Chapter 3 Solution - CF2 PDF

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CHAPTER 3CAPITAL BUDGETINGBASIC1. NPV and APV Zoso is a rental car company that is trying to determine whether to add 25 cars to its fleet. The company fully depreciates all its rental cars over five years using the straight-line method. The new cars are expected to generate $215,000 per year in ear...

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CHAPTER 3 CAPITAL BUDGETING BASIC 1. NPV and APV Zoso is a rental car company that is trying to determine whether to add 25 cars to its fleet. The company fully depreciates all its rental cars over five years using the straight-line method. The new cars are expected to generate $215,000 per year in earnings before taxes and depreciation for five years. The company is entirely financed by equity and has a 35 percent tax rate. The required return on the company’s unlevered equity is 13 percent, and the new fleet will not change the risk of the company. a. What is the maximum price that the company should be willing to pay for the new fleet of cars if it remains an all-equity company? EBIT = 215000 NPV = initial cost + Depreciation tax shield + Present value of ebit = 0 -P + 0.35x P/5x1/08%x(1-1/1.08^5) + 65%x215000/13%x(1-1/1.13^5) = 0 -P + 0.2795xP+491533=0 P =$682,201.3 b. Suppose the company can purchase the fleet of cars for $650,000. Additionally, assume the company can issue $430,000 of five-year debt to finance the project at the risk-free rate of 8 percent. All principal will be repaid in one balloon payment at the end of the fifth year. What is the adjusted present value (APV) of the project? Depreciation = 650000/5=130000 interest aftertax per year=430000x8%x65%=22360 NPV (all equity)= -650000 + 35%x130000/8%x(1-1/1.08^5)+65%x215000/13%x(1-1/1.13^5)=23,201 NPV (loan) = Proceeds - PV of aftertax interest - PV of principle payment =430000 - 22360xPVIFA(8%,5) - 430/(1+8%)^5 = APV = NPV + NPVF=

2. APV Gemini, Inc., an all-equity firm, is considering an investment of $1.4 million that will be depreciated according to the straight-line method over its four-year life. The project is expected to generate earnings before taxes and depreciation of $502,000 per year for four years. The investment will not change the risk level of the firm. The company can obtain a four-year, 9.5 percent loan to finance the project from a local bank. All principal will be repaid in one balloon payment at the end of the fourth year. The bank will charge the firm $45,000 in flotation fees, which will be amortized over the four-year life of the loan. If the company financed the project entirely with equity, the firm’s cost of capital would be 13 percent. The corporate tax rate is 30 percent. Using the adjusted present value method, determine whether the company should undertake the project. Initial cost = 1.4 million

Depreciation = 1400000/4=350,000 + With all equity, the value of the project is: NPV =intial cost + Depreciation tax shield + PV = -1,400,000 + 30%x350,000/9.5%x(1-1/1.095^4) + 70%x502,000/0.13x(1-1/1.13^4) = -18300.26 -

Financing wide effect

Flotation cost: -45000+45000/4x0.3xPVIFA(9.5%,4) = -32382.4 (Tax shield from flotation costs per year is 45000/4x30%=3937.5 NPV of tax shield = 3937.5/9.5%x(1-1/1.4^4)=12617.6 The implies a net cost of flotation of: 45000-12617.6=32382.4)

+ Proceeds = 1400000-45000= interest cost aftertax/year = 1445 NPVF = Proceeds(Net of flotation) – Aftertax PV(Interest Payments) – PV(Principal Payments)+ PV(Flotation Cost Tax Shield) =1.4-0.045 -1.4x9.5%x70%xPVIFA(9.5%,4) - 1.4/1.095^4 + 30%x0.045/4xPVIFA(9.5%,4) = 93674 APV = NPV + NPVF = -18300.26+93674= 3. FTE Milano Pizza Club owns three identical restaurants popular for their specialty pizzas. Each restaurant has a debt–equity ratio of 40 percent and makes interest payments of $41,000 at the end of each year. The cost of the firm’s levered equity is 19 percent. Each store estimates that annual sales will be $1.45 million; annual cost of goods sold will be $785,000; and annual general and administrative costs will be $435,000. These cash flows are expected to remain the same forever. The corporate tax rate is 40 percent. a. Use the flow to equity approach to determine the value of the company’s equity. EBT = 1.45x3 - 0.785x3 - 0.435x3 -0.041x3= 0.567 NI = 0.567x(1-40%) = 0.3402 PV = LCF/Rs = 0.3402/19% = 1.79 b. What is the total value of the company? B = 40%xS = 40%x1.79=0.716 VL = S+B = 0.716+1.79= 2.506 4. WACC If Wild Widgets, Inc., were an all-equity company, it would have a beta of .95. The company has a target debt–equity ratio of .40. The expected return on the market portfolio is 11 percent, and Treasury bills currently yield 4 percent. The company has one bond issue outstanding that matures in 20 years and has a coupon rate of 6.5 percent. The bond currently sells for $1,080. The corporate tax rate is 34 percent. a. What is the company’s cost of debt? PV of bond = 65/2/Rb x(1-1/(1+Rb)^40)+1000/(1+Rb)^40=1080 Rb = 5.81% b. What is the company’s cost of equity?

