Chapter 18 &19
公司金融课后题答案CHAPTER 18
CHAPTER 18VALUATION AND CAPITAL BUDGETING FOR THE LEVERED FIRMAnswers to Concepts Review and Critical Thinking Questions1.APV is equal to the NPV of the project (i.e. the value of the project for an unlevered firm)plus the NPV of financing side effects.2. The WACC is based on a target debt level while the APV is based on the amount ofdebt.3.FTE uses levered cash flow and other methods use unlevered cash flow.4.The WACC method does not explicitly include the interest cash flows, but it doesimplicitly include the interest cost in the WACC. If he insists that the interest payments are explicitly shown, you should use the FTE method.5. You can estimate the unlevered beta from a levered beta. The unlevered beta is the betaof the assets of the firm; as such, it is a measure of the business risk. Note that the unlevered beta will always be lower than the levered beta (assuming the betas are positive). The difference is due to the leverage of the company. Thus, the second risk factor measured by a levered beta is the financial risk of the company.Solutions to Questions and ProblemsNOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.Basic1. a.The maximum price that the company should be willing to pay for the fleet of carswith all-equity funding is the price that makes the NPV of the transaction equal tozero. The NPV equation for the project is:NPV = –Purchase Price + PV[(1 – t C )(EBTD)] + PV(Depreciation Tax Shield)If we let P equal the purchase price of the fleet, then the NPV is:NPV = –P + (1 – .35)($140,000)PVIFA13%,5 + (.35)(P/5)PVIFA13%,5Setting the NPV equal to zero and solving for the purchase price, we find:0 = –P + (1 – .35)($140,000)PVIFA13%,5 + (.35)(P/5)PVIFA13%,5P = $320,068.04 + (P)(0.35/5)PVIFA13%,5P = $320,068.04 + .2462P.7538P = $320,068.04P = $424,609.54b.The adjusted present value (APV) of a project equals the net present value of theproject if it were funded completely by equity plus the net present value of any financing side effects. In this case, the NPV of financing side effects equals the after-tax present value of the cash flows resulting from the firm’s debt, so:APV = NPV(All-Equity) + NPV(Financing Side Effects)So, the NPV of each part of the APV equation is:NPV(All-Equity)NPV = –Purchase Price + PV[(1 – t C )(EBTD)] + PV(Depreciation Tax Shield)The company paid $395,000 for the fleet of cars. Because this fleet will be fullydepreciated over five years using the straight-line method, annual depreciationexpense equals:Depreciation = $395,000/5Depreciation = $79,000So, the NPV of an all-equity project is:NPV = –$395,000 + (1 – 0.35)($140,000)PVIFA13%,5 + (0.35)($79,000)PVIFA13%,5 NPV = $22,319.49NPV(Financing Side Effects)The net present value of financing side effects equals the after-tax present value of cash flows resulting from the firm’s debt, so:NPV = Proceeds – Aftertax PV(Interest Payments) – PV(Principal Payments)Given a known level of debt, debt cash flows should be discounted at the pre-tax cost of debt R B. So, the NPV of the financing side effects are:NPV = $260,000 – (1 – 0.35)(0.08)($260,000)PVIFA8%,5– [$260,000/(1.08)5]NPV = $29,066.93So, the APV of the project is:APV = NPV(All-Equity) + NPV(Financing Side Effects) APV = $22,319.49 + 29,066.93APV = $51,386.422.The adjusted present value (APV) of a project equals the net present value of the projectif it were funded completely by equity plus the net present value of any financing side effects. In this case, the NPV of financing side effects equals the after-tax present value of the cash flows resulting from the firm’s debt, so:APV = NPV(All-Equity) + NPV(Financing Side Effects)So, the NPV of each part of the APV equation is:NPV(All-Equity)NPV = –Purchase Price + PV[(1 – t C )(EBTD)] + PV(Depreciation Tax Shield)Since the initial investment of $1.9 million will be fully depreciated over four yearsusing the straight-line method, annual depreciation expense is:Depreciation = $1,900,000/4Depreciation = $475,000NPV = –$1,900,000 + (1 – 0.30)($685,000)PVIFA9.5%,4 + (0.30)($475,000)PVIFA13%,4 NPV (All-equity) = – $49,878.84NPV(Financing Side Effects)The net present value of financing side effects equals the aftertax present value of cash flows resulting from the firm’s debt. So, the NPV of the financing side effects are:NPV = Proceeds(Net of flotation) – Aftertax PV(Interest Payments) – PV(PrincipalPayments)+ PV(Flotation Cost Tax Shield)Given a known level of debt, debt cash flows should be discounted at the pre-tax cost of debt, R B. Since the flotation costs will be amortized over the life of the loan, the annual flotation costs that will be expensed each year are:Annual flotation expense = $28,000/4Annual flotation expense = $7,000NPV = ($1,900,000 – 28,000) – (1 – 0.30)(0.095)($1,900,000)PVIFA9.5%,4–$1,900,000/(1.095)4+ 0.30($7,000) PVIFA9.5%,4NPV = $152,252.06So, the APV of the project is:APV = NPV(All-Equity) + NPV(Financing Side Effects) APV = –$49,878.84 + 152,252.06APV = $102,373.233. a.In order to value a firm’s equity using the flow-to-equity approach, discount thecash flows available to equity holders at the cost of the firm’s levered equity. Thecash flows to equity holders will be the firm’s net income. Remembering that thecompany has three stores, we find:Sales $3,600,000COGS 1,530,000G & A costs 1,020,000Interest 102,000EBT $948,000Taxes 379,200NISince this cash flow will remain the same forever, the present value of cash flowsavailable to the firm’s equity holders is a perpetuity. We can discount at the leveredcost of equity, so, the value of the company’s equity is:PV(Flow-to-equity) = $568,800 / 