Problem Set PROBLEM SET: Valuation Exercise 1. Amarindo [15] Amarindo, Inc. (AMR), is a newly public rm with 10 million shares outstanding. You are doing a valuation analysis of AMR. You estimate its free cash ow in the coming year to be $15 million, and you expect the rm's free cash ows to grow by 4% per year in subsequent years. Because the rm has only been listed on the stock exchange for a short time, you do not have an accurate assessment of AMR's equity beta. However, you do have beta data for UAL, another rm in the same industry: Equity Beta Debt Beta Debt/Equity Ratio UAL 1.5 0.30 1 AMR has a much lower debt-equity ratio of 0.30, which is expected to remain stable, and its debt is risk free. AMR's corporate tax rate is 40%, the risk-free rate is 5%, and the expected return on the market portfolio is 11%. 1. Estimate AMR's equity cost of capital. 2. Estimate AMR's share price. Exercise 2. PG [10] Prokter and Gramble (PG) has historically maintained a debt-equity ratio of approximately 0.20. Its current stock price is $50 per share, with 2.5 billion shares outstanding. The rm enjoys very stable demand for its products, and consequently it has a low equity beta of 0.50 and can borrow at 4.20%, just 20 basis points over the risk free rate of 4%. The expected return on the market is 10%, and PG's tax rate is 35%. (a) This year, PG is expected to have free cash ows of $6.0 billion. What constant expected growth rate of free cash ow is consistent with its current stock price? Exercise 3. Markum You are a consultant who was hired to evaluate a new product line for Markum Enterprises. The upfront investment required to launch the product line is $10 million. The product will generate free cash ow of $750,000 the rst year, and this free cash ow is expected to grow at a rate of 4% per year. Markum has an equity cost of capital of 11.3%, a debt cost of capital of 5%, and a tax rate of 35%. Markum maintains a debt-equity ratio of 0.40. 1. What is the NPV of the new product line (including any tax shields from leverage)? 2. How much debt will Markum initially take on as a result of launching this product line? 3. How much of the product line's value is attributable to the present value of interest tax shields? Exercise 4. Which of the following methods are used in capital budgeting decisions? A) Weighted average cost of capital (WACC) method B) Adjusted present value (APV) method C) Flow-to-equity (FTE) method D) All of the above are used in capital budgeting decisions. 1 Exercise 5. Section: 18.2 The Weighted Average Cost of Capital Method Skill: Conceptual 2) Which of the following statements is FALSE? A) The WACC can be used throughout the rm as the company wide cost of capital for new investments that are of comparable risk to the rest of the rm and that will not alter the rm's debt-equity ratio. B) A disadvantage of the WACC method is that you need to know how the rm's leverage policy is implemented to make the capital budgeting decision. C) The intuition for the WACC method is that the rm's weighted average cost of capital represents the average return the rm must pay to its investors (both debt and equity holders) on an after-tax basis. D) To be protable, a project should generate an expected return of at least the rm's weighted average cost of capital. Exercise 6. Consider the following equation: W ACC = D E rD (1 − τ ) + rE D+E D+E the term rE in this equation is: A the after-tax required rate of return on debt. B the required rate of return on debt. C the required rate of return on equity. D the dollar amount of equity. Exercise 7. Consider the information for the following four rms: Firm Eenie Meenie Minie Moe Cash $0 $0 $25 $50 Debt $150 $250 $175 $350 Equity $150 $750 $325 $150 rD 5% 6% 6% 7.50% rE 10% 12% 11% 15% τc 21% 21% 21% 21% 13) The weighted average cost of capital for "Moe" is closest to: A) 10.00%. B) 7.75%. C) 8.25%. D) 9.00%. Exercise 8. Section: 18.2 The Weighted Average Cost of Capital Method Skill: Analytical 24) Suppose Luther Industries is considering divesting one of its product lines. The product line is expected to generate free cash ows of $2 million per year, growing at a rate of 3% per year. Luther has an equity cost of 2 capital of 10%, a debt cost of capital of 7%, a corporate tax rate of 21%, and a debt-equity ratio of 2. If this product line is of average risk and Luther plans to maintain a constant debt-equity ratio, what after-tax amount must it receive for the product line in order for the divestiture to be protable? Exercise 9. The Aardvark Corporation is considering launching a new product and is trying to determine an appropriate discount rate for evaluating