Questions and Exercises

Cost of equity: Ro= 4% +0.95x(11%-4%) = 10.65% Rs = Ro + (t-tax)xB/Sx(Ro-Rb) = 11.92% c. What is the company’s weighted average cost of capital? Debt - equity = 40% B/V = 2/7, S/V =5/7 Rwacc = 2/7x5.8%x(1-34%) + 5/7x11.92% =9.6% 5. Beta and Leverage North Pole Fishing Equipment Corporation and South Pole Fishing Equipment Corporation would have identical equity betas of 1.10 if both were all equity financed. The market value information for each company is shown here:

The expected return on the market portfolio is 10.9 percent, and the risk-free rate is 3.2 percent. Both companies are subject to a corporate tax rate of 35 percent. Assume the beta of debt is zero. a. What is the equity beta of each of the two companies? North: Beta equity = (1+ Debt/Equityx(1-tax))xBeta unleverred = (1+ 2.7/3.9x65%)x1.1=1.595 South: Beta equity = (1+3.9/2.7x65%) x1.1 = 2.13 b. What is the required rate of return on each of the two companies’ equity? R north = 3.2% + 1.595x(10.9%-3.2%) = 15.48% R south = 3.2% + 2.13x(10.9%-3.2%) = 19.6% 6. NPV for an All-Equity Company Watson, Inc., is an all-equity firm. The cost of the company’s equity is currently 11.9 percent, and the risk-free rate is 3.5 percent. The company is currently considering a project that will cost $10.6 million and last six years. The project will generate revenues minus expenses each year in the amount of $3.1 million. If the company has a tax rate of 40 percent, should it accept the project? NPV = intial cost + PV of depreciation tax shield + PV of aftertax revenue =-10.6 + 40%x10.6/6xPVIFA(3.5%, 6) + (1-40%)x3.1xPVIFA(11.9%,6) = 0.83 7. WACC Bolero, Inc., has compiled the following information on its financing costs:

The company is in the 35 percent tax bracket and has a target debt–equity ratio of 60 percent. The target short-term debt/long-term debt ratio is 20 percent.

a. What is the company’s weighted average cost of capital using book value weights? Rwacc = 12/41x4.1%x(1-35%)+20/41x7.2%x(1-35%) + 9/41x13.8% =6.09% b. What is the company’s weighted average cost of capital using market value weights? Rwacc = 12.5/89.5x4.1%x65%+32/89.5x7.2%x65% + 54/89.5x13.8%=10.37% c. What is the company’s weighted average cost of capital using target capital structure weights? B/S = 0.6 →B/V = 0.375, S/V = 0.625 → (STD+LTD)/V = 0.375, STD/LTD = 20% → STD/V = 0.0625, LTD/V = 0.3125 Rwacc = 0.0625x4.1%x65% + 0.3125x7.2%x65%+ 0.625x13.8%=10.25% d. What is the difference between WACCs? Which is the correct WACC to use for project evaluation? The differences in the WACCs are due to the different weighting schemes. The company’sWACC will most closely resemble the WACC calculated using target weights since future projects will be financed at the target ratio. Therefore, the WACC computed with target weights should be used for project evaluation INTERMEDIATE 8. APV Triad Corporation has established a joint venture with Tobacco Road Construction, Inc., to build a toll road in North Carolina. The initial investment in paving equipment is $93 million. The equipment will be fully depreciated using the straight-line method over its economic life of five years. Earnings before interest, taxes, and depreciation collected from the toll road are projected to be $12.9 million per annum for 20 years starting from the end of the first year. The corporate tax rate is 35 percent. The required rate of return for the project under all-equity financing is 13 percent. The pretax cost of debt for the joint partnership is 8.5 percent. To encourage investment in the country’s infrastructure, the U.S. government will subsidize the project with a $30 million, 15-year loan at an interest rate of 5 percent per year. All principal will be repaid in one balloon payment at the end of Year 15. What is the adjusted present value of this project? NPV = initial investment + PV of cash flow aftertax + PV of depreciation tax shield = -93 + (1-35%)x12.9xPVIFA(13%,20) + 35%x93/5xPVIFa(8.5%,5) = -8.44 + interest aftertax = 30x5%x65%=0.975 NPVF = Proceed - PV of interest aftertax - PV of principle payment = 30 - 0.975xPVIFA(8.5%, 15) - 30/(1.085^15)=13.08 APV = NPV + NPVF = -8.44+13.08 = 4.64 9. WACC Neon Corporation’s stock returns have a covariance with the market portfolio of .0415. The standard deviation of the returns on the market portfolio is 20 percent, and the expected market risk premium is 7.5 percent (Rm-Rf). The company has bonds outstanding with a total market value of $45 million and a yield to maturity of 6.5 percent. The company also has 4.2 million shares of common stock outstanding, each selling for $30. The company’s CEO considers the firm’s current debt–equity ratio optimal. The corporate tax rate is 35 percent, and Treasury bills currently yield 3.4 percent (Rf). The company is considering the purchase of additional equipment that would cost $47 million. The expected unlevered cash flows from the equipment are $13.5 million per year for five years. Purchasing the equipment will not change the risk level of the firm. a. Use the weighted average cost of capital approach to determine whether Neon should purchase

