%,t)Miller Corporation bond:P0= £40(PVIFA3%,26) + £1,000(PVIF3%,26) = £1,178.77P1= £40(PVIFA3%,24) + £1,000(PVIF3%,24) = £1,169.36P3= £40(PVIFA3%,20) + £1,000(PVIF3%,20) = £1,148.77P7= £40(PVIFA3%,12) + £1,000(PVIF3%,12) = £1,099.54P12= £40(PVIFA3%,2) + £1,000(PVIF3%,2) = £1,019.13P13= £1,000Modigliani Company bond:Y: P0= £30(PVIFA4%,26) + £1,000(PVIF4%,26) = £840.17P1= £30(PVIFA4%,24) + £1,000(PVIF4%,24) = £847.53P3= £30(PVIFA4%,20) + £1,000(PVIF4%,20) = £864.10P7= £30(PVIFA4%,12) + £1,000(PVIF4%,12) = £906.15P12= £30(PVIFA4%,2) + £1,000(PVIF4%,2) = £981.14P13= £1,000All else held equal, the premium over par value for a premium bond declines as maturity approaches, and the discount from par value for a discount bond declines as maturity approaches. This is called “pull to par.” In both cases, the largest percentage price changes occur at the shortest maturity lengths.Also, notice that the price of each bond when no time is left to maturity is the par value, even though the purchaser would receive the par value plus the coupon payment immediately. This is because we calculate the clean price of the bond.12.Any bond that sells at par has a YTM equal to the coupon rate. Both bonds sell at par, so the initial YTM on both bonds is the coupon rate, 10 percent. If the YTM suddenly rises to 12 percent: P Evans= €50(PVIFA6%,4) + €1,000(PVIF6%,4) = €965.35P Troxel= €50(PVIFA6%,30) + €1,000(PVIF6%,30) = €862.35The percentage change in price is calculated as:Percentage change in price = (New price – Original price) / Original price∆P Evans% = (€965.35 – 1,000) / €1,000 = – 3.47%∆P Troxel% = (€862.35 – 1,000) / €1,000 = – 13.76%If the YTM suddenly falls to 8 percent:P Evans= €50(PVIFA4%,4) + €1,000(PVIF4%,4) = €1,036.30P Troxel= €50(PVIFA4%,30) + €1,000(PVIF4%,30) = €1,172.92∆P Evans% = (€1,036.30 – 1,000) / €1,000 = + 3.63%∆P Troxel% = (€1,172.92 – 1,000) / €1,000 = + 17.29%All else the same, the longer the maturity of a bond, the greater is its price sensitivity to changes in interest rates.13.Initially, at a YTM of 7 percent, the prices of the two bonds are:P Busan= ฿25(PVIFA3.5%,16) + ฿1,000(PVIF3.5%,16) = ฿879.06P Iksan= ฿55(PVIFA3.5%,16) + ฿1,000(PVIF3.5%,16) = ฿1,241.88If the YTM rises from 7 percent to 9 percent:P Busan= ฿25(PVIFA4.5%,16) + ฿1,000(PVIF4.5%,16) = ฿775.32P Iksan= ฿55(PVIFA4.5%,16) + ฿1,000(PVIF4.5%,16) = ฿1,112.34The percentage change in price is calculated as:Percentage change in price = (New price – Original price) / Original price∆P Busan% = (฿775.32 – 879.06) / ฿879.06 = – 11.80%∆P Iksan% = (฿1,112.34 – 1,241.88) / ฿1,241.88 = – 10.43%If the YTM declines from 7 percent to 5 percent:P Busan= ฿25(PVIFA2.5%,16) + ฿1,000(PVIF2.5%,16) = ฿1,000.000P Iksan= ฿55(PVIFA2.5%,16) + ฿1,000(PVIF2.5%,16) = ฿1,391.65∆P Busan% = (฿1,000.00 – 879.06) / ฿879.06 = + 13.76%∆P Iksan% = (฿1,391.65 – 1,241.88) / ฿1,241.88 = + 12.06%All else the same, the lower the coupon rate on a bond, the greater is its price sensitivity to changes in interest rates.14.The bond price equation for this bond is:P0 = $1,040 = $45(PVIFA R%,18) + $1,000(PVIF R%,18)Using a spreadsheet, financial calculator, or trial and error we find:R = 4.179%This is the semiannual interest rate, so the YTM is:YTM = 2 ⨯ 4.179% = 8.359%The current yield is:Current yield = Annual coupon payment / Price = $90 / $1,040 = 8.65%The effective annual yield is the same as the EAR, so using the EAR equation from the previous chapter:Effective annual yield = (1 + 0.04179)2– 1 = 8.532%15.The company should set the coupon rate on its new bonds equal to the required return. The required return can be observed in the market by finding the YTM on outstanding bonds of the company. So, the YTM on the bonds currently sold in the market is:P = 元1,100 = 元40(PVIFA R%,40) + 元1,000(PVIF R%,40)Using a spreadsheet, financial calculator, or trial and error we find:R = 3.5295%This is the semiannual interest rate, so the YTM is:YTM = 2 ⨯ 3.5295% = 7.059%16. Accrued interest is the coupon payment for the period times the fraction of the period that has passed since the last coupon payment. Since we have a semiannual coupon bond, the coupon payment per six months is one-half of the annual coupon payment. There are four months until the next coupon payment, so one month has passed since the last coupon payment. The accrued interest for the bond is:Accrued interest = $72/2 × 2/6 = $12And we calculate the clean price as:Clean price = Dirty price – Accrued interest = $1,140 – 12 = $1,12817. Accrued interest is the coupon payment for the period times the fraction of the period that has passed since the last coupon payment. Since we have a semiannual coupon bond, the coupon payment per six months is one-half of the annual coupon payment. There are three months until the next coupon payment, so three months have passed since the last coupon payment. The accrued interest for the bond is:Accrued interest = €65/2 × 3/6 = €16.25And we calculate the dirty price as:Dirty price = Clean price + Accrued interest = €865 + 16.25 = €881.2518.To find the number of years to maturity for the bond, we need to find the price of the bond. Since we already have the coupon rate, we can use the bond price equation, and solve for the number of years to maturity. We are given the current yield of the bond, so we can calculate the price as:Current yield = .0906 = $110/P0P0 = $110/.0906 = $1,214.13Now that we have the price of the bond, the bond price equation is:P = $1,214.13 = $110[(1 – (1/1.085)t ) / .085 ] + $1,000/1.085tWe can solve this equation for t as follows:$1,214.13 (1.085)t = $1,294.12 (1.085)t– 1,294.12 + 1,000294.12 = 79.99(1.085)t3.6769 = 1.085tt = log 3.6769 / log 1.085 = 15.96 ≈ 16 yearsThe bond has 16 years to maturity.19.The bond has 10 years to maturity, so the bond price equation is:P = $769.355 = $36.875(PVIFA R%,20) + $1,000(PVIF R%,20)Using a spreadsheet, financial calculator, or trial and error we find:R = 5.64%This is the semiannual interest rate, so the YTM is:YTM = 2 ⨯ 5.64% = 11.28%The current yield is the annual coupon payment divided by the bond price, so:Current yield = $73.75 / $769.355 = 9.59%The “EST Spread” column shows the difference between the YTM of the bond quoted and the YTM of the U.S. Treasury bond with a similar maturity. The column lists the spread in basis points. One basis point is one-hundredth of one percent, so 100 basis points equals one percent. The spread for this bond is 468 basis points, or 4.68%. This makes the equivalent Treasury yield:Equivalent Treasury yield = 11.28% – 4.68% = 6.60%20.We found the maturity of a bond in Problem 18. However, in this case, the maturity is indeterminate. A bond selling at par can have any length of maturity. In other words, when we solve the bond pricing equation as we did in Problem 18, the number of periods can be any positive number.Challenge21.To find the capital gains yield and the current yield, we need to find the price of the bond. Thecurrent price of Bond P and the price of Bond P in one year is:P: P0 = $100(PVIFA8%,5) + $1,000(PVIF8%,5) = $1,079.85P1 = $100(PVIFA8%,4) + $1,000(PVIF8%,4) = $1,066.24Current yield = $100 / $1,079.85 = 9.26%The capital gains yield is:Capital gains yield = (New price – Original price) / Original price Capital gains yield = ($1,066.24 – 1,079.85) / $1,079.85 = –1.26%The current price of Bond D and the price of Bond D in one year is:D: P0 = $60(PVIFA8%,5) + $1,000(PVIF8%,5) = $920.15P1 = $60(PVIFA8%,4) + $1,000(PVIF8%,4) = $933.76Current yield = $60 / $920.15 = 6.52%Capital gains yield = ($933.76 – 920.15) / $920.15 = +1.48%All else held constant, premium bonds pay high current income while having price depreciation as maturity nears; discount bonds do not pay high current income but have price appreciation as maturity nears. For either bond, the total return is still 8%, but this return is distributed differently between current income and capital gains.22.a. The rate of return you expect to earn if you purchase a bond and hold it until maturity is theYTM. The bond price equation for this bond is:P0 = €1,150 = €80(PVIFA R%,10) + €1,000(PVIF R%,10)Using a spreadsheet, financial calculator, or trial and error we find:R = YTM = 5.97%b. To find our HPY, we need to find the price of the bond in two years. The price of the bond intwo years, at the new interest rate, will be:P2 = €80(PVIFA4.97%,8) + €1,000(PVIF4.97%,8) = €1,196.41To calculate the HPY, we need to find the interest rate that equates the price we paid for the bond with the cash flows we received. The cash flows we received were €80 each year for two years, and the price of the bond when we sold it. The equation to find our HPY is:P0 = €1,150 = €80(PVIFA R%,2) + €1,196.41(PVIF R%,2)Solving for R, we get:R = HPY = 8.89%The realized HPY is greater than the expected YTM when the bond was bought because interest rates dropped by 1 percent; bond prices rise when yields fall.23.The price of any bond (or financial instrument) is the PV of the future cash flows. Even though Bond M makes different coupons payments, to find the price of the bond, we just find the PV of the cash flows. The PV of the cash flows for Bond M is:P M= €1,200(PVIFA5%,16)(PVIF5%,12) + €1,500(PVIFA5%,12)(PVIF5%,28) + €20,000(PVIF5%,40) P M= €13,474.20Notice that for the coupon payments of €1,500, we found the PVA for the coupon payments, and then discounted the lump sum back to today.Bond N is a zero coupon bond with a €20,000 par value, therefore, the price of the bond is the PV of the par, or:P N= €20,000(PVIF5%,40) = €2,840.9124.To calculate this, we need to set up an equation with the callable bond equal to a weighted average of the noncallable bonds. We will invest X percent of our money in the first noncallable bond, which means our investment in Bond 3 (the other noncallable bond) will be (1 – X). The equation is: C2 = C1 X + C3(1 – X)8.25 = 6.50 X + 12(1 – X)8.25 = 6.50 X + 12 – 12 XX = 0.68182So, we invest about 68 percent of our money in Bond 1, and about 32 percent in Bond 3. This combination of bonds should have the same value as the callable bond, excluding the value of the call. So: P2= 0.68182P1 + 0.31819P3P2= 0.68182(106.375) + 0.31819(134.96875)P2= 115.4730The call value is the difference between this implied bond value and the actual bond price. So, the call value is:Call value = 115.4730 – 103.50 = 11.9730Assuming $1,000 par value, the call value is $119.73. 