0.19PV(Flow-to-equity) = $2,993,684.21b.The value of a firm is equal to the sum of the market values of its debt and equity, or:V L = B + SWe calculated the value of the company’s equity in part a, so now we need tocalculate the value of debt. The company has a debt-to-equity ratio of 0.40, whichcan be written algebraically as:B / S = 0.40We can substitute the value of equity and solve for the value of debt, doing so, wefind:B / $2,993,684.21 = 0.40B = $1,197,473.68So, the value of the company is:V = $2,993,684.21 + 1,197,473.68V = $4,191,157.894. a.I n order to determine the cost of the firm’s debt, we need to find the yield tomaturity on its current bonds. With semiannual coupon payments, the yield tomaturity in the company’s bonds is:$975 = $40(PVIFA R%,40) + $1,000(PVIF R%,40)R = .0413 or 4.13%Since the coupon payments are semiannual, the YTM on the bonds is:YTM = 4.13%× 2YTM = 8.26%b.We can use the Capital Asset Pricing Model to find the return on unlevered equity.According to the Capital Asset Pricing Model:R0 = R F+ βUnlevered(R M– R F)R0 = 5% + 1.1(12% – 5%)R0 = 12.70%Now we can find the cost of levered equity. According to Modigliani-MillerProposition II with corporate taxesR S = R0 + (B/S)(R0– R B)(1 – t C)R S = .1270 + (.40)(.1270 – .0826)(1 – .34)R S = .1387 or 13.87%c.In a world with corporate taxes, a firm’s weighted average cost of capital is equalto:R WACC = [B / (B + S)](1 – t C)R B + [S / (B + S)]R SThe problem does not provide either the debt-value ratio or equity-value ratio.H owever, the firm’s debt-equity ratio of is:B/S = 0.40Solving for B:B = 0.4SSubstituting this in the debt-value ratio, we get:B/V = .4S / (.4S + S)B/V = .4 / 1.4B/V = .29And the equity-value ratio is one minus the debt-value ratio, or:S/V = 1 – .29S/V = .71So, the WACC for the company is:R WACC = .29(1 – .34)(.0826) + .71(.1387) R WACC = .1147 or 11.47%5. a.The equity beta of a firm financed entirely by equity is equal to its unlevered beta.Since each firm has an unlevered beta of 1.25, we can find the equity beta for each.Doing so, we find:North PoleβEquity = [1 + (1 – t C)(B/S)]βUnleveredβEquity = [1 + (1 – .35)($2,900,000/$3,800,000](1.25)βEquity = 1.87South PoleβEquity = [1 + (1 – t C)(B/S)]βUnleveredβEquity = [1 + (1 – .35)($3,800,000/$2,900,000](1.25)βEquity = 2.31b.We can use the Capital Asset Pricing Model to find the required return on eachfirm’s equity. Doing so, we find:North Pole:R S = R F+ βEquity(R M– R F)R S = 5.30% + 1.87(12.40% – 5.30%)R S = 18.58%South Pole:R S = R F+ βEquity(R M– R F)R S = 5.30% + 2.31(12.40% – 5.30%)R S = 21.73%6. a.If flotation costs are not taken into account, the net present value of a loan equals:NPV Loan = Gross Proceeds – Aftertax present value of interest and principalpaymentsNPV Loan = $5,350,000 – .08($5,350,000)(1 – .40)PVIFA8%,10– $5,350,000/1.0810NPV Loan = $1,148,765.94b.The flotation costs of the loan will be:Flotation costs = $5,350,000(.0125)Flotation costs = $66,875So, the annual flotation expense will be:Annual flotation expense = $66,875 / 10 Annual flotation expense = $6,687.50If flotation costs are taken into account, the net present value of a loan equals:NPV Loan = Proceeds net of flotation costs – Aftertax present value of interest andprincipalpayments + Present value of the flotation cost tax shieldNPV Loan = ($5,350,000 – 66,875) – .08($5,350,000)(1 – .40)(PVIFA8%,10)– $5,350,000/1.0810 + $6,687.50(.40)(PVIFA8%,10)NPV Loan = $1,099,840.407.First we need to find the aftertax value of the revenues minus expenses. The aftertaxvalue is:Aftertax revenue = $3,800,000(1 – .40)Aftertax revenue = $2,280,000Next, we need to find the depreciation tax shield. The depreciation tax shield each year is:Depreciation tax shield = Depreciation(t C)Depreciation tax shield = ($11,400,000 / 6)(.40)Depreciation tax shield = $760,000Now we can find the NPV of the project, which is:NPV = Initial cost + PV of depreciation tax shield + PV of aftertax revenueTo find the present value of the depreciation tax shield, we should discount at the risk-free rate, and we need to discount the aftertax revenues at the cost of equity, so:NPV = –$11,400,000 + $760,000(PVIFA6%,6) + $2,280,000(PVIFA14%,6)NPV = $1,203,328.438.Whether the company issues stock or issues equity to finance the project is irrelevant.The company’s optimal capital structure determines the WACC. In a world wi th corporate taxes, a firm’s weighted average cost of capital equals:R WACC = [B / (B + S)](1 – t C)R B + [S / (B + S)]R SR WACC = .80(1 – .34)(.072) + .20(.1140)R WACC = .0608 or 6.08%Now we can use the weighted average cost of capital to discount NEC’s unlevered cash flows. Doing so, we find the NPV of the project is:NPV = –$40,000,000 + $2,600,000 / 0.0608NPV = $2,751,907.399. a.The company has a capital structure with three parts: long-term debt, short-termdebt, and equity. Since interest payments on both long-term and short-term debt aretax-deductible, multiply the pretax costs by (1 – t C) to determine the aftertax coststo be used in the weighted average cost of capital calculation. The WACC using thebook value weights is:R WACC = (w STD)(R STD)(1 – t C) + (w LTD)(R LTD)(1 – t C) + (w Equity)(R Equity)R WACC = ($3 / $19)(.035)(1 – .35) + ($10 / $19)(.068)(1 – .35) + ($6 / $19)(.145)R WACC = 0.0726 or 7.26%ing the market value weights, the company’s WACC is:R WACC = (w STD)(R STD)(1 – t C) + (w LTD)(R LTD)(1 – t C) + (w Equity)(R Equity)R WACC = ($3 / $40)(.035)(1 – .35) + ($11 / $40)(.068)(1 – .35) + ($26 / $40)(.145) R WACC = 0.1081 or 10.81%ing the target debt-equity ratio, the target debt-value ratio for the company is:B/S = 0.60B = 0.6SSubstituting this in