Questions and Exercises

the equipment. B = 45million, Rb=YTM = 6.5% S = 4.2x30 =126 million beta =Cov/var = 0.0415/(0.2^2) = 1.0375 CAPM: Rs = Rf + betax(Rm-Rf) = 3.4% +1.0375x7.5%=11.18% WACC = 45/(45+126)x6.5%x65%+126/(45+126)x11.18%=9.35% NPV = initial cost + PV of UCF = -47 + 13.5xPVIFA(9.35%, 5) =5.036 >0 b. Suppose the company decides to fund the purchase of the equipment entirely with debt. What is the cost of capital for the project now? Explain. 10. Beta and Leverage Dorman Industries has a new project available that requires an initial investment of $4.3 million. The project will provide unlevered cash flows of $710,000 per year for the next 20 years. The company will finance the project with a debt-to-value ratio of .40. The company’s bonds have a YTM of 6.8 percent. The companies with operations comparable to this project have unlevered betas of 1.15, 1.08, 1.30, and 1.25. The risk-free rate is 3.8 percent, and the market risk premium is 7 percent. The company has a tax rate of 34 percent. What is the NPV of this project? Average Beta of unlevered firm = (1.15+1.08+1.3+1.25)/4=1.195 B/V = 0.4→ B/S = 2/3 Beta equity = (1+0.66x2/3)x1.195 = 1.72 CAPM: Rs = 3.8% + 1.72x7% = 15.84% WACC = 0.4x6.8% + 0.6x15.84% = 11.3% NPV = initial cost + present value of cashflow = -4.3 + 0.71xPVIFA(wacc, 20)= 1.24 CHALLENGE 11. APV, FTE, and WACC Newkirk, Inc., is an unlevered firm with expected annual earnings before taxes of $21 million in perpetuity. The current required return on the firm’s equity is 16 percent, and the firm distributes all of its earnings as dividends at the end of each year. The company has 1.3 million shares of common stock outstanding and is subject to a corporate tax rate of 35 percent. The firm is planning a recapitalization under which it will issue $30 million of perpetual 9 percent debt and use the proceeds to buy back shares. a. Calculate the value of the company before the recapitalization plan is announced. What is the value of equity before the announcement? What is the price per share? Vu = EBTx(1-tax)/Ro = 21x65%/16% = 85.3 Price/share = 85.3/1.3 = b. Use the APV method to calculate the company value after the recapitalization plan is announced. What is the value of equity after the announcement? What is the price per share? NPV= initial cost + c. How many shares will be repurchased? What is the value of equity after the repurchase has been completed? What is the price per share? d. Use the flow to equity method to calculate the value of the company’s equity after the

recapitalization. 12. Projects That Are Not Scale Enhancing Blue Angel, Inc., a private firm in the holiday gift industry, is considering a new project. The company currently has a target debt–equity ratio of .40, but the industry target debt–equity ratio is .35. The industry average beta is 1.2. The market risk premium is 7 percent, and the risk-free rate is 5 percent. Assume all companies in this industry can issue debt at the risk-free rate. The corporate tax rate is 40 percent. The project requires an initial outlay of $785,000 and is expected to result in a $93,000 cash inflow at the end of the first year. The project will be financed at the company’s target debt–equity ratio. Annual cash flows from the project will grow at a constant rate of 5 percent until the end of the fifth year and remain constant forever thereafter. Should Blue Angel invest in the project? Rs (industry) = ….0.1340 Ro (company) = 0.1360 Rs(company) = 0.1194 WACC = 10.57% NPV = initial cost + ∑CFi/(1+wacc)^t) + terminal value...