25.In general, this is not likely to happen, although it can (and did). The reason this bond has a negative YTM is that it is a callable U.S. Treasury bond. Market participants know this. Given the high coupon rate of the bond, it is extremely likely to be called, which means the bondholder will not receive all the cash flows promised. A better measure of the return on a callable bond is the yield to call (YTC). The YTC calculation is the basically the same as the YTM calculation, but the number of periods is the number of periods until the call date. If the YTC were calculated on this bond, it would be positive.26.To find the present value, we need to find the real weekly interest rate. To find the real return, we need to use the effective annual rates in the Fisher equation. So, we find the real EAR is:(1 + R) = (1 + r)(1 + h)1 + .104 = (1 + r)(1 + .039)r = .0626 or 6.26%Now, to find the weekly interest rate, we need to find the APR. Using the equation for discrete compounding:EAR = [1 + (APR / m)]m– 1We can solve for the APR. Doing so, we get:APR = m[(1 + EAR)1/m– 1]APR = 52[(1 + .0626)1/52– 1]APR = .0607 or 6.07%So, the weekly interest rate is:Weekly rate = APR / 52Weekly rate = .0607 / 52Weekly rate = .0012 or 0.12%Now we can find the present value of the cost of the roses. The real cash flows are an ordinary annuity, discounted at the real interest rate. So, the present value of the cost of the roses is:PVA = C({1 – [1/(1 + r)]t } / r)PVA = $5({1 – [1/(1 + .0012)]30(52)} / .0012)PVA = $3,588.6627.To answer this question, we need to find the monthly interest rate, which is the APR divided by 12. We also must be careful to use the real interest rate. The Fisher equation uses the effective annual rate, so, the real effective annual interest rates, and the monthly interest rates for each account are:Stock account:(1 + R) = (1 + r)(1 + h)1 + .11 = (1 + r)(1 + .04)r = .0673 or 6.73%APR = m[(1 + EAR)1/m– 1]APR = 12[(1 + .0673)1/12– 1]APR = .0653 or 6.53%Monthly rate = APR / 12Monthly rate = .0653 / 12Monthly rate = .0054 or 0.54%Bond account:(1 + R) = (1 + r)(1 + h)1 + .07 = (1 + r)(1 + .04)r = .0288 or 2.88%APR = m[(1 + EAR)1/m– 1]APR = 12[(1 + .0288)1/12– 1]APR = .0285 or 2.85%Monthly rate = APR / 12Monthly rate = .0285 / 12Monthly rate = .0024 or 0.24%Now we can find the future value of the retirement account in real terms. The future value of each account will be:Stock account:FVA = C {(1 + r )t– 1] / r}FVA = £700{[(1 + .0054)360 – 1] / .0054]}FVA = £779,103.15Bond account:FVA = C {(1 + r )t– 1] / r}FVA = £300{[(1 + .0024)360 – 1] / .0024]}FVA = £170,316.78The total future value of the retirement account will be the sum of the two accounts, or:Account value = £779,103.15 + 170,316.78Account value = £949,419.93Now we need to find the monthly interest rate in retirement. We can use the same procedure that we used to find the monthly interest rates for the stock and bond accounts, so:(1 + R) = (1 + r)(1 + h)1 + .09 = (1 + r)(1 + .04)r = .0481 or 4.81%APR = m[(1 + EAR)1/m– 1]APR = 12[(1 + .0481)1/12– 1]APR = .0470 or 4.70%Monthly rate = APR / 12Monthly rate = .0470 / 12Monthly rate = .0039 or 00.39%N ow we can find the real monthly withdrawal in retirement. Using the present value of an annuity equation and solving for the payment, we find:PVA = C({1 – [1/(1 + r)]t } / r )£949,419.93 = C({1 – [1/(1 + .0039)]300 } / .0039)C = £5,388.21This is the real pound amount of the monthly withdrawals. The nominal monthly withdrawals will increase by the inflation rate each month. To find the nominal pound amount of the last withdrawal, we can increase the real pound withdrawal by the inflation rate. We can increase the real withdrawal by the effective annual inflation rate since we are only interested in the nominal amount of the last withdrawal. So, the last withdrawal in nominal terms will be:FV = PV(1 + r)tFV = £5,388.21(1 + .04)(30 + 25)FV = £46,588.4228.In this problem, we need to calculate the future value of the annual savings after the five years of operations. The savings are the revenues minus the costs, or:Savings = Revenue – CostsSince the annual fee and the number of members are increasing, we need to calculate the effective growth rate for revenues, which is:Effective growth rate = (1 + .10)(1 + .03) – 1Effective growth rate = .1330 or 13.30%The revenue for the current year is the number of members times the annual fee, or:Current revenue = 500(元400)Current revenue = 元200,000The revenue will grow at 13.30 percent, and the costs will grow at 2 percent, so the savings each year for the next five years will be:Year Revenue Costs Savings1 元 226,600.00 元 81,600.00 元 145,000.002 256,737.80 83,232.00 173,505.803 290,883.93 84,896.64 205,987.294 329,571.49 86,594.57 242,976.925 373,404.50 88,326.46 285,078.03Now we can find the value of each year’s savings using the future value of a lump sum equation, so:FV = PV(1 + r)tYear Future Value1 元145,000.00(1 + .08)4 = 元197,270.902 元173,505.80(1 + .08)3 = 218,567.343 元205,978.29(1 + .08)2 = 240,263.574 元242,976.92(1 + .08)1 = 262,415.075 285,078.03Total future value of savings = 元1,203,594.91He will spend 元500,000 on a luxury boat, so the value of his account will be:Value of account = 元1,203,594.91 – 500,000Value of account = 元703,594.91Now we can use the present value of an annuity equation to find the payment. Doing so, we find:PVA = C({1 – [1/(1 + r)]t } / r )元703,591.51 = C({1 – [1/(1 + .08)]16 } / .08)C = 元79,489.57。
罗斯《公司理财》第9版笔记和课后习题(含考研真题)详解[视频详解](折现现金流量估价)【圣才出品】
【圣才出品】](https://img.taocdn.com/s3/m/810ed282482fb4daa58d4bf0.png)
罗斯《公司理财》第9版笔记和课后习题（含考研真题）详解[视频详解]第4章折现现金流量估价[视频讲解]4.1复习笔记当前的1美元与未来的1美元的价值是不同的，因为当前1美元用于投资，在未来可以得到更多，而且未来的1美元具有不确定性。
这种区别正是“货币的时间价值”。
货币的时间价值概念是金融投资和融资的基石之一，资本预算、项目决策、融资管理和兼并等领域均有涉及。
因此有必要理解和掌握相关的现值、终值、年金和永续年金的概念和计算公式。
1．现值与净现值现值是未来资金在当前的价值，是把未来的现金流按照一定的贴现率贴现到当前的价值。
以单期为例，一期后的现金流的现值：其中，C1是一期后的现金流，r是适当贴现率。
在多期的情况下，求解PV的公式可写为：其中，C T是在T期的现金流，r是适当贴现率。
净现值的计算公式为：NPV=-成本+PV。
也就是说，净现值NPV是这项投资未来现金流的现值减去成本的现值所得的结果。
一种定量的财务决策方法是净现值分析法。
产生N期现金流的投资项目的净现值为：NPV=其中，-C0是初始现金流，由于它代表了一笔投资，即现金流出，因而是负值。
2．终值一笔投资在多期以后终值的一般计算公式可以写为：FV=C0×（1+r）T其中，C0是期初投资的金额，r是利息率，T是资金投资持续的期数。
一项投资每年按复利计息m次的年末终值为：其中：C0是投资者的初始投资；r是名义年利率。
当m趋近于无限大时，则是连续复利计息，这时T年后的终值可以表示为：C0×e rT。
连续复利在高级金融中有广泛的应用。
3．名义利率和实际利率名义年利率是不考虑年内复利计息的，不同的银行或金融机构有不同的称谓，比较通用的是年百分比利率（APR）；实际利率（EAR）是指在年内考虑复利计息的，然后折算成一年的利率。
名义利率和实际利率之间的差别在于名义利率只有给出计息间隔期下才有意义。
4．年金年金是指一系列稳定有规律的，持续一段固定时期的现金收付活动，即在一定期间内，每隔相同时期（一年、半年或一季等）收入或支出相等金额的款项。
罗斯《公司理财》英文习题答案DOCchap004
公司理财习题答案第四章Chapter 4: Net Present Value4.1 a. $1,000 ⨯ 1.0510 = $1,628.89b. $1,000 ⨯ 1.0710 = $1,967.15c. $1,000 ⨯ 1.0520 = $2,653.30d. Interest compounds on the I nterest already earned. Therefore, the interest earnedin part c, $1,653.30, is more than double the amount earned in part a, $628.89.4.2 a. $1,000 / 1.17 = $513.16b. $2,000 / 1.1 = $1,818.18c. $500 / 1.18 = $233.254.3 You can make your decision by computing either the present value of the $2,000 that youcan receive in ten years, or the future value of the $1,000 that you can receive now.Present value: $2,000 / 1.0810 = $926.39Future value: $1,000 ⨯ 1.0810 = $2,158.93Either calculation indicates you should take the $1,000 now.4.4 Since this bond has no interim coupon payments, its present value is simply the presentvalue of the $1,000 that will be received in 25 years. Note: As will be discussed in the next chapter, the present value of the payments associated with a bond is the price of that bond.PV = $1,000 /1.125 = $92.304.5 PV = $1,500,000 / 1.0827 = $187,780.234.6 a. At a discount rate of zero, the future value and present value are always the same.Remember, FV = PV (1 + r) t. If r = 0, then the formula reduces to FV = PV.Therefore, the values of the options are $10,000 and $20,000, respectively. Youshould choose the second option.b. Option one: $10,000 / 1.1 = $9,090.91Option two: $20,000 / 1.15 = $12,418.43Choose the second option.c. Option one: $10,000 / 1.2 = $8,333.33Option two: $20,000 / 1.25 = $8,037.55Choose the first option.d. You are indifferent at the rate that equates the PVs of the two alternatives. Youknow that rate must fall between 10% and 20% because the option you wouldchoose differs at these rates. Let r be the discount rate that makes you indifferentbetween the options.$10,000 / (1 + r) = $20,000 / (1 + r)5(1 + r)4 = $20,000 / $10,000 = 21 + r = 1.18921r = 0.18921 = 18.921%4.7 PV of Joneses’ offer = $150,000 / (1.1)3 = $112,697.22Since the PV of Joneses’ offer is less than Smiths’ offer, $115,000, you should chooseSmiths’ offer.4.8 a. P0 = $1,000 / 1.0820 = $214.55b. P10 = P0 (1.08)10 = $463.20c. P15 = P0 (1.08)15 = $680.594.9 The $1,000 that you place in the account at the end of the first year will earn interest for sixyears. The $1,000 that you place in the account at the end of the second year will earninterest for five years, etc. Thus, the account will have a balance of$1,000 (1.12)6 + $1,000 (1.12)5 + $1,000 (1.12)4 + $1,000 (1.12)3= $6,714.614.10 PV = $5,000,000 / 1.1210 = $1,609,866.184.11 a. The cost of investment is $900,000.PV of cash inflows = $120,000 / 1.12 + $250,000 / 1.122 + $800,000 / 1.123= $875,865.52Since the PV of cash inflows is less than the cost of investment, you should notmake the investment.b. NPV = -$900,000 + $875,865.52= -$24,134.48c. NPV = -$900,000 + $120,000 / 1.11 + $250,000 / 1.112 + $800,000 / 1.113= $-4,033.18Since the NPV is still negative, you should not make the investment.4.12 NPV = -($340,000 + $10,000) + ($100,000 - $10,000) / 1.1+ $90,000 / 1.12 + $90,000 / 1.13 + $90,000 / 1.14 + $100,000 / 1.15= -$2,619.98Since the NPV is negative, you should not buy it.If the relevant cost of capital is 9 percent,NPV = -$350,000 + $90,000 / 1.09 + $90,000 / 1.092 + $90,000 / 1.093+ $90,000 / 1.094 + $100,000 / 1.095= $6,567.93Since the NPV is positive, you should buy it.4.13 a. Profit = PV of revenue - Cost = NPVNPV = $90,000 / 1.15 - $60,000 = -$4,117.08No, the firm will not make a profit.b. Find r that makes zero NPV.