the debt-value ratio, we get:B/V = .6S / (.6S + S)B/V = .6 / 1.6B/V = .375And the equity-value ratio is one minus the debt-value ratio, or:S/V = 1 – .375S/V = .625We can use the ratio of short-term debt to long-term debt in a similar manner to find the short-term debt to total debt and long-term debt to total debt. Using the short-term debt to long-term debt ratio, we get:STD/LTD = 0.20STD = 0.2LTDSubstituting this in the short-term debt to total debt ratio, we get:STD/B = .2LTD / (.2LTD + LTD)STD/B = .2 / 1.2STD/B = .167And the long-term debt to total debt ratio is one minus the short-term debt to total debt ratio, or:LTD/B = 1 – .167LTD/B = .833Now we can find the short-term debt to value ratio and long-term debt to value ratio by multiplying the respective ratio by the debt-value ratio. So:STD/V = (STD/B)(B/V) STD/V = .167(.375) STD/V = .063And the long-term debt to value ratio is:LTD/V = (LTD/B)(B/V)LTD/V = .833(.375)LTD/V = .313So, using the target capital structure weights, the company’s WACC is:R WACC = (w STD)(R STD)(1 – t C) + (w LTD)(R LTD)(1 – t C) + (w Equity)(R Equity)R WACC = (.06)(.035)(1 – .35) + (.31)(.068)(1 – .35) + (.625)(.145)R WACC = 0.1059 or 10.59%d.The differences in the WACCs are due to the different weighting schemes. Thecompany’s WACC will most closely resemble the WACC calculated using targetweights since future projects will be financed at the target ratio. Therefore, theWACC computed with target weights should be used for project evaluation.Intermediate10.The adjusted present value of a project equals the net present value of the project underall-equity financing plus the net present value of any financing side effects. In the joint venture’s case, the NPV of financing side effects equals the aftertax present value of cash flows resulting from the firms’ debt. So, the APV is:APV = NPV(All-Equity) + NPV(Financing Side Effects)The NPV for an all-equity firm is:NPV(All-Equity)NPV = –Initial Investment + PV[(1 – t C)(EBITD)] + PV(Depreciation Tax Shield)Since the initial investment will be fully depreciated over five years using the straight-line method, annual depreciation expense is:Annual depreciation = $30,000,000/5Annual depreciation = $6,000,000NPV = –$30,000,000 + (1 – 0.35)($3,800,000)PVIFA5.13%,20 +(0.35)($6,000,000)PVIFA5,13%,20NPV = –$5,262,677.95NPV(Financing Side Effects)The NPV of financing side effects equals the after-tax present value of cash flows resulting from the firm’s debt. The coupon rate on the debt is relevant to determine the interest payments, but the resulting cash flows should still be discounted at the pretax cost of debt. So, the NPV of the financing effects is:NPV = Proceeds – Aftertax PV(Interest Payments) – PV(Principal Repayments)NPV = $18,000,000 – (1 – 0.35)(0.05)($18,000,000)PVIFA8.5%,15– $18,000,000/1.08515 NPV = $7,847,503.56So, the APV of the project is:APV = NPV(All-Equity) + NPV(Financing Side Effects)APV = –$5,262,677.95 + $7,847,503.56APV = $2,584,825.6111.If the company had to issue debt under the terms it would normally receive, the interestrate on the debt would increase to the company’s normal cost of debt. The NPV of an all-equity project would remain unchanged, but the NPV of the financing side effects would change. The NPV of the financing side effects would be:NPV = Proceeds – Aftertax PV(Interest Payments) – PV(Principal Repayments)NPV = $18,000,000 – (1 – 0.35)(0.085)($18,000,000)PVIFA8.5%,15–$18,000,000/((1.085)15NPV = $4,446,918.69Using the NPV of an all-equity project from the previous problem, the new APV of the project would be:APV = NPV(All-Equity) + NPV(Financing Side Effects)APV = –$5,262,677.95 + $4,446,918.69APV = –$815,759.27The gain to the company from issuing subsidized debt is the difference between the two APVs, so:Gain from subsidized debt = $2,584,825.61 – (–815,759.27)Gain from subsidized debt = $3,400,584.88Most of the value of the project is in the form of the subsidized interest rate on the debt issue.12.The adjusted present value of a project equals the net present value of the project underall-equity financing plus the net present value of any financing side effects. First, we need to calculate the unlevered cost of equity. According to Modigliani-Miller Proposition II with corporate taxes:R S = R0 + (B/S)(R0– R B)(1 – t C).16 = R0 + (0.50)(R0– 0.09)(1 – 0.40)R0 = 0.1438 or 14.38%Now we can find the NPV of an all-equity project, which is:NPV = PV(Unlevered Cash Flows)NPV = –$21,000,000 + $6,900,000/1.1438 + $11,000,000/(1.1438)2 +$9,500,000/(1.1438)3NPV = –$212,638.89Next, we need to find the net present value of financing side effects. This is equal the aftertax present value of cash flows resulting from the firm’s debt. So:NPV = Proceeds – Aftertax PV(Interest Payments) – PV(Principal Payments)Each year, an equal principal payment will be made, which will reduce the interest accrued during the year. Given a known level of debt, debt cash flows should be discounted at the pre-tax cost of debt, so the NPV of the financing effects are:NPV = $7,000,000 – (1 – .40)(.09)($7,000,000) / (1.09) – $2,333,333.33/(1.09)– (1 – .40)(.09)($4,666,666.67)/(1.09)2– $2,333,333.33/(1.09)2– (1 – .40)(.09)($2,333,333.33)/(1.09)3– $2,333,333.33/(1.09)3 NPV = $437,458.31So, the APV of project is:APV = NPV(All-equity) + NPV(Financing side effects)APV = –$212,638.89 + 437,458.31APV = $224,819.4213. a.To calculate the NPV of the project, we first need to find the company’s WACC. Ina world with corporate taxes, a firm’s weighted average cost of ca pital equals:R WACC = [B / (B + S)](1 – t C)R B + [S / (B + S)]R SThe market value of the company’s equity is:Market value