this new product. Aardvark has identied the following information for three single division rms that oer products similar to the one Aardvark is interested in launching: Comparable Firm Anteater Enterprises Armadillo Industries Antelope Inc. Equity Cost of Capital Debt Cost of Capital 12.50% 13% 14% 6.50% 6.10% 7.10% Debt-to-Value Ratio 50% 40% 60% The unlevered cost of capital for Antelope Incorporated is closest to: A) 10.3%. B) 9.9%. C) 10.1%. D) 9.5%. Exercise 10. UA [4] UtilityAnalysis is examining a major new venture. The rm has provided you with the following estimates: the risk free rate is 7.5%, which is also the costs of debt for Utility; the tax rate is 40%; the beta of the rm's equity is 1, the expected return on the market portfolio is 16%, and the proportion of debt in the capital structure is 10%. The new venture requires an outlay of $1,800, and will produce after-tax operating cash inows of $550 for each of 5 years. 1. Determine whether the rm should make the investment. 3 Solutions PROBLEM SET: Valuation Solution to Exercise 1. Amarindo [15] 1. UAL Asset beta = (1/2) 1.5 + (1/2) 0.3 = 0.90 We can use this for AMR's asset beta. To derive the equity beta, since AMR's debt is risk free we have Equity Beta = Asset Beta (1 + D/E) = 0.9 × 1.30 = 1.17. From the SML re = 5% + 1.17(11% − 5%) = 12.02%. Alternatively, given an asset or unlevered beta of 0.90 for AMR, we have (from SML): ru = 5% + 0.90(11% − 5%) = 10.4%. Then we can solve for r e re = 10.4% + 0.30(10.4% − 5%) = 12.02%. b. Since D / E ratio is stable, we can value AMR using the WACC approach. W ACC = (1/1.3)12.02% + (.3/1.3)5%(1 − 40%) = 9.94% Levered value of AMR (as a constant growth perpetuity): D+E =VL = 15 F CF = = $252.52million (rwacc − g) (9.94% − 4%) E = (E/(D + E))V L = 252.52/1.3 = $194.25million Share price = 194.25 / 10 = $19.43 Solution to Exercise 2. PG [10] The growth rate g is calculated from V = Firm where F CF F1 are the freee cash ows to the rm, Current value of equity: E = 50 × 2.5 billion = r Value = the WACC F CF F1 r−g and g the growth rate. 125 billion. Given a debt/equity ratio of 0.2 D D = 0.2 = = 0.2 E 125 D = 0.2 × 125 = 25 V = 25 + 125 = 150 rE = 0.04 + 0.5(0.10 − 0.04) = 7% rD = 0.042 25 125 W ACC = 0.042 · (1 − 0.35) + 0.07 ≈ 0.0629 25 + 125 150 There is an ambiguity in the way the FCF this year is specied. Since it is expected, most reasonable to set 6 as 150 = 6 0.0629 − g 4 F CF1 6 = 0.0629 − g 150 g = 0.0629 − 0.0375 = 0.0258 = 2.58% Alternatively, one can assume that 6 is the current year's FCF (F CF0 ), in which case you would calculate F CF1 = F CF0 (1 + g). 6(1 + g) 0.0629 − g 150 × W ACC − 6 g= = 2.2% 150 + 6 150 = Either of those are possible answers. Solution to Exercise 3. Markum 1. Find NPV W ACC = (1/1.4)(11.3%) + (.4/1.4)(5%)(1 − 0.35) = 9% VL = 0.75 / ( 9 % - 4 %) = $15 million NPV = 10 + 15 = $5 million 2. Debt b. Debt-to-Value ratio is (0.4) / (1.4) = 28.57%. Therefore Debt is 28.57% Ö $15 million = $4.29 million. 3. Tax Shields: u u Discounting at r gives unlevered value. r = ( 1 / 1.4 ) 11.3 % + ( .4 / 1.4 ) 5 % = 9.5 % u V = 0.75 / ( 9.5 % - 4 %) = $13.64 million Tax shield value is therefore 15 13.64 = 1.36 million. Alternatively, initial debt is $4.29 million, for a tax shield in the rst year of 4.29 Ö 5% Ö 0.35 = 0.075 million. Then PV(ITS) = 0.075 / (9.5% 4%) = 1.36 million. Solution to Exercise 4. Answer: D Di: 1 Solution to Exercise 5. Answer: B Explanation: An advantage of the WACC method is that you do not need to know how the rm's leverage policy is implemented to make the capital budgeting decision. Di: 1 Solution to Exercise 6. Answer: C Di: 1 Solution to Exercise 7. Answer: D Explanation: rwacc = rE + rD (1 - τ c ), where D = Net Debt = Debt - Cash Firm Cash Debt Equity rD rE τc Eenie $0 $150 $150 5% 10% 21% 6.98% Meenie $0 $250 $750 6% 12% 21% 10.19% Minie $25 $175 $325 6% 11% 21% 9.02% Moe $50 $350 $150 7.50% 15% 21% 8.95% 5 Wacc Di: 2 Solution to Exercise 8. Answer: rwacc = (.10) + (.07)(1 - .21) = .07020 = = $49.751 million Di: 2 Solution to Exercise 9. Answer: B Explanation: rU = rE + rD rU Comparable Firm Equity Cost of Capital Debt Cost of Capital Debt-to-Value Ratio Anteater Enterprises 12.50% 6.50% 50% 9.50% Armadillo Industries 13% 6.10% 40% 10.24% Antelope Inc. 14% 7.10% 60% 9.86% Di: 1 Solution to Exercise 10. UA [4] Need to calculate WACC: W ACC = D E (1 − τ )rD + rE D+E E+D Here rD = 0.075 rE = 0.075 + 1(0.16 − 0.075) = 0.16 90 10 (1 − 0.4)0.075 + 0.16 = 0.1485 W ACC = 100 100 t 0 1 2 3 4 5 N P V = −1800 + Ct −1800 550 550 550 550 550 550 550 550 550 550 + + + + = 50.2522 (1 + 0.1485)1 (1 + 0.1485)2 (1 + 0.1485)3 (1 + 0.1485)4 (1 + 0.1485)5 6