$90,000 / (1+r)5 - $60,000 = $0(1+r)5 = 1.5r = 0.08447 = 8.447%4.14 The future value of the decision to own your car for one year is the sum of the trade-invalue and the benefit from owning the car. Therefore, the PV of the decision to own thecar for one year is$3,000 / 1.12 + $1,000 / 1.12 = $3,571.43Since the PV of the roommate’s offer, $3,500, is lower than the aunt’s offer, you shouldaccept aunt’s offer.4.15 a. $1.000 (1.08)3 = $1,259.71b. $1,000 [1 + (0.08 / 2)]2 ⨯ 3 = $1,000 (1.04)6 = $1,265.32c. $1,000 [1 + (0.08 / 12)]12 ⨯ 3 = $1,000 (1.00667)36 = $1,270.24d. $1,000 e0.08 ⨯ 3 = $1,271.25公司理财习题答案第四章e. The future value increases because of the compounding. The account is earninginterest on interest. Essentially, the interest is added to the account balance at theend of every compounding period. During the next period, the account earnsinterest on the new balance. When the compounding period shortens, the balancethat earns interest is rising faster.4.16 a. $1,000 e0.12 ⨯ 5 = $1,822.12b. $1,000 e0.1 ⨯ 3 = $1,349.86c. $1,000 e0.05 ⨯ 10 = $1,648.72d. $1,000 e0.07 ⨯ 8 = $1,750.674.17 PV = $5,000 / [1+ (0.1 / 4)]4 ⨯ 12 = $1,528.364.18 Effective annual interest rate of Bank America= [1 + (0.041 / 4)]4 - 1 = 0.0416 = 4.16%Effective annual interest rate of Bank USA= [1 + (0.0405 / 12)]12 - 1 = 0.0413 = 4.13%You should deposit your money in Bank America.4.19 The price of the consol bond is the present value of the coupon payments. Apply theperpetuity formula to find the present value. PV = $120 / 0.15 = $8004.20 Quarterly interest rate = 12% / 4 = 3% = 0.03Therefore, the price of the security = $10 / 0.03 = $333.334.21 The price at the end of 19 quarters (or 4.75 years) from today = $1 / (0.15 ÷ 4) = $26.67The current price = $26.67 / [1+ (.15 / 4)]19 = $13.254.22 a. $1,000 / 0.1 = $10,000b. $500 / 0.1 = $5,000 is the value one year from now of the perpetual stream. Thus,the value of the perpetuity is $5,000 / 1.1 = $4,545.45.c. $2,420 / 0.1 = $24,200 is the value two years from now of the perpetual stream.Thus, the value of the perpetuity is $24,200 / 1.12 = $20,000.4.23 The value at t = 8 is $120 / 0.1 = $1,200.Thus, the value at t = 5 is $1,200 / 1.13 = $901.58.4.24 P = $3 (1.05) / (0.12 - 0.05) = $45.004.25 P = $1 / (0.1 - 0.04) = $16.674.26 The first cash flow will be generated 2 years from today.The value at the end of 1 year from today = $200,000 / (0.1 - 0.05) = $4,000,000.Thus, PV = $4,000,000 / 1.1 = $3,636,363.64.4.27 A zero NPV-$100,000 + $50,000 / r = 0-r = 0.54.28 Apply the NPV technique. Since the inflows are an annuity you can use the present valueof an annuity factor.NPV = -$6,200 + $1,200 8A1.0= -$6,200 + $1,200 (5.3349)= $201.88Yes, you should buy the asset.4.29 Use an annuity factor to compute the value two years from today of the twenty payments.Remember, the annuity formula gives you the value of the stream one year before the first payment. Hence, the annuity factor will give you the value at the end of year two of the stream of payments. Value at the end of year two = $2,000 20A08.0= $2,000 (9.8181)= $19,636.20The present value is simply that amount discounted back two years.PV = $19,636.20 / 1.082 = $16,834.884.30 The value of annuity at the end of year five= $500 15A = $500 (5.84737) = $2,923.6915.0The present value = $2,923.69 / 1.125 = $1,658.984.31 The easiest way to do this problem is to use the annuity factor. The annuity factor must beequal to $12,800 / $2,000 = 6.4; remember PV =C A t r. The annuity factors are in theappendix to the text. To use the factor table to solve this problem, scan across the rowlabeled 10 years until you find 6.4. It is close to the factor for 9%, 6.4177. Thus, the rate you will receive on this note is slightly more than 9%.You can find a more precise answer by interpolating between nine and ten percent.10% ⎤ 6.1446 ⎤a ⎡ r ⎥bc ⎡ 6.4 ⎪ d⎣ 9% ⎦⎣ 6.4177 ⎦By interpolating, you are presuming that the ratio of a to b is equal to the ratio of c to d.(9 - r ) / (9 - 10) = (6.4177 - 6.4 ) / (6.4177 - 6.1446)r = 9.0648%The exact value could be obtained by solving the annuity formula for the interest rate.Sophisticated calculators can compute the rate directly as 9.0626%.公司理财习题答案第四章4.32 a. The annuity amount can be computed by first calculating the PV of the $25,000which you need in five years. That amount is $17,824.65 [= $25,000 / 1.075].Next compute the annuity which has the same present value.$17,824.65 = C 5A.007$17,824.65 = C (4.1002)C = $4,347.26Thus, putting $4,347.26 into the 7% account each year will provide $25,000 fiveyears from today.b. The lump sum payment must be the present value of the $25,000, i.e., $25,000 /1.075 = $17,824.65The formula for future value of any annuity can be used to solve the problem (seefootnote 14 of the text).4.33The amount of loan is $120,000 ⨯ 0.85 = $102,000.20C A= $102,000.010The amount of equal installments isC = $102,000 / 20A = $102,000 / 8.513564 = $11,980.8810.04.34 The present value of salary is $5,000 36A = $150,537.53.001The present value of bonus is $10,000 3A = $23,740.42 (EAR = 12.68% is used since.01268bonuses are paid annually.)The present value of the contract = $150,537.53 + $23,740.42 = $174,277.944.35 The amount of loan is $15,000 ⨯ 0.8 = $12,000.C 48A = $12,0000067.0The amount of monthly installments isC = $12,000 / 48A = $12,000 / 40.96191 = $292.960067.04.36 Option one: This cash flow is an annuity due. To value it, you must use the after-taxamounts. The after-tax payment is $160,000 (1 - 0.28) = $115,200. Value all except the first payment using the standard annuity formula, then add back the first payment of$115,200 to obtain the value of this option.Value = $115,200 + $115,200 30A10.0= $115,200 + $115,200 (9.4269)= $1,201,178.88Option two: This option is valued similarly. You are able to have $446,000 now; this is already on an after-tax basis. You will receive an annuity of $101,055 for each of the next thirty years. Those payments are taxable when you receive them, so your after-taxpayment is $72,759.60 [= $101,055 (1 - 0.28)].Value = $446,000 + $72,759.60 30A.010= $446,000 + $72,759.60 (9.4269)= $1,131,897.47Since option one has a higher PV, you should choose it.4.37 The amount of loan is $9,000. The monthly payment C is given by solving the equation: C 60008.0A = $9,000 C = $9,000 / 47.5042 = $189.46In October 2000, Susan Chao has 35 (= 12 ⨯ 5 - 25) monthly payments left, including the one due in October 2000.Therefore, the balance of the loan on November 1, 2000 = $189.46 + $189.46 34008.0A = $189.46 + $189.46 (29.6651) = $5,809.81Thus, the total amount of payoff = 1.01 ($5,809.81) = $5,867.91 4.38 Let r be the rate of interest you must earn. $10,000(1 + r)12 = $80,000 (1 + r)12 = 8 r = 0.18921 = 18.921%4.39 First compute the present value of all the payments you must make for your children’s education. The value as of one year before matriculation of one child’s education is$21,000 415.0A= $21,000 (2.8550) = $59,955. This is the value of the elder child’s education fourteen years from now. It is the value of the younger child’s education sixteen years from today. The present value of these is PV = $59,955 / 1.1514 + $59,955 / 1.1516 = $14,880.44You want to make fifteen equal payments into an account that yields 15% so that the present value of the equal payments is $14,880.44. Payment = $14,880.44 / 1515.0A = $14,880.44 / 5.8474 = $2,544.804.40 The NPV of the policy isNPV = -$750 306.0A - $800306.0A / 1.063 + $250,000 / [(1.066) (1.0759)] = -$2,004.76 - $1,795.45 + $3,254.33= -$545.88 Therefore, you should not buy the policy.4.41 The NPV of the lease offer isNPV = $120,000 - $15,000 - $15,000 908.0A - $25,000 / 1.0810= $105,000 - $93,703.32 - $11,579.84 = -$283.16 Therefore, you should not accept the offer.4.42 This problem applies the growing annuity formula. The first payment is $50,000(1.04)2(0.02) = $1,081.60. PV = $1,081.60 [1 / (0.08 - 0.04) - {1 / (0.08 - 0.04)}{1.04 / 1.08}40]= $21,064.28 This is the present value of the payments, so the value forty years from today is $21,064.28 (1.0840) = $457,611.46公司理财习题答案第四章4.43 Use the discount factors to discount the individual cash flows. Then compute the NPV ofthe project. Notice that the four $1,000 cash flows form an annuity. You can still use the factor tables to compute their PV. Essentially, they form cash flows that are a six year annuity less a two year annuity. Thus, the appropriate annuity factor to use with them is 2.6198 (= 4.3553 - 1.7355).Year Cash Flow Factor PV 1 $700 0.9091 $636.37 2 900 0.8264 743.76 3 1,000 ⎤ 4 1,000 ⎥ 2.6198 2,619.80 5 1,000 ⎥ 6 1,000 ⎦ 7 1,250 0.5132 641.50 8 1,375 0.4665 641.44 Total $5,282.87NPV = -$5,000 + $5,282.87 = $282.87 Purchase the machine.4.44 Weekly inflation rate = 0.039 / 52 = 0.00075 Weekly interest rate = 0.104 / 52 = 0.002 PV = $5 [1 / (0.002 - 0.00075)] {1 – [(1 + 0.00075) / (1 + 0.002)]52 ⨯ 30} = $3,429.384.45 Engineer:NPV = -$12,000 405.0A + $20,000 / 1.055 + $25,000 / 1.056 - $15,000 / 1.057- $15,000 / 1.058 + $40,000 2505.0A / 1.058= $352,533.35 Accountant:NPV = -$13,000 405.0A + $31,000 3005.0A / 1.054= $345,958.81 Become an engineer.After your brother announces that the appropriate discount rate is 6%, you can recalculate the NPVs. Calculate them the same way as above except using the 6% discount rate. Engineer NPV = $292,419.47 Accountant NPV = $292,947.04Your brother made a poor decision. At a 6% rate, he should study accounting.4.46 Since Goose receives his first payment on July 1 and all payments in one year intervalsfrom July 1, the easiest approach to this problem is to discount the cash flows to July 1 then use the six month discount rate (0.044) to discount them the additional six months. PV = $875,000 / (1.044) + $650,000 / (1.044)(1.09) + $800,000 / (1.044)(1.092) + $1,000,000 / (1.044)(1.093) + $1,000,000/(1.044)(1.094) + $300,000 / (1.044)(1.095)+ $240,000 1709.0A / (1.044)(1.095) + $125,000 1009.0A / (1.044)(1.0922) = $5,051,150Remember that the use of annuity factors to discount the deferred payments yields the value of the annuity stream one period prior to the first payment. Thus, the annuity factor applied to the first set of deferred payments gives the value of those payments on July 1 of 1989. Discounting by 9% for five years brings the value to July 1, 1984. The use of the six month discount rate (4.4%) brings the value of the payments to January 1, 1984. Similarly, the annuity factor applied to the second set of deferred payments yields the value of those payments in 2006. Discounting for 22 years at 9% and for six months at 4.4% provides the value at January 1, 1984.The equivalent five-year, annual salary is the annuity that solves: $5,051,150 = C 509.0A C = $5,051,150/3.8897C = $1,298,596The student must be aware of possible rounding errors in this problem. The differencebetween 4.4% semiannual and 9.0% and for six months at 4.4% provides the value at January 1, 1984. 4.47 PV = $10,000 + ($35,000 + $3,500) [1 / (0.12 - 0.04)] [1 - (1.04 / 1.12) 25 ]= $415,783.604.48 NPV = -$40,000 + $10,000 [1 / (0.10 - 0.07)] [1 - (1.07 / 1.10)5 ] = $3,041.91 Revise the textbook.4.49The amount of the loan is $400,000 (0.8) = $320,000 The monthly payment is C = $320,000 / 3600067.0.0A = $ 2,348.10 Thirty years of payments $ 2,348.10 (360) = $ 845,316.00 Eight years of payments $2,348.10 (96) = $225,417.60 The difference is the balloon payment of $619,898.404.50 The lease payment is an annuity in advanceC + C 2301.0A = $4,000 C (1 + 20.4558) = $4,000 C = $186.424.51 The effective annual interest rate is[ 1 + (0.08 / 4) ] 4 – 1 = 0.0824The present value of the ten-year annuity is PV = 900 100824.0A = $5,974.24 Four remaining discount periodsPV = $5,974.24 / (1.0824) 4 = $4,352.43公司理财习题答案第四章4.52The present value of Ernie’s retirement incomePV = $300,000 20A / (1.07) 30 = $417,511.5407.0The present value of the cabinPV = $350,000 / (1.07) 10 = $177,922.25The present value of his savingsPV = $40,000 10A = $280,943.26.007In present value terms he must save an additional $313,490.53 In future value termsFV = $313,490.53 (1.07) 10 = $616,683.32He must saveC = $616.683.32 / 20A = $58,210.5407.0。