of equity = 6,000,000($20)Market value of equity = $120,000,000So, the debt-value ratio and equity-value ratio are:Debt-value = $35,000,000 / ($35,000,000 + 120,000,000)Debt-value = .2258Equity-value = $120,000,000 / ($35,000,000 + 120,000,000)Equity-value = .7742Since the CEO believes its current capital structure is optimal, these values can beused as the target weights in the firm’s weighted average cost of capital calculation.The yield to maturity of the company’s debt is its pretax cost of debt. To find thecompany’s cost of equity, we need to calculate the stock beta. The stock beta can becalculated as:β = σS,M / σ2Mβ = .036 / .202β = 0.90Now we can use the Capital Asset Pricing Model to determine the cost of equity. The Capital Asset Pricing Model is:R S = R F+ β(R M– R F)R S = 6% + 0.90(7.50%)R S = 12.75%Now, we can calculate the company’s WACC, which is:R WACC = [B / (B + S)](1 – t C)R B + [S / (B + S)]R SR WACC = .2258(1 – .35)(.08) + .7742(.1275)R WACC = .1105 or 11.05%Finally, we can use the WACC to discount the unlevered cash flows, which givesus an NPV of:NPV = –$45,000,000 + $13,500,000(PVIFA11.05%,5)NPV = $4,837,978.59b.The weighted average cost of capital used in part a will not change if the firmchooses to fund the project entirely with debt. The weighted average cost of capitalis based on optimal capital structure weights. Since the current capital structure isoptimal, all-debt funding for the project simply implies that the firm will have touse more equity in the future to bring the capital structure back towards the target.Challenge14. a.The company is currently an all-equity firm, so the value as an all-equity firmequals the present value of aftertax cash flows, discounted at the cost of the firm’sunlevered cost of equity. So, the current value of the company is:V U = [(Pretax earnings)(1 – t C)] / R0V U = [($28,000,000)(1 – .35)] / .20V U = $91,000,000The price per share is the total value of the company divided by the sharesoutstanding, or:Price per share = $91,000,000 / 1,500,000Price per share = $60.67b.The adjusted present value of a firm equals its value under all-equity financing plusthe net present value of any financing side effects. In this case, the NPV offinancing side effects equals the aftertax present value of cash flows resulting fromthe firm’s debt. Given a known level of debt, debt cash flows can be discounted atthe pretax cost of debt, so the NPV of the financing effects are:NPV = Proceeds – Aftertax PV(Interest Payments)NPV = $35,000,000 – (1 – .35)(.09)($35,000,000) / .09NPV = $12,250,000So, the value of the company after the recapitalization using the APV approach is:V = $91,000,000 + 12,250,000V = $103,250,000Since the company has not yet issued the debt, this is also the value of equity after the announcement. So, the new price per share will be:New share price = $103,250,000 / 1,500,000New share price = $68.83c.The company will use the entire proceeds to repurchase equity. Using the shareprice we calculated in part b, the number of shares repurchased will be:Shares repurchased = $35,000,000 / $68.83Shares repurchased = 508,475And the new number of shares outstanding will be:New shares outstanding = 1,500,000 – 508,475New shares outstanding = 991,525The value of the company increased, but part of that increase will be funded by the new debt. The value of equity after recapitalization is the total value of thecompany minus the value of debt, or:New value of equity = $103,250,000 – 35,000,000New value of equity = $68,250,000So, the price per share of the company after recapitalization will be:New share price = $68,250,000 / 991,525New share price = $68.83The price per share is unchanged.d.In order to v alue a firm’s equity using the flow-to-equity approach, we mustdiscount the cash flows available to equity holders at the cost of the firm’s levered equity. According to Modigliani-Miller Proposition II with corporate taxes, the required return of levered equity is:R S = R0 + (B/S)(R0– R B)(1 – t C)R S = .20 + ($35,000,000 / $68,250,000)(.20 – .09)(1 – .35)R S = .2367 or 23.67%After the recapitalization, the net income of the company will be:EBIT $28,000,000Interest 3,150,000EBT $24,850,000 Taxes 8,697,500 Net incomeThe firm pays all of its earnings as dividends, so the entire net income is availableto shareholders. Using the flow-to-equity approach, the value of the equity is:S = Cash flows available to equity holders / R SS = $16,152,500 / .2367S = $68,250,00015. a.If the company were financed entirely by equity, the value of the firm would beequal to the present value of its unlevered after-tax earnings, discounted at itsunlevered cost of capital. First, we need to find the company’s unlevered cash flows,which are:Sales $28,900,000Variable costs 17,340,000EBT $11,560,000Tax 4,624,000Net incomeSo, the value of the unlevered company is:V U = $6,936,000 / .17V U = $40,800,000b.According to Modigliani-Miller Proposition II with corporate taxes, the value oflevered equity is:R S = R0 + (B/S)(R0– R B)(1 – t C)R S = .17 + (.35)(.17 – .09)(1 – .40)R S = .1868 or 18.68%c.In a world with corporate taxes, a firm’s weighted average cost of capital equals:R WACC = [B / (B + S)](1 – t C)R B + [S / (B + S)]R SSo we need the debt-value and equity-value ratios for the company. The debt-equityratio for the company is:B/S = 0.35B = 0.35SSubstituting this in the debt-value ratio, we get:B/V = .35S / (.35S + S)B/V = .35 / 1.35B/V = .26And the equity-value ratio is one minus the debt-value ratio, or:S/V = 1 – .26S/V = .74So, using the capital structure weights, the comp any’s WACC is:R WACC = [B / (B + S)](1 – t C)R B + [S / (B + S)]R SR WACC = .26(1 – .40)(.09) + .74(.1868)R WACC = .1524 or 15.24%We can use the weighted average cost of capital to discount the firm’s unlevered aftertax earnings to value the company. Doing so, we find:V L = $6,936,000 / .1524V L = $45,520,661.16Now we can use the debt-value ratio and equity-value ratio to find the value of debt and equity, which are:B = V L(Debt-value)B = $45,520,661.16(.26)B = $11,801,652.89S = V L(Equity-value)S = $45,520,661.16(.74)S = $33,719,008.26d.In order to value a firm’s equity using the flow-to-equity approach, we can discountthe cash flows available to equity holders at the cost of the firm’s levered equity.First, we need to calculate the levered cash flows available to shareholders, which are:Sales $28,900,000Variable costs 17,340,000EBIT $11,560,000Interest 1,062,149EBT $10,497,851Tax 4,199,140Net incomeSo, the value of equity with the flow-to-equity method is:S = Cash flows available to equity holders / R SS = $6,298,711 / .1868 S = $33,719,008.2616. a.Since the company is currently an all-equity firm, its value equals the present valueof its unlevered after-tax earnings, discounted at its unlevered cost of capital. Thecash flows to shareholders for the unlevered firm are:EBIT $83,000Tax 33,200Net incomeSo, the value of the company is:V U = $49,800 / .15V U = $332,000b.The adjusted present value of a firm equals its value under all-equity financing plusthe net present value of any financing side effects. In this case, the NPV offinancing side effects equals the after-tax present value of cash flows resulting fromdebt. Given a known level of debt, debt cash flows should be discounted at thepre-tax cost of debt, so:NPV = Proceeds – Aftertax PV(Interest payments)NPV = $195,000 – (1 – .40)(.09)($195,000) / 0.09NPV = $78,000So, using the APV method, the value of the company is:APV = V U + NPV(Financing side effects)APV = $332,000 + 78,000APV = $410,000The value of the debt is given, so the value of equity is the value of the companyminus the value of the debt, or:S = V – BS = $410,000 – 195,000S = $215,000c.According to Modigliani-Miller Proposition II with corporate taxes, the requiredreturn of levered equity is:R S = R0 + (B/S)(R0– R B)(1 – t C)R S = .15 + ($195,000 / $215,000)(.15 – .09)(1 – .40)R S = .1827 or 18.27%d.In order to value a firm’s equity using the flow-to-equity approach, we can discountthe cash flows available to equity holders at the cost of the firm’s levered equity.First, we need to calculate the levered cash flows available to shareholders, whichare:EBIT $83,000Interest 17,550EBT $65,450Tax 26,180Net incomeSo, the value of equity with the flow-to-equity method is:S = Cash flows available to equity holders / R SS = $39,270 / .1827S = $215,00017.Since the company is not publicly traded, we need to use the industry numbers tocalculate the industry levered return on equity. We can then find the industry unlevered return on equity, and re-lever the industry return on equity to account for the different use of leverage. So, using the CAPM to calculate the industry levered return on equity, we find:R S = R F+ β(MRP)R S = 5% + 1.2(7%)R S = 13.40%Next, to find the average cost of unlevered equity in the holiday gift industry we can use Modigliani-Miller Proposition II with corporate taxes, so:R S = R0 + (B/S)(R0– R B)(1 – t C).1340 = R0 + (.35)(R0– .05)(1 – .40)R0 = .1194 or 11.94%Now, we can use the Modigliani-Miller Proposition II with corporate taxes to re-lever the return on equity to account for this company’s debt-equity ratio. Doing so, we find:R S = R0 + (B/S)(R0– R B)(1 – t C)R S = .1194 + (.40)(.1194 – .05)(1 – .40)R S = .1361 or 13.61%Since the project is financed at the firm’s target debt-equity ratio, it must be discounted at t he company’s weighted average cost of capital. In a world with corporate taxes, a firm’s weighted average cost of capital equals:。
曼昆经济学原理Chapter18生产要素市场 中英文笔记
Chapter 18 生产要素市场The Markets for Factors of Production §1. 生产要素市场一．定义：生产要素Factors of production是指用于生产物品与劳务的投入the inputs used to produce goods and services 二．联系：生产要素市场类似于物品与服务市场不同点在于生产要素的需求是派生需求derived demand即企业的生产要素需求，是从它向另一个市场供给物品的决策派生出来的§2. 劳动需求The Demand for Labor一．劳动需求1.联系：与经济中的其它市场一样，劳动市场也是由供求力量支配的2.结论：大多数劳动服务不是作为最终产品供消费者享用的，而是投入到其它物品的生产中二．生产函数与劳动的边际产量The Production Function and The Marginal Product of Labor1.生产函数The production function：说明用于生产一种物品的投入量与该物品产量之间的关系。
2.劳动的边际产量The marginal product of labor：增加的一个单位劳动所引起的产量增加量。
公式：MPL = ΔQ/ΔL = (Q2–Q1)/(L2–L1)3.边际产量递减Diminishing Marginal Product of Labor随着工人数量增加，劳动的边际产量递减；随着雇佣的工人越来越多，每个增加的工人对苹果产量的贡献越来越小；生产函数随着工人数量增加而变得越来越平坦；这种性质被称为边际产量递减。
三．劳动边际产量值与劳动需求The Value of the Marginal Product of Labor and the Demand for Labor1.边际产量值The value of the marginal product：一种投入的边际产量乘以该产品的价格。
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金融机构与市场chapter18课件
PPT学习交流
3
Insurance Companies
• Insurance companies assume the risk of their clients in return for a fee, called the premium.
• Most people purchase insurance because they are risk-averse—they would rather pay a certainty equivalent (the premium) than accept a gamble
• Insurance Companies • Fundamentals of Insurance • Growth and Organization of Insurance Companies • Types of Insurance
PPT学习交流
2
Chapter Preview
• Pensions • Types of Pensions • Regulation of Pension Plans • The Future of Pension Funds
PPT学习交流
9
Adverse Selection in Insurance
The adverse selection problem raises the issue of which policies an insurance company should accept: • Those most likely to suffer loss are most likely to apply for insurance. • In the extreme, insurance companies should turn down anyone who applies for an insur policy.