英文版罗斯公司理财习题答案ChapWord版
CHAPTER 8MAKING CAPITAL INVESTMENT DECISIONSAnswers to Concepts Review and Critical Thinking Questions1.In this context, an opportunity cost refers to the value of an asset or other input that will be used in aproject. The relevant cost is what the asset or input is actually worth today, not, for example, what it cost to acquire.2. a.Yes, the reduction in the sales of the company’s other products, referred to as erosion, andshould be treated as an incremental cash flow. These lost sales are included because they are a cost (a revenue reduction) that the firm must bear if it chooses to produce the new product.b. Yes, expenditures on plant and equipment should be treated as incremental cash flows. Theseare costs of the new product line. However, if these expenditures have already occurred, they are sunk costs and are not included as incremental cash flows.c. No, the research and development costs should not be treated as incremental cash flows. Thecosts of research and development undertaken on the product during the past 3 years are sunk costs and should not be included in the evaluation of the project. Decisions made and costs incurred in the past cannot be changed. They should not affect the decision to accept or reject the project.d. Yes, the annual depreciation expense should be treated as an incremental cash flow.Depreciation expense must be taken into account when calculating the cash flows related to a given project. While depreciation is not a cash expense that directly affects cash flow, it decreases a firm’s net income and hence, lowers its tax bill for the year. Because of this depreciation tax shield, the firm has more cash on hand at the end of the year than it would have had without expensing depreciation.e.No, dividend payments should not be treated as incremental cash flows. A firm’s decision topay or not pay dividends is independent of the decision to accept or reject any given investment project. For this reason, it is not an incremental cash flow to a given project. Dividend policy is discussed in more detail in later chapters.f.Yes, the resale value of plant and equipment at the end of a project’s life should be treated as anincremental cash flow. The price at which the firm sells the equipment is a cash inflow, and any difference between the book value of the equipment and its sale price will create gains or lossesthat result in either a tax credit or liability.g.Yes, salary and medical costs for production employees hired for a project should be treated asincremental cash flows. The salaries of all personnel connected to the project must be included as costs of that project.3.Item I is a relevant cost because the opportunity to sell the land is lost if the new golf club is produced. Item II is also relevant because the firm must take into account the erosion of sales of existing products when a new product is introduced. If the firm produces the new club, the earnings from the existing clubs will decrease, effectively creating a cost that must be included in the decision.Item III is not relevant because the costs of Research and Development are sunk costs. Decisions made in the past cannot be changed. They are not relevant to the production of the new clubs.4.For tax purposes, a firm would choose MACRS because it provides for larger depreciationdeductions earlier. These larger deductions reduce taxes, but have no other cash consequences.Notice that the choice between MACRS and straight-line is purely a time value issue; the total depreciation is the same; only the timing differs.5.It’s probably only a mild over-simplification. Current liabilities will all be paid, presumably. Thecash portion of current assets will be retrieved. Some receivables won’t be collected, and some inventory will not be sold, of course. Counterbalancing these losses is the fact that inventory sold above cost (and not replaced at the end of the project’s life) acts to increase working capital. These effects tend to offset one another.6.Management’s discretion to set the firm’s capital structure is applicable at the firm level. Since anyone particular project could be financed entirely with equity, another project could be financed with debt, and the firm’s overall capital structure remains unchanged, financing cost s are not relevant in the analysis of a project’s incremental cash flows according to the stand-alone principle.7.The EAC approach is appropriate when comparing mutually exclusive projects with different livesthat will be replaced when they wear out. This type of analysis is necessary so that the projects havea common life span over which they can be compared; in effect, each project is assumed to existover an infinite horizon of N-year repeating projects. Assuming that this type of analysis is valid implies that the project cash flows remain the same forever, thus ignoring the possible effects of, among other things: (1) inflation, (2) changing economic conditions, (3) the increasing unreliability of cash flow estimates that occur far into the future, and (4) the possible effects of future technology improvement that could alter the project cash flows.8.Depreciation is a non-cash expense, but it is tax-deductible on the income statement. Thusdepreciation causes taxes paid, an actual cash outflow, to be reduced by an amount equal to the depreciation tax shield, t c D. A reduction in taxes that would otherwise be paid is the same thing as a cash inflow, so the effects of the depreciation tax shield must be added in to get the total incremental aftertax cash flows.9.There are two particularly important considerations. The first is erosion. Will the “essentialized”book simply displace copies of the existing book that would have otherwise been sold? This is of special concern given the lower price. The second consideration is competition. Will other publishers step in and produce such a product? If so, then any erosion is much less relevant. A particular concern to book publishers (and producers of a variety of other product types) is that the publisher only makes money from the sale of new books. Thus, it is important to examine whether the new book would displace sales of used books (good from the publisher’s perspective) or new books (not good). The concern arises any time there is an active market for used product.10.Definitely. The damage to Porsche’s reputation is definitely a factor the company needed to consider.If the reputation was damaged, the company would have lost sales of its existing car lines.11.One company may be able to produce at lower incremental cost or market better. Also, of course,one of the two may have made a mistake!12.Porsche would recognize that the outsized profits would dwindle as more products come to marketand competition becomes more intense.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 tax shield approach to calculating OCF, we get:OCF = (Sales – Costs)(1 – t C) + t C DepreciationOCF = [($5 × 2,000 – ($2 × 2,000)](1 – 0.35) + 0.35($10,000/5)OCF = $4,600So, the NPV of the project is:NPV = –$10,000 + $4,600(PVIFA17%,5)NPV = $4,7172.We will use the bottom-up approach to calculate the operating cash flow for each year. We also mustbe sure to include the net working capital cash flows each year. So, the total cash flow each year will be:Year 1 Year 2 Year 3 Year 4 Sales Rs.7,000 Rs.7,000 Rs.7,000 Rs.7,000Costs 2,000 2,000 2,000 2,000Depreciation 2,500 2,500 2,500 2,500EBT Rs.2,500 Rs.2,500 Rs.2,500 Rs.2,500Tax 850 850 850 850Net income Rs.1,650 Rs.1,650 Rs.1,650 Rs.1,650OCF 0 Rs.4,150 Rs.4,150 Rs.4,150 Rs.4,150Capital spending –Rs.10,000 0 0 0 0NWC –200 –250 –300 –200 950Incremental cashflow –Rs.10,200 Rs.3,900 Rs.3,850 Rs.3,950 Rs.5,100The NPV for the project is:NPV = –Rs.10,200 + Rs.3,900 / 1.10 + Rs.3,850 / 1.102 + Rs.3,950 / 1.103 + Rs.5,100 / 1.104NPV = Rs.2,978.333. Using the tax shield approach to calculating OCF, we get:OCF = (Sales – Costs)(1 – t C) + t C DepreciationOCF = (R2,400,000 – 960,000)(1 – 0.30) + 0.30(R2,700,000/3)OCF = R1,278,000So, the NPV of the project is:NPV = –R2,700,000 + R1,278,000(PVIFA15%,3)NPV = R217,961.704.The cash outflow at the beginning of the project will increase because of the spending on NWC. Atthe end of the project, the company will recover the NWC, so it will be a cash inflow. The sale of the equipment will result in a cash inflow, but we also must account for the taxes which will be paid on this sale. So, the cash flows for each year of the project will be:Year Cash Flow0 – R3,000,000 = –R2.7M – 300K1 1,278,0002 1,278,0003 1,725,000 = R1,278,000 + 300,000 + 210,000 + (0 – 210,000)(.30)And the NPV of the project is:NPV = –R3,000,000 + R1,278,000(PVIFA15%,2) + (R1,725,000 / 1.153)NPV = R211,871.465. First we will calculate the annual depreciation for the equipment necessary for the project. Thedepreciation amount each year will be:Year 1 depreciation = R2.7M(0.3330) = R899,100Year 2 depreciation = R2.7M(0.4440) = R1,198,800Year 3 depreciation = R2.7M(0.1480) = R399,600So, the book value of the equipment at the end of three years, which will be the initial investment minus the accumulated depreciation, is:Book value in 3 years = R2.7M – (R899,100 + 1,198,800 + 399,600)Book value in 3 years = R202,500The asset is sold at a gain to book value, so this gain is taxable.Aftertax salvage value = R202,500 + (R202,500 – 210,000)(0.30)Aftertax salvage value = R207,750To calculate the OCF, we will use the tax shield approach, so the cash flow each year is:OCF = (Sales – Costs)(1 – t C) + t C DepreciationYear Cash Flow0 – R3,000,000 = –R2.7M – 300K1 1,277,730.00 = (R1,440,000)(.70) + 0.30(R899,100)2 1,367,640.00 = (R1,440,000)(.70) + 0.30(R1,198,800)3 1,635,630.00 = (R1,440,000)(.70) + 0.30(R399,600) + R207,750 + 300,000Remember to include the NWC cost in Year 0, and the recovery of the NWC at the end of the project.The NPV of the project with these assumptions is:NPV = – R3.0M + (R1,277,730/1.15) + (R1,367,640/1.152) + (R1,635,630/1.153)NPV = R220,655.206. First, we will calculate the annual depreciation of the new equipment. It will be:Annual depreciation charge = €925,000/5Annual depreciation charge = €185,000The aftertax salvage value of the equipment is:Aftertax salvage value = €90,000(1 – 0.35)Aftertax salvage value = €58,500Using the tax shield approach, the OCF is:OCF = €360,000(1 – 0.35) + 0.35(€185,000)OCF = €298,750Now we can find the project IRR. There is an unusual feature that is a part of this project. Accepting this project means that we will reduce NWC. This reduction in NWC is a cash inflow at Year 0. This reduction in NWC implies that when the project ends, we will have to increase NWC. So, at the end of the project, we will have a cash outflow to restore the NWC to its level before the project. We also must include the aftertax salvage value at the end of the project. The IRR of the project is:NPV = 0 = –€925,000 + 125,000 + €298,750(PVIFA IRR%,5) + [(€58,500 – 125,000) / (1+IRR)5]IRR = 23.85%7.First, we will calculate the annual depreciation of the new equipment. It will be:Annual depreciation = £390,000/5Annual depreciation = £78,000Now, we calculate the aftertax salvage value. The aftertax salvage value is the market price minus (or plus) the taxes on the sale of the equipment, so:Aftertax salvage value = MV + (BV – MV)t cVery often, the book value of the equipment is zero as it is in this case. If the book value is zero, the equation for the aftertax salvage value becomes:Aftertax salvage value = MV + (0 – MV)t cAftertax salvage value = MV(1 – t c)We will use this equation to find the aftertax salvage value since we know the book value is zero. So, the aftertax salvage value is:Aftertax salvage value = £60,000(1 – 0.34)Aftertax salvage value = £39,600Using the tax shield approach, we find the OCF for the project is:OCF = £120,000(1 – 0.34) + 0.34(£78,000)OCF = £105,720Now we can find the project NPV. Notice that we include the NWC in the initial cash outlay. The recovery of the NWC occurs in Year 5, along with the aftertax salvage value.NPV = –£390,000 – 28,000 + £105,720(PVIFA10%,5) + [(£39,600 + 28,000) / 1.15]NPV = £24,736.268.To find the BV at the end of four years, we need to find the accumulated depreciation for the firstfour years. We could calculate a table with the depreciation each year, but an easier way is to add the MACRS depreciation amounts for each of the first four years and multiply this percentage times the cost of the asset. We can then subtract this from the asset cost. Doing so, we get:BV4 = $9,300,000 – 9,300,000(0.2000 + 0.3200 + 0.1920 + 0.1150)BV4 = $1,608,900The asset is sold at a gain to book value, so this gain is taxable.Aftertax salvage value = $2,100,000 + ($1,608,900 – 2,100,000)(.40)Aftertax salvage value = $1,903,5609. We will begin by calculating the initial cash outlay, that is, the cash flow at Time 0. To undertake theproject, we will have to purchase the equipment and increase net working capital. So, the cash outlay today for the project will be:Equipment –€2,000,000NWC –100,000Total –€2,100,000Using the bottom-up approach to calculating the operating cash flow, we find the operating cash flow each year will be:Sales €1,200,000Costs 300,000Depreciation 500,000EBT €400,000Tax 140,000Net income €260,000The operating cash flow is:OCF = Net income + DepreciationOCF = €260,000 + 500,000OCF = €760,000To find the NPV of the project, we add the present value of the project cash flows. We must be sure to add back the net working capital at the end of the project life, since we are assuming the net working capital will be recovered. So, the project NPV is:NPV = –€2,100,000 + €760,000(PVIFA14%,4) + €100,000 / 1.144NPV = €173,629.3810.We will need the aftertax salvage value of the equipment to compute the EAC. Even though theequipment for each product has a different initial cost, both have the same salvage value. The aftertax salvage value for both is:Both cases: aftertax salvage value = $20,000(1 – 0.35) = $13,000To calculate the EAC, we first need the OCF and NPV of each option. The OCF and NPV for Techron I is:OCF = – $34,000(1 – 0.35) + 0.35($210,000/3) = $2,400NPV = –$210,000 + $2,400(PVIFA14%,3) + ($13,000/1.143) = –$195,653.45EAC = –$195,653.45 / (PVIFA14%,3) = –$84,274.10And the OCF and NPV for Techron II is:OCF = – $23,000(1 – 0.35) + 0.35($320,000/5) = $7,450NPV = –$320,000 + $7,450(PVIFA14%,5) + ($13,000/1.145) = –$287,671.75EAC = –$287,671.75 / (PVIFA14%,5) = –$83,794.05The two milling machines have unequal lives, so they can only be compared by expressing both on an equivalent annual basis, which is what the EAC method does. Thus, you prefer the Techron II because it has the lower (less negative) annual cost.。
Cha08 罗斯公司理财第九版原版书课后习题
Earlier in the chapter, we saw how bonds were rated based on their credit risk. What you will find if you start looking at bonds of different ratings is that lower-rated bonds have higher yields.We stated earlier in this chapter that a bond’s yield is calculated assuming that all the promised payments will be made. As a result, it is really a promised yield, and it may or may not be what you will earn. In particular, if the issuer defaults, your actual yield will be lower, probably much lower. This fact is particularly important when it comes to junk bonds. Thanks to a clever bit of marketing, such bonds are now commonly called high-yield bonds, which has a much nicer ring to it; but now you recognize that these are really high promised yield bonds.Next, recall that we discussed earlier how municipal bonds are free from most taxes and, as a result, have much lower yields than taxable bonds. Investors demand the extra yield on a taxable bond as compensation for the unfavorable tax treatment. This extra compensation is the taxability premium.Finally, bonds have varying degrees of liquidity. As we discussed earlier, there are an enormous number of bond issues, most of which do not trade on a regular basis. As a result, if you wanted to sell quickly, you would probably not get as good a price as you could otherwise. Investors prefer liquid assets to illiquid ones, so they demand a liquidity premium on top of all the other premiums we have discussed. As a result, all else being the same, less liquid bonds will have higher yields than more liquid bonds.ConclusionIf we combine everything we have discussed, we find that bond yields represent the combined effect of no fewer than six factors. The first is the real rate of interest. On top of the real rate are five premiums representing compensation for (1) expected future inflation, (2) interest rate risk, (3) default risk, (4) taxability, and (5) lack of liquidity. As a result, determining the appropriate yield on a bond requires careful analysis of each of these factors.Summary and ConclusionsThis chapter has explored bonds, bond yields, and interest rates. We saw that:1. Determining bond prices and yields is an application of basic discounted cash flow principles.2. Bond values move in the direction opposite that of interest rates, leading to potential gains orlosses for bond investors.3. Bonds are rated based on their default risk. Some bonds, such as Treasury bonds, have no riskof default, whereas so-called junk bonds have substantial default risk.4. Almost all bond trading is OTC, with little or no market transparency in many cases. As a result,bond price and volume information can be difficult to find for some types of bonds.5. Bond yields and interest rates reflect six different factors: the real interest rate and fivepremiums that investors demand as compensation for inflation, interest rate risk, default risk, taxability, and lack of liquidity.In closing, we note that bonds are a vital source of financing to governments and corporations of all types. Bond prices and yields are a rich subject, and our one chapter, necessarily, touches on only the most important concepts and ideas. There is a great deal more we could say, but, instead, we will move on to stocks in our next chapter.Concept Questions1. Treasury Bonds Is it true that a U.S. Treasury security is risk-free?2. Interest Rate Risk Which has greater interest rate risk, a 30-year Treasury bond or a 30-year21. Using Bond Quotes Suppose the following bond quote for IOU Corporation appears in thefinancial page of today’s newspaper. Assume the bond has a face value of $1,000 and the current date is April 15, 2010. What is the yield to maturity of the bond? What is the current yield?22. Finding the Maturity You’ve just found a 10 percent coupon bond on the market that sells forpar value. What is the maturity on this bond?CHALLENGE (Questions 23–30)23. Components of Bond Returns Bond P is a premium bond with a 9 percent coupon. Bond D isa 5 percent coupon bond currently selling at a discount. Both bonds make annual payments, havea YTM of 7 percent, and have five years to maturity. What is the current yield for Bond P? For BondD? If interest rates remain unchanged, what is the expected capital gains yield over the next year for Bond P? For Bond D? Explain your answers and the interrelationship among the various types of yields.24. Holding Period Yield The YTM on a bond is the interest rate you earn on your investment ifinterest rates don’t change. If you actually sell the bond before it matures, your realized return is known as the holding period yield (HPY).1. Suppose that today you buy a 9 percent annual coupon bond for $1,140. The bond has 10years to maturity. What rate of return do you expect to earn on your investment?2. Two years from now, the YTM on your bond has declined by 1 percent, and you decide tosell. What price will your bond sell for? What is the HPY on your investment? Compare this yield to the YTM when you first bought the bond. Why are they different?25. Valuing Bonds The Morgan Corporation has two different bonds currently outstanding. Bond Mhas a face value of $20,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $800 every six months over the subsequent eight years, and finally pays $1,000 every six months over the last six years. Bond N also has a face value of $20,000 and a maturity of20 years; it makes no coupon payments over the life of the bond. If the required return on boththese bonds is 8 percent compounded semiannually, what is the current price of Bond M? Of Bond N?26. R eal Cash Flows When Marilyn Monroe died, ex-husband Joe DiMaggio vowed to place freshflowers on her grave every Sunday as long as he lived. The week after she died in 1962, a bunch of fresh flowers that the former baseball player thought appropriate for the star cost about $8.Based on actuarial tables, “Joltin’ Joe” could expect to live for 30 years after the actress died.Assume that the EAR is 10.7 percent. Also, assume that the price of the flowers will increase at 3.5 percent per year, when expressed as an EAR. Assuming that each year has exactly 52 weeks, what is the present value of this commitment? Joe began purchasing flowers the week after Marilyn died.27. Real Cash Flows You are planning to save for retirement over the next 30 years. To save forretirement, you will invest $800 a month in a stock account in real dollars and $400 a month in a bond account in real dollars. The effective annual return of the stock account is expected to be 12 percent, and the bond account will earn 7 percent. When you retire, you will combine your money into an account with an 8 percent effective return. The inflation rate over this period is expected to be 4 percent. How much can you withdraw each month from your account in real terms assuminga 25-year withdrawal period? What is the nominal dollar amount of your last withdrawal?28. Real Cash Flows Paul Adams owns a health club in downtown Los Angeles. He charges hiscustomers an annual fee of $500 and has an existing customer base of 500. Paul plans to raise the annual fee by 6 percent every year and expects the club membership to grow at a constant rate of3 percent for the next five years. The overall expenses of running the health club are $75,000 ayear and are expected to grow at the inflation rate of 2 percent annually. After five years, Paul2. How many of the coupon bonds must East Coast Yachts issue to raise the $40 million? Howmany of the zeroes must it issue?3. In 20 years, what will be the principal repayment due if East Coast Yachts issues the couponbonds? What if it issues the zeroes?4. What are the company’s considerations in issuing a coupon bond compared to a zero couponbond?5. Suppose East Coast Yachts issues the coupon bonds with a make-whole call provision. Themake-whole call rate is the Treasury rate plus .40 percent. If East Coast calls the bonds in 7 years when the Treasury rate is 5.6 percent, what is the call price of the bond? What if it is 9.1 percent?6. Are investors really made whole with a make-whole call provision?7. After considering all the relevant factors, would you recommend a zero coupon issue or aregular coupon issue? Why? Would you recommend an ordinary call feature or a make-whole call feature? Why?。
罗斯-公司理财-英文练习题-附带答案-第九章
罗斯-公司理财-英文练习题-附带答案-第九章CHAPTER 9Risk Analysis, Real Options, and Capital Budgeting Multiple Choice Questions:I. DEFINITIONSSCENARIO ANALYSISb 1. An analysis of what happens to the estimate of the net present value when you examinea number of different likely situations is called _____ analysis.a. forecastingb. scenarioc. sensitivityd. simulatione. break-evenDifficulty level: EasySENSITIVITY ANALYSISc 2. An analysis of what happens to the estimate of net present value when only onevariable is changed is called _____ analysis.a. forecastingb. scenarioc. sensitivityd. simulatione. break-evenDifficulty level: EasySIMULATION ANALYSISd 3. An analysis which combines scenario analysis with sensitivity analysis is called _____analysis.a. forecastingb. scenarioc. sensitivityd. simulatione. break-evenDifficulty level: EasyBREAK-EVEN ANALYSISe 4. An analysis of the relationship between the sales volume and various measures ofprofitability is called _____ analysis.a. forecastingb. scenarioc. sensitivityd. simulatione. break-evenDifficulty level: EasyVARIABLE COSTSa 5. Variable costs:a. change in direct relationship to the quantity of output produced.b. are constant in the short-run regardless of the quantity of output produced.c. reflect the change in a variable when one more unit of output is produced.d. are subtracted from fixed costs to compute the contribution margin.e. form the basis that is used to determine the degree of operating leverage employed by afirm.Difficulty level: EasyFIXED COSTSb 6. Fixed costs:a. change as the quantity of output produced changes.b. are constant over the short-run regardless of the quantity of output produced.c. reflect the change in a variable when one more unit of output is produced.d. are subtracted from sales to compute the contribution margin.e. can be ignored in scenario analysis since they are constant over the life of a project.Difficulty level: EasyACCOUNTING BREAK-EVENc 7. The sales level that results in a project’s net income exactly equaling zero is called the_____ break-even.a. operationalb. leveragedc. accountingd. cashe. present valueDifficulty level: EasyPRESENT VALUE BREAK-EVENe 8. The sales level that results in a project’s net present value exactly equaling zero iscalled the _____ break-even.a. operationalb. leveragedc. accountingd. cashe. present valueDifficulty level: EasyII. CONCEPTSSCENARIO ANALYSISb 9. Conducting scenario analysis helps managers see the:a. impact of an individual variable on the outcome of a project.b. potential range of outcomes from a proposed project.c. changes in long-term debt over the course of a proposed project.d. possible range of market prices for their stock over the life of a project.e. allocation distribution of funds for capital projects under conditions of hard rationing.Difficulty level: EasySENSITIVITY ANALYSISb 10. Sensitivity analysis helps you determine the:a. range of possible outcomes given possible ranges for every variable.b. degree to which the net present value reacts to changes in a single variable.c. net present value given the best and the worst possible situations.d. degree to which a project is reliant upon the fixed costs.e. level of variable costs in relation to the fixed costs of a project.Difficulty level: EasySENSITIVITY ANALYSISc 11. As the degree of sensitivity of a project to a single variable rises, the:a. lower the forecasting risk of the project.b. smaller the range of possible outcomes given a pre-defined range of values for theinput.c. more attention management should place on accurately forecasting the future value ofthat variable.d. lower the maximum potential value of the project.e. lower the maximum potential loss of the project.Difficulty level: MediumSENSITIVITY ANALYSISc 12. Sensitivity analysis is conducted by:a. holding all variables at their base level and changing the required rate of returnassigned to a project.b. changing the value of two variables to determine their interdependency.c. changing the value of a single variable and computing the resulting change in thecurrent value of a project.d. assigning either the best or the worst possible value to each variable and comparing theresults to those achieved by the base case.e. managers after a project has been implemented to determine how each variable relatesto the level of output realized.Difficulty level: MediumSENSITIVITY ANALYSISd 13. To ascertain whether the accuracy of the variable cost estimate for a project will havemuch effect on the final outcome of the project, you should probably conduct _____analysis.a. leverageb. scenarioc. break-evend. sensitivitye. cash flowDifficulty level: EasySIMULATIONd 14. Simulation analysis is based on assigning a _____ and analyzing the results.a. narrow range of values to a single variableb. narrow range of values to multiple variables simultaneouslyc. wide range of values to a single variabled. wide range of values to multiple variables simultaneouslye. single value to each of the variablesDifficulty level: MediumSIMULATIONe 15. The type of analysis that is most dependent upon the use of a computer is _____analysis.a. scenariob. break-evenc. sensitivityd. degree of operating leveragee. simulationDifficulty level: EasyVARIABLE COSTSd 16. Which one of the following is most likely a variable cost?a. office rentb. property taxesc. property insuranced. direct labor costse. management salariesDifficulty level: EasyVARIABLE COSTSa 17. Which of the following statements concerning variable costs is (are) correct?I. Variable costs minus fixed costs equal marginal costs.II. Variable costs are equal to zero when production is equal to zero.III. An increase in variable costs increases the operating cash flow.a. II onlyb. III onlyc. I and III onlyd. II and III onlye. I and II onlyDifficulty level: MediumVARIABLE COSTSa 18. All else constant, as the variable cost per unit increases, the:a. contribution margin decreases.b. sensitivity to fixed costs decreases.c. degree of operating leverage decreases.d. operating cash flow increases.e. net profit increases.Difficulty level: MediumFIXED COSTSc 19. Fixed costs:I. are variable over long periods of time.II. must be paid even if production is halted.III. are generally affected by the amount of fixed assets owned by a firm.IV. per unit remain constant over a given range of production output.a. I and III onlyb. II and IV onlyc. I, II, and III onlyd. I, II, and IV onlye. I, II, III, and IVDifficulty level: MediumCONTRIBUTION MARGINc 20. The contribution margin must increase as:a. both the sales price and variable cost per unit increase.b. the fixed cost per unit declines.c. the gap between the sales price and the variable cost per unit widens.d. sales price per unit declines.e. the sales price minus the fixed cost per unit increases.Difficulty level: MediumACCOUNTING BREAK-EVENa 21. Which of the following statements are correct concerning the accounting break-evenpoint?I. The net income is equal to zero at the accounting break-even point.II. The net present value is equal to zero at the accounting break-even point.III. The quantity sold at the accounting break-even point is equal to the total fixed costs plus depreciation divided by the contribution margin.IV. The quantity sold at the accounting break-even point is equal to the total fixed costs divided by the contribution margin.a. I and III onlyb. I and IV onlyc. II and III onlyd. II and IV onlye. I, II, and IV onlyDifficulty level: MediumACCOUNTING BREAK-EVENb 22. All else constant, the accounting break-even level of sales will decrease when the:a. fixed costs increase.b. depreciation expense decreases.c. contribution margin decreases.d. variable costs per unit increase.e. selling price per unit decreases.Difficulty level: MediumPRESENT VALUE BREAK-EVENd 23. The point where a project produces a rate of return equal to the required return isknown as the:a. point of zero operating leverage.b. internal break-even point.c. accounting break-even point.d. present value break-even point.e. internal break-even point.Difficulty level: EasyPRESENT VALUE BREAK-EVENb 24. Which of the following statements are correct concerning the present value break-evenpoint of a project?I. The present value of the cash inflows equals the amount of the initial investment.II. The payback period of the project is equal to the life of the project.III. The operating cash flow is at a level that produces a net present value of zero.IV. The project never pays back on a discounted basis.a. I and II onlyb. I and III onlyc. II and IV onlyd. III and IV onlye. I, III, and IV onlyDifficulty level: MediumINVESTMENT TIMING DECISIONb 25. The investment timing decision relates to:a. how long the cash flows last once a project is implemented.b. the decision as to when a project