Chapter 18 关系分句
Chapter 18 关系分句1.whose和of which必备知识Li Dong’s house 所有关系The tapping of the sea 动宾关系The development of economy主谓关系在非人称现行词后⑴表示“所有”时意义时，既可用whose 又可用of whichThe house whose windowsthe windows of whichof which the windowsare broken is unoccupied.⑵表示“部分”意义时，只能用of whichI can lend you five books,none of whichof whichare very good.whose none不能用在非人称现行词后⑴表示“所有”时，只能用whoseNicholas, whose wife teaches singing, ishimself a teacher of the piano.People whose rents have been raised can appeal.⑵表示“部分”意义时，只能用of whomThe eighty-nine passengers, four of whomof whomwere British, all escaped without serious injury.It’s a family of eight children, all of whomof whom all are studying music.2.as和which作关系代词⑴作宾语（一般可以替换）He saw the girl, as / which he had hoped.⑵作主语（一般可以替换）He was late for school, as / which was usual with him.⑶as分句可以视为“状语+定语”的混合She has married again, as (it) often happens,3.the same … as…和such … as…中的as⑴the same … as …的词性This is the same sum as was spent on books last year. 关系代词John works as Mary does. 关系副词⑵such … as …①关系代词We were interested in opinions as could be elicited by short questions.②与其它从句的转换Such girls as he knew were teachers.= The girls whom he knew were teachers. We’ll each of us give you such a thrashing 鞭打as you’ll remember.….. that you’ll remember.You can use my bicycle, such as it is. ……………………….., though it is of poor quality.4.to do和doing后的关系分句He betrayed the cause which he was paid to support.………………………to support which he was paid.Such was the ingratitude of the man whom he almost lost his life in defending. ………………………………in defending whom he almost list his life.He told us the object of his life, to gain which he had run such dangers and undergone such toil.Profits had to be increased, to achieve which object became the main occupation of business executives.They take a rigorous严厉的examination, passing which confers on赋予the student a virtual guarantee of a place at the university.5.接续性关系分句转换成并列句I gave the message to Peter, who was supposed to pass it on to you.→....., and he …….I must appreciate that book of yours, which I finished reading last night. →....., and I finished reading it last night. That evening we went to the cinema, where we met a group of friends.→....., and we met a group of friends.You had better call again at 12 o’clock, when my father will be home. →....., an then my father will be home.6.关系分句的并列Peter shared a flat with a boy philosophy student and who wanted to sit up half the night discussing philosophy.使用相同的关系代词The doctor told me that the major’s wife, who was very young and whom he had not married until he was definitely invalid伤残out of war, had died of pneumonia. 使用不同的关系代词He’s the person I meet at the club every dayandtonight.前者省略，后者不能省略且要使用准确的关系代词7.双重限制关系分句和后进先出关系分句Are there any jobs that men can doHe is one of the men whom I feel I can trust.8.带有介词的关系分句Boston is the city to which I flew / which I flew to.介词前后均可I didn’t buy the book which I came across.只能放在后面He fought ten campaigns, in the course of which he never lost a battle.To the left is a door to which the key has been lost. 与动词无关Exercises1.Will you please show me the girl __C__ name is Lucy?A.herB.who’sC.whoseD.which2.It was raining again, ___D_ is very bad for our crops.A.itB.thatC.whatD.which3.Do you know the student _C___?A.whom I often talkB.with who I often talkC.I often talk withD.That I often talk4.The world __D__ is made up of matter.A.in that we liveB.on which we liveC.where we live inD.we live in5.This is the most difficult book __D__.A.what I have ever readB.which I have ever readC.I have ever read itD.that I have ever read6.The size of the audience, ___B_ we had expected, was well over twenty thousand.A.whomB.asC.whichD.that7.The two friends __C__ met by chance on atrain for Shanghai.A.whom had not been seen by each otherfor many yearsB.had not seen each other for many yearsC.who had not seen each other for manyyearsD.who had not seen each other for manyyears and8.The __B__ why Elaine didn’t turn up was not made clear.A.causeB.reasonC.matterD.excuse9.The farmer uses wood to build a house _D___ to store gains.A.with whichB.whereC.whichD.in which10.This was the place __A__ last year.A.which I visitedB.where I visitedC.when I visitedD.in which I visitedrry Chan __B__ was here yesterday.A.whom we had heard so muchB.about whom we had heard so muchC.who we had heard so muchD.most of whom we had heard so much12.The audience, __B__, enjoyed the performance very much.A.most of them were studentsB.most of whom were studentsC.most of which were studentsD.most of whom being students13.The tree, __A__ are almost bare, is a very old one.A.whose branchesB.its branchesC.which’s branchesD.on which the branches14.He studied hard at school when he was young __A__ contributes to his success inlater life.A.whichB.thatC.thisD.so that15.My eldest sister __B__ is now studying in the university.A.whom is twentyB.who is twentyC.that is twentyD.whose age is twenty16.Unfortunately there was ____ to prevent the accident.A.something that we could doB.anything that we could doC.nothing which we could doD.nothing we could do17.Joseph’s car has a flat tire. _A___ now is to walk to the nearest telephone.A.That he can doB.All what he can doC.All he can doD.He can do something18.Mr. Smith will move into his new house next Monday, ____ it will be completely finished.A.by that timeB.by which timeC.by thenD.by the time19.You may rely on it _C__ everything will be ready on Monday.A.whenB.whichC.thatD.what20.Hangzhou, __A__ we spent last spring, is one of the most beautiful cities in China.A.whereB.whichC.thatD.when21.__D__ is often the case with a new idea, much preliminary activity and optimisticdiscussion produce no concrete proposals.A.ThatB.ItC.WhichD.As22.The detective was talking to the boy __B__.A.of whom the watch had been stolenB.whose watch had been stolenC.the watch of his had been stolenD.his watch had been stolen23.The reason __C__ he gives for not coming is that his mother won’t let him.A.whyB.for whichC.whichD.about which24.I am pleased with what you have given me and __B__ you have told me.A.thatB.all thatC.whichD.all what25.Angles was the girl __B__ when you got here.A.to whom talked youB.you talked toC.whom you talkedD.who talked you26.In Sweden all real estate belongs to the Crown, and there is __B__ as private land.A.no owners suchB.no such thingC.such private ownersD.as many owners27.The days __A__ you could travel withouta passport are a thing of the past.A.in whichB.on whichC.of whichD.by which28.I was in China _A___ Dr. Bethune gave his life to the revolutionary cause.A.thatB.whereC.in whichD.at which29.When they went into the shop and asked to look at the engagement rings that girl brought out the cheaper ones, __C__ she had arranged with James.A.those were whatB.what was thatC.which was whatD.that was what30.That’s the hotel __B__ last year.A.which we stayedB.at which we stayedC.where we stayed atD.where we stayed in。
米什金货币金融学英文版习题答案chapter18英文习题