should be started.c. how frequently the cash flows of a project occur.d. how frequently the interest on the debt incurred to finance a project is compounded.e. the decision to either finance a project over time or pay out the initial cost in cash.Difficulty level: MediumOPTION TO WAITe 26. The timing option that gives the option to wait:I. may be of minimal value if the project relates to a rapidly changing technology.II. is partially dependent upon the discount rate applied to the project being evaluated.III. is defined as the situation where operations are shut down for a period of time.IV. has a value equal to the net present value of the project if it is started today versus the net present value if it is started at some later date.a. I and III onlyb. II and IV onlyc. I and II onlyd. II, III, and IV onlye. I, II, and IV onlyDifficulty level: ChallengeOPTION TO EXPANDb 27. Last month you introduced a new product to the market. Consumer demand has beenoverwhelming and appears that strong demand will exist over the long-term. Given thissituation, management should consider the option to:a. suspend.b. expand.c. abandon.d. contract.e. withdraw.Difficulty level: EasyOPTION TO EXPANDc 28. Including the option to expand in your project analysis will tend to:a. extend the duration of a project but not affect the project’s net present value.b. incre ase the cash flows of a project but decrease the project’s net present value.c. increase the net present value of a project.d. decrease the net present value of a project.e. have no effect on either a project’s c ash flows or its net present value.Difficulty level: MediumSENSITIVITY AND SENARIO ANALYSISd 29. Theoretically, the NPV is the most appropriate method to determine the acceptabilityof a project. A false sense of security can be overwhelm the decision-maker when theprocedure is applied properly and the positive NPV resultsare accepted blindly.Sensitivity and scenario analysis aid in the process bya. changing the underlying assumptions on which the decision is based.b. highlights the areas where more and better data are needed.c. providing a picture of how an event can affect the calculations.d. All of the above.e. None of the above.Difficulty level: MediumDECSION TREEa 30. In order to make a decision with a decision treea. one starts farthest out in time to make the first decision.b. one must begin at time 0.c. any path can be taken to get to the end.d. any path can be taken to get back to the beginning.e. None of the above.Difficulty level: MediumDECISION TREEc 31. In a decision tree, the NPV to make the yes/no decision is dependent ona. only the cash flows from successful path.b. on the path where the probabilities add up to one.c. all cash flows and probabilities.d. only the cash flows and probabilities of the successful path.e. None of the above.Difficulty level: MediumDECISION TREEe 32. In a decision tree, caution should be used in analysis becausea. early stage decisions are probably riskier and should not likely use the same discountrate.b. if a negative NPV is actually occurring, management should opt out of the project andminimize their loss.c. decision trees are only used for planning, not actually daily management.d. Both A and C.e. Both A and B.Difficulty level: MediumSENSITIVITY ANALYSISd 33. Sensitivity analysis evaluates the NPV with respect toa. changes in the underlying assumptions.b. one variable changing while holding the others constant.c. different economic conditions.d. All of the above.e. None of the above.Difficulty level: MediumSENSITIVITY ANALYSISd 34. Sensitivity analysis provides information ona. whether the NPV should be trusted, it may provide a false sense of security if allNPVs are positive.b. the need for additional information as it tests each variablein isolation.c. the degree of difficulty in changing multiple variables together.d. Both A and B.e. Both A and C.Difficulty level: MediumFIXED COSTSb 35. Fixed production costs area. directly related to labor costs.b. measured as cost per unit of time.c. measured as cost per unit of output.d. dependent on the amount of goods or services produced.e. None of the above.Difficulty level: MediumVARIABLE COSTSd 36. Variable costsa. change as the quantity of output changes.b. are zero when production is zero.c. are exemplified by direct labor and raw materials.d. All of the above.e. None of the above.Difficulty level: EasySENSITIVITY ANALYSISb 37. An investigation of the degree to which NPV depends on assumptions made about anysingular critical variable is called a(n)a. operating analysis.b. sensitivity analysis.c. marginal benefit analysis.d. decision tree analysis.e. None of the above.Difficulty level: EasySENSITIVITY AND SCENARIOS ANALYSISb 38. Scenario analysis is different than sensitivity analysisa. as no economic forecasts are changed.b. as several variables are changed together.c. because scenario analysis deals with actual data versus sensitivity analysis which dealswith a forecast.d. because it is short and simple.e. because it is 'by the seat of the pants' technique.Difficulty level: MediumEQUIVALENT ANNUAL COSTc 39. In the present-value break-even the EAC is used toa. determine the opportunity cost of investment.b. allocate depreciation over the life of the project.c. allocate the initial investment at its opportunity cost over the life of the project.d. determine the contribution margin to fixed costs.e. None of the above.Difficulty level: MediumBREAK-EVENb 40. The present value break-even point is superior to the accounting break-even pointbecausea. present value break-even is more complicated to calculate.b. present value break-even covers the economic opportunity costs of the investment.c. present value break-even is the same as sensitivity analysis.d. present value break-even covers the fixed costs of production, which the accountingbreak-even does not.e. present value break-even covers the variable costs of production, which the accountingbreak-even does not.Difficulty level: EasyABANDONMENTd 41. The potential decision to abandon a project has option value becausea. abandonment can occur at any future point in time.b. a project may be worth more dead than alive.c. management is not locked into a negative outcome.d. All of the above.e. None of the above.Difficulty level: EasyTYPES OF BREAK-EVEN ANALYSISd 42. Which of the following are types of break-even analysis?a. present value break-evenb. accounting profit break-evenc. market value break-evend. Both A and B.e. Both A and C.Difficulty level: EasyMONTE CARLO SIMULATIONc 43. The approach that further attempts to model real word uncertainty by analyzingprojects the way one might analyze gambling strategies is calleda. gamblers approach.b. blackjack approach.c. Monte Carlo simulation.d. scenario analysis.e. sensitivity analysis.Difficulty level: MediumMONTE CARLO SIMULATIONc 44. Monte Carlo simulation isa. the most widely used by executives.b. a very simple formula.c. provides a more complete analysis that sensitivity or scenario.d. the oldest capital budgeting technique.e. None of the above.Difficulty level: EasyOPTIONS IN CAPITAL BUDGETINGd 45. Which of the following are hidden options in capital budgeting?a. option to expand.b. timing option.c. option to abandon.d. All of the above.e. None of the above.Difficulty level: EasyIII. PROBLEMSUse this information to answer questions 46 through 50.The Adept Co. is analyzing a proposed project. The company expects to sell 2,500units, give or take 10 percent. The expected variable cost per unit is $8 and the expected fixed costs are $12,500. Cost estimates are considered accurate within a plus or minus 5 percent range. The depreciation expense is $4,000. The sale price is estimated at $16 aunit, give or take 2 percent. The company bases their sensitivity analysis on the expected case scenario.SCENARIO ANALYSISd 46. What is the sales revenue under the optimistic case scenario?a. $40,000b. $43,120c. $44,000d. $44,880e. $48,400Difficulty level: MediumSCENARIO ANALYSISd 47. What is the contribution margin under the expected case scenario?a. $2.67b. $3.00c. $7.92d. $8.00e. $8.72Difficulty level: MediumSCENARIO ANALYSISc 48. What is the amount of the fixed cost per unit under the pessimistic case scenario?a. $4.55b. $5.00c. $5.83d. $6.02e. $6.55Difficulty level: MediumSENSITIVITY ANALYSISb 49. The company is conducting a sensitivity analysis on the sales price using a salesprice estimate of $17. Using this value, the earnings before interest and taxes will be:a. $4,000b. $6,000c. $8,500d. $10,000e. $18,500Difficulty level: MediumSENSITIVITY ANALYSISb 50. The company conducts a sensitivity analysis using a variable cost of $9. The totalvariable cost estimate will be:a. $21,375b. $22,500c. $23,625d. $24,125e. $24,750Difficulty level: MediumUse this information to answer questions 51 through 55.The Can-Do Co. is analyzing a proposed project. The company expects to sell 12,000units, give or take 4 percent. The expected variable cost per unit is $7 and the expectedfixed cost is $36,000. The fixed and variable cost estimates are considered accuratewithin a plus or minus 6 percent range. The depreciation expense is $30,000. The tax rate is 34 percent. The sale price is estimated at $14 a unit, give or take 5 percent. Thecompany bases their sensitivity analysis on the expected case scenario.SCENARIO ANALYSISa 51. What is the earnings before interest and taxes under the expected case scenario?a. $18,000b. $24,000c. $36,000d. $48,000e. $54,000Difficulty level: MediumSCENARIO ANALYSISc 52. What is the earnings before interest and taxes under anoptimistic case scenario?a. $22,694.40b. $24,854.40c. $37,497.60d. $52,694.40e. $67,947.60Difficulty level: ChallengeSCENARIO ANALYSISb 53. What is the earnings before interest and taxes under the pessimistic case scenario?b. -$422.40c. -$278.78d. $3,554.50e. $5,385.60Difficulty level: ChallengeSENSITIVITY ANALYSISd 54. What is the operating cash flow for a sensitivity analysis using total fixed costs of$32,000?a. $14,520b. $16,520c. $22,000d. $44,520e. $52,000Difficulty level: MediumSENSITIVITY ANALYSISd 55. What is the contribution margin for a sensitivity analysis using a variable cost per unitof $8?a. $3b. $4c. $5d. $6e. $7Difficulty level: MediumVARIABLE COSTc 56. A firm is reviewing a project with labor cost of $8.90 per unit, raw materials cost of$21.63 a unit, and fixed costs of $8,000 a month. Sales are projected at 10,000 unitsover the three-month life of the project. What are the total variable costs of the project?a. $216,300b. $297,300c. $305,300d. $313,300e. $329,300Difficulty level: MediumVARIABLE COSTd 57. A project has earnings before interest and taxes of $5,750, fixed costs of $50,000, aselling price of $13 a unit, and a sales quantity of 11,500 units. Depreciation is $7,500.What is the variable cost per unit?a. $6.75c. $7.25d. $7.50e. $7.75Difficulty level: MediumFIXED COSTb 58. At a production level of 5,600 units a project has total costs of $89,000. The variablecost per unit is $11.20. What is the amount of the total fixed costs?a. $24,126b. $26,280c. $27,090d. $27,820e. $28,626Difficulty level: MediumFIXED COSTe 59. At a production level of 6,000 units a project has total costs of $120,000. The variablecost per unit is $14.50. What is the amount of the total fixed costs?a. $25,165b. $28,200c. $30,570d. $32,000e. $33,000Difficulty level: MediumCONTRIBUTION MARGINc 60. Wilson’s Meats has computed their fixed costs to be $.60 for every pound of meatthey sell given an average daily sales level of 500 pounds. They charge $3.89 perpound of top-grade ground beef. The variable cost perpound is $2.99. What is thecontribution margin per pound of ground beef sold?a. $.30b. $.60c. $.90d. $2.99e. $3.89Difficulty level: MediumCONTRIBUTION MARGINe 61. Ralph and Emma’s is considering a project with total sales of $17,500, total variablecosts of $9,800, total fixed costs of $3,500, and estimated production of 400 units. Thedepreciation expense is $2,400 a year. What is the contribution margin per unit?a. $4.50b. $10.50d. $19.09e. $19.25Difficulty level: MediumACCOUNTING BREAK-EVENa 62. You are considering a new project. The project has projected depreciation of $720,fixed costs of $6,000, and total sales of $11,760. The variable cost per unit is$4.20. What is the accounting break-even level of production?a. 1,200 unitsb. 1,334 unitsc. 1,372 unitsd. 1,889 unitse. 1,910 unitsDifficulty level: MediumACCOUNTING BREAK-EVENb 63. The accounting break-even production quantity for a project is 5,425 units. The fixedcosts are $31,600 and the contribution margin is $6. What is the projecteddepreciation expense?a. $700b. $950c. $1,025d. $1,053e. $1,100Difficulty level: MediumACCOUNTING BREAK-EVENd 64. A project has an accounting break-even point of 2,000 units. The fixed costs are$4,200 and the depreciation expense is $400. The projected variable cost per unit is$23.10. What is the projected sales price?a. $20.80b. $21.00c. $21.20d. $25.40e. $25.60Difficulty level: MediumACCOUNTING BREAK-EVENa 65. A proposed project has fixed costs of $3,600,depreciation expense of $1,500, and asales quantity of 1,300 units. What is the contribution margin if the projected level ofsales is the accounting break-even point?a. $3.92c. $4.50d. $4.80e. $5.00Difficulty level: MediumPRESENT VALUE BREAK-EVENc 66. A project has a contribution margin of $5, projected fixed costs of $12,000, projectedvariable cost per unit of $12, and a projected present value break-even point of 5,000units. What is the operating cash flow at this level of output?a. $1,000b. $12,000c. $13,000d. $68,000e. $73,000Difficulty level: MediumPRESENT VALUE BREAK-EVENa 67. Thompson & Son have been busy analyzing a new product. They have determined thatan operating cash flow of $16,700 will result in a zero net present value, which is acompany requirement for project acceptance. The fixed costs are $12,378 and thecontribution margin is $6.20. The company feels that they can realistically capture10 percent of the 50,000 unit market for this product. Should the company develop thenew product? Why or why not?a. yes; because 5,000 units of sales exceeds the quantity required for a zero net presentvalueb. yes; because the internal break-even point is less than 5,000 unitsc. no; because the firm can not generate sufficient sales to obtain at least a zero netpresent valued. no; because the project has an expected internal rate of return of negative 100percente. no; because the project will not pay back on a discounted basisDifficulty level: ChallengePRESENT VALUE BREAK-EVENe 68. Kurt Neal and Son is considering a project with a discounted payback just equal to theproject’s life. The projections include a sales price of $11, variable cost per unit of$8.50, and fixed costs of $4,500. The operating cash flow is $6,200. What is the break-even quantity?a. 1,800 unitsb. 2,480 unitsc. 3,057 unitsd. 3,750 unitse. 4,280 unitsDECISION TREE NET PRESENT VALUEb 69. At stage 2 of the decision tree it shows that if a project is successful, the payoff will be$53,000 with a 2/3 chance of occurrence. There is also the 1/3 chance of a $-24,000payoff. The cost of getting to stage 2 (1 year out) is $44,000. The cost of capital is15%. What is the NPV of the project at stage 1?a. $-13,275b. $-20,232c. $ 2,087d. $ 7,536e. Can not be calculated without the exact timing of future cash flows.Difficulty level: MediumUse the following to answer questions 70-71:The Quick-Start Company has the following pattern of potential cash flows with their planned investment in a new cold weather starting system for fuel injected cars.DECISION TREEa 70. If the company has a discount rate of 17%, what is the value closest to time 1 netpresent value?a. $ 48.6 millionb. $ 80.9 millionc. $108.2 milliond. $181.4 millione. None of the above.DECISION TREEb 71. If the company has a discount rate of 17%, should they decide to invest?a. yes, NPV = $ 2.2 millionb. yes, NPV = $ 21.6 millionc. no, NPV = $-1.9 milliond. yes, NPV = $ 8.6 millione. No, since more than one branch is NPV = 0 or negative you must reject.Difficulty level: ChallengeACCOUNTING BREAK-EVENe 72. The Mini-Max Company has the following cost information on their new prospectiveproject. Calculate the accounting break-even point.Initial investment: $700。
公司理财第九版罗斯课后案例答案 Case Solutions Corporate Finance
公司理财第九版罗斯课后案例答案 Case Solutions CorporateFinance1. 案例一：公司资金需求分析问题：一家公司需要资金支持其新项目。
通过分析现金流量，推断该公司是否需要向外部借款或筹集其他资金。
解答：为了确定公司是否需要外部资金，我们需要分析公司的现金流量状况。
首先，我们需要计算公司的净现金流量（净收入加上非现金项目）。
然后，我们需要将净现金流量与项目的投资现金流量进行对比。
假设公司预计在项目开始时投资100万美元，并在项目运营期为5年。
预计该项目每年将产生50万美元的净现金流量。
现在，我们需要进行以下计算：净现金流量 = 年度现金流量 - 年度投资现金流量年度投资现金流量 = 100万美元年度现金流量 = 50万美元净现金流量 = 50万美元 - 100万美元 = -50万美元根据计算结果，公司的净现金流量为负数（即净现金流出），意味着公司每年都会亏损50万美元。
因此，公司需要从外部筹集资金以支持项目的运营。
2. 案例二：公司股权融资问题：一家公司正在考虑通过股权融资来筹集资金。
根据公司的财务数据和资本结构分析，我们需要确定公司最佳的股权融资方案。
解答：为了确定最佳的股权融资方案，我们需要参考公司的财务数据和资本结构分析。
首先，我们需要计算公司的资本结构比例，即股本占总资本的比例。
然后，我们将不同的股权融资方案与资本结构比例进行对比，选择最佳的方案。
假设公司当前的资本结构比例为60%的股本和40%的债务，在当前的资本结构下，公司的加权平均资本成本（WACC）为10%。
现在，我们需要进行以下计算：•方案一：以新股发行筹集1000万美元，并将其用于项目投资。
在这种方案下，公司的资本结构比例将发生变化。
假设公司的股本增加至80%，债务比例减少至20%。
根据资本结构比例的变化，WACC也将发生变化。
新的WACC可以通过以下公式计算得出：新的WACC = (股本比例 * 股本成本) + (债务比例 * 债务成本)假设公司的股本成本为12%，债务成本为8%：新的WACC = (0.8 * 12%) + (0.2 * 8%) = 9.6%•方案二：以新股发行筹集5000万美元，并将其用于项目投资。
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5-8
5.4 The Internal Rate of Return
IRR: the discount rate that sets NPV to zero Minimum Acceptance Criteria:
Ranking Criteria:
Accept if the IRR exceeds the required return Select alternative with the highest IRR
Independent Projects: accepting or rejecting one project does not affect the decision of the other projects.
Must exceed a MINIMUM acceptance criteria
5-2
5.1 Why Use Net Present Value?
Accepting positive NPV projects benefits shareholders.
NPV
uses cash flows NPV uses all the cash flows of the project NPV discounts the cash flows properly
Mutually Exclusive Projects: only ONE of several potential projects can be chosen, e.g., acquiring an accounting system.
RANK all alternatives, and select the best one.
Advantages:
Easy to understand Biased toward liquidity
5-7
5.3 The Discounted Payback Period
How long does it take the project to “pay back” its initial investment, taking the time value of money into account? Decision rule: Accept the project if it pays back on a discounted basis within the specified time. By the time you have discounted the cash flows, you might as well calculate the NPV.
Reinvestment assumption:
All future cash flows are assumed to be reinvested at the IRR
Байду номын сангаас
5-9
Internal Rate of Return (IRR)
Disadvantages:
Does not distinguish between investing and borrowing IRR may not exist, or there may be multiple IRRs Problems with mutually exclusive investments
$50 $100 $150 NPV 0 200 2 (1 IRR ) (1 IRR ) (1 IRR )3
5-11
NPV Payoff Profile
If we graph NPV versus the discount rate, we can see the IRR as the x-axis intercept.
5-13
5.5 Problems with IRR
Multiple IRRs Are We Borrowing or Lending The Scale Problem The Timing Problem
5-14
Mutually Exclusive vs. Independent
5-5
5.2 The Payback Period Method
How long does it take the project to “pay back” its initial investment? Payback Period = number of years to recover initial costs Minimum Acceptance Criteria:
Chapter 5
Net Present Value and Other Investment Rules
McGraw-Hill/Irwin
Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.
Key Concepts and Skills
NPV
$50.00 $0.00 -1% ($50.00) ($100.00) Discount rate
IRR = 19.44%
9% 19% 29% 39%
5-12
Calculating IRR with Spreadsheets
You start with the same cash flows as you did for the NPV. You use the IRR function:
You first enter your range of cash flows, beginning with the initial cash flow. You can enter a guess, but it is not necessary. The default format is a whole percent – you will normally want to increase the decimal places to at least two.
5-3
The Net Present Value (NPV) Rule
Net Present Value (NPV) = Total PV of future CF’s + Initial Investment Estimating NPV:
1. Estimate future cash flows: how much? and when? 2. Estimate discount rate 3. Estimate initial costs
5-1
Chapter Outline
5.1 Why Use Net Present Value? 5.2 The Payback Period Method 5.3 The Discounted Payback Period Method 5.4 The Internal Rate of Return 5.5 Problems with the IRR Approach 5.6 The Profitability Index 5.7 The Practice of Capital Budgeting
5-17
The Scale Problem
Would you rather make 100% or 50% on your investments? What if the 100% return is on a $1 investment, while the 50% return is on a $1,000 investment?
0% 4% 8% 12% 16% 20% 24% 28% 32% 36% 40% 44% $100.00 $73.88 $51.11 $31.13 $13.52 ($2.08) ($15.97) ($28.38) ($39.51) ($49.54) ($58.60) ($66.82)
$150.00 $100.00
100% = IRR2
200%
Discount rate
0% = IRR1
5-16
Modified IRR
Calculate the net present value of all cash outflows using the borrowing rate. Calculate the net future value of all cash inflows using the investing rate. Find the rate of return that equates these values. Benefits: single answer and specific rates for borrowing and reinvestment
Be able to compute payback and discounted payback and understand their shortcomings Be able to compute the internal rate of return and profitability index, understanding the strengths and weaknesses of both approaches Be able to compute net present value and understand why it is the best decision criterion
Minimum Acceptance Criteria: Accept if NPV > 0 Ranking Criteria: Choose the highest NPV