米什金货币金融学英文版习题答案chapter18英文习题Economics of Money, Banking, and Financial Markets, 11e, Global Edition (Mishkin) Chapter 18 The Foreign Exchange Market18.1 Foreign Exchange Market1) The exchange rate isA) the price of one currency relative to gold.B) the value of a currency relative to inflation.C) the change in the value of money over time.D) the price of one currency relative to another.Answer: DAACSB: Reflective Thinking2) Exchange rates are determined inA) the money market.B) the foreign exchange market.C) the stock market.D) the capital market.Answer: BAACSB: Reflective Thinking3) Although foreign exchange market trades are said to involve the buying and selling of currencies, most trades involve the buying and selling ofA) bank deposits denominated in different currencies.B) SDRs.C) gold.D) ECUs.Answer: AAACSB: Reflective Thinking4) The immediate (two-day) exchange of one currency foranother is aA) forward transaction.B) spot transaction.C) money transaction.D) exchange transaction.Answer: BAACSB: Reflective Thinking5) An agreement to exchange dollar bank deposits for euro bank deposits in one month is aA) spot transaction.B) future transaction.C) forward transaction.D) deposit transaction.Answer: CAACSB: Reflective Thinking6) Today 1 euro can be purchased for $1.10. This is theA) spot exchange rate.B) forward exchange rate.C) fixed exchange rate.D) financial exchange rate.Answer: AAACSB: Reflective Thinking7) In an agreement to exchange dollars for euros in three months at a price of $0.90 per euro, the price is theA) spot exchange rate.B) money exchange rate.C) forward exchange rate.D) fixed exchange rate.Answer: CAACSB: Reflective Thinking8) When the value of the British pound changes from $1.25 to $1.50, the pound has ________ and the U.S. dollar has ________.A) appreciated; appreciatedB) depreciated; appreciatedC) appreciated; depreciatedD) depreciated; depreciatedAnswer: CAACSB: Reflective Thinking9) When the value of the British pound changes from $1.50 to $1.25, then the pound has________ and the U.S. dollar has ________.A) appreciated; appreciatedB) depreciated; appreciatedC) appreciated; depreciatedD) depreciated; depreciatedAnswer: BAACSB: Reflective Thinking10) When the value of the dollar changes from ￡0.5 to ￡0.75, then the British pound has________ and the U.S. dollar has ________.A) appreciated; appreciatedB) depreciated; appreciatedC) appreciated; depreciatedD) depreciated; depreciatedAnswer: BAACSB: Reflective Thinking11) When the value of the dollar changes from ￡0.75 to ￡0.5, then the British pound has________ and the U.S. dollar has ________.A) appreciated; appreciatedB) depreciated; appreciatedC) appreciated; depreciatedD) depreciated; depreciatedAnswer: CAACSB: Reflective Thinking12) When the exchange rate for the Mexican peso changes from 9 pesos to the U.S. dollar to 10 pesos to the U.S. dollar, then the Mexican peso has ________ and the U.S. dollar has ________.A) appreciated; appreciatedB) depreciated; appreciatedC) appreciated; depreciatedD) depreciated; depreciatedAnswer: BAACSB: Reflective Thinking13) When the exchange rate for the Mexican peso changes from 10 pesos to the U.S dollar to 9 pesos to the U.S. dollar, then the Mexican peso has ________ and the U.S. dollar has ________.A) appreciated; appreciatedB) depreciated; appreciatedC) appreciated; depreciatedD) depreciated; depreciatedAnswer: CAACSB: Reflective Thinking14) On January 25, 2009, one U.S. dollar traded on the foreign exchange market for about 0.75 euros. Therefore, one euro would have purchased about ________ U.S. dollars.A) 0.75B) 1.00C) 1.33D) 1.75Answer: CAACSB: Analytical Thinking15) On January 25, 2009, one U.S. dollar traded on the foreign exchange market for about 49.0 Indian rupees. Thus, one Indian rupee would have purchased about ________ U.S. dollars.A) 0.02B) 1.20C) 7.00D) 49.0Answer: AAACSB: Analytical Thinking16) On January 25, 2009, one U.S. dollar traded on the foreign exchange market for about 1.15 Swiss francs. Therefore, one Swiss franc would have purchased about ________ U.S. dollars.A) 0.30B) 0.87C) 1.15D) 3.10Answer: BAACSB: Analytical Thinking17) On January 25, 2009, one U.S. dollar traded on the foreign exchange market for about 3.33 Romanian new lei. Therefore, one Romanian new lei would have purchased about ________ U.S. dollars.A) 0.30B) 1.86C) 2.86D) 3.33Answer: AAACSB: Analytical Thinking18) If the U.S. dollar appreciates from 1.25 Swiss franc per U.S. dollar to 1.5 francs per dollar, then the franc depreciates from ________ U.S. dollars per franc to ________ U.S. dollars per franc.A) 0.80; 0.67B) 0.67; 0.80C) 0.50; 0.33D) 0.33; 0.50Answer: AAACSB: Analytical Thinking19) If the British pound appreciates from $0.50 per pound to $0.75 per pound, the U.S. dollar depreciates from ________ per dollar to ________ per dollar.A) ￡2; ￡2.5B) ￡2; ￡1.33C) ￡2; ￡1.5D) ￡2; ￡1.25Answer: BAACSB: Analytical Thinking20) If the Japanese yen appreciates from $0.01 per yen to $0.02 per yen, the U.S. dollar depreciates from ________ per dollar to ________ per dollar.A) 100￥; 50￥B) 10￥; 5￥C) 5￥; 10￥D) 50￥; 100￥Answer: AAACSB: Analytical Thinking21) If the dollar appreciates from 1.5 Brazilian reals per dollar to 2.0 reals per dollar, the real depreciates from ________ per real to ________ per real.A) $0.67; $0.50B) $0.33; $0.50C) $0.75; $0.50D) $0.50; $0.67E) $0.50; $0.75Answer: AAACSB: Analytical Thinking22) When the exchange rate for the British pound changes from $1.80 per pound to $1.60 per pound, then, holding everything else constant, the pound has ________ and ________ expensive.A) appreciated; British cars sold in the United States become moreB) appreciated; British cars sold in the United States become lessC) depreciated; American wheat sold in Britain becomes moreD) depreciated; American wheat sold in Britain becomes lessAnswer: CAACSB: Analytical Thinking23) If the dollar depreciates relative to the Swiss francA) Swiss chocolate will become cheaper in the United States.B) American computers will become more expensive in Switzerland.C) Swiss chocolate will become more expensive in the United States.D) Swiss computers will become cheaper in the United States.Answer: CAACSB: Analytical Thinking24) Everything else held constant, when a country's currencyappreciates, the country's goods abroad become ________ expensive and foreign goods in that country become ________ expensive.A) more; lessB) more; moreC) less; lessD) less; moreAnswer: AAACSB: Analytical Thinking25) Everything else held constant, when a country's currency depreciates, its goods abroad become ________ expensive while foreign goods in that country become ________ expensive.A) more; lessB) more; moreC) less; lessD) less; moreAnswer: DAACSB: Analytical Thinking。
电子课件 [数学物理方法与仿真(第3版)][杨华军][电子教案(PPT版本)]chapter18
![电子课件 [数学物理方法与仿真(第3版)][杨华军][电子教案(PPT版本)]chapter18](https://img.taocdn.com/s3/m/9c1a118526fff705cc170a89.png)
sech(x) 是钟形的正割双曲函数，其图形与浅水槽中观察到 的孤立波的形状相同．上述 KdV 方程的行波解(18.2.8)称为孤立 波解，从而在数学上证实了孤立波的存在．20 世纪 70 年代两 位美国科学家(Zabusky 和 Kruskal)用数值模拟证实了：两个相 对运动的孤立波在碰撞之后仍为两个稳定的，形状与碰撞前相 同的孤立波，仅仅相位发生了变化，也就是说两个孤立波的碰 撞类似于粒子之间的碰撞．这种孤立波具有类似粒子的性能， 因而这两位科学家将孤立波命名为“孤立子”（Solition）．
3du d u 3c u
查积分表,可解得
(18.2.6)
Au
3du
3c u
1 ln c
3c 3c
3c u 3c u
(18.2.7)
其中 A 为积分常数.不妨设 A=0 (否则对 作平移), 则(18.2.7) 式可化简为
c
c
u 3c sech2 ( c ) 3c (e 2 e 2 )2 ,
现在来寻求方程(18.2.1)的平面前进波(简称行波)
解,令
x ct,u(x,t) u( )
(18.2.2)
其中c 是常数，将(18.2.2)式代入(18.2.1),得
cu uu u 0
对 积分一次得
cu
2
u2
u
A
（ A 为任意常数）
用u 乘(18.2.3)式两边,并对 积分,得
的解为
u(
x,
y)
_____________________
.
uy (x, 0) 0
二．试用行波法求解右行波的初值问题 (20 分)
uut (x,a0u)x
0, ( (x)
Chapter 18 English for Academic Purposes 第十八章 学术用途英语
2. Background
Strevens(1977a) A branch of the larger field of English for specific purposes (ESP) a. a move away from an emphasis on the literature and culture of English speakers and towards teaching for practical command of the language. b. a move towards a view that the teaching of the language should be matched to the needs and purposes of the language learner.
and is then evaluated for effectiveness.
3. Research
Work in needs analysis Weir (1988)：the development of the Association Examing Board’s TEAP West (1994): in geographic and educational contexts Jordan (1997:29): four dimensions of needs those of the target situation of the employer or sponsor of the student of the course designer anrse
genre
The specification of objectives & an assessment of available resources and constraints The syllabus and methodology The syllabus is implemented through teaching materials
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American Agriculture
The leading farm products in the U.S are corn, wheat, rice, soybeans, oranges, meat, milk, apple, oats, cotton, tobacco, etc. The cultivated land in the U.S makes up 21% of the total land, and people who are engaged in farming make up only 2.7% of the total population. Yet the U.S grows nearly one fourth of the world's grain and supplies a half of all the exports of grain in the world. It is the world's leading exporter of agricultural products. The U.S ranks first in the production and export of corn. It produces nearly 50% of the corn in the world. The Corn Belt is in the Midwest. Iowa is the leading corn-producing state. The Midwest is the most important agricultural region of the U.S. Wheat is American's most important food crop. It is second only to corn in production every year. The Wheat Belt is located near the Corn Belt in the Midwest. The U.S ranks second in the export of rice in the world after Thailand.
Foreign Trade
Currently U.S. exports are about 15% of the world's total. The U.S imports bout 13% of all world imports, Canada is the largest single source of goods imports by the U.S., outside of North American, Europe is the largest source of imports. The continuous, long-run US trade deficit: ① Large trade deficits add to the US international debt which must eventually be repaid ② The loss of potential jobs for US citizens
Chapter 18 The Economy vs.
Chapter 19 The Political Institutions
Outline of the US Economy
The biggest industrial country in the world. It is first in such advanced field as computers, space, nuclear energy and electronics. European market: transistors, oil refining, farm products, telecommunications, and computers.(>50%) The U.S has less than 6% of the world's population. Yet, it produces about 25% of the total world output. Factors: ① Geographical location; ② Mineral resources, fertile farm soil, moderate climate ③ Enough labor force ④ The quality of available labor
The Presidency The Presidency
The electors of all fifty states and the District of Columbia -a total of 538 persons -- comprise what is known as the Electoral College. To be successful, a candidate for the Presidency must receive 270 votes. Winner-take-all system: The presidential electors, equal to the number of Senators and Representatives each state has in Congress. The presidential candidate with the highest number of votes in each state wins all the electoral votes of that state. In American, the" winner-take-all" system applies in all states expect Maine. The presidential term of 4 years begin on Jan 20 following the November election, The president publicly takes an oath of office, which is administered by the Chief Justice of the U.S. A. President can be elected to office only twice.
Natural Resources:
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Naห้องสมุดไป่ตู้ural Resources:
Fertile soil, forests, water, and minerals are the major natural resources in the US. Forest resources: forest account for 31% of the total land. Water resources: Northeast, Pacific Northwest, The Mississippi Mineral resources: coal, iron ore, copper, oil, sulfur, lead, zinc Petroleum industry
Chapter 19 Political Institutions
The American Constitution is the oldest written constitution in the world. It was draw up in 1787 and went into effect in 1789.
Separation of powers: "checks and balances" ;Each branch has part of the powers but not all the powers. Provisions for Amendment: the congress by 2/3 vote in each house; legislatures of 2/3 of the states may ask the Congress to call a national conference; amendments must have the approval of threefourths of the states before they enter into force. Bill of Rights
Problems in the US Economy
Unemployment, inflation, financial deficit, and trade deficit are the trouble that always face the US. Low rate of saving, economic insecurity, income inequality
U.S. Gross Domestic Product, 1947-2009
The Economic System of The United States
The U.S has a free-marked economy with a dominant private sector. The privately owned and operated businesses, including farms, produce about 85% of the total output of goods and services. postwar years :government involvement was emphasized again ;Keynesian theory 1970s:stagflation 1980s: Trickle-down Economics ① ② ③ Monopoly (conglomerate): Automobile: General Motors, Ford, Chrysler Electronics: General Electronics Computers: IBM, Apple