MSF_6223_Problem_Set_2

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Apr 3, 2024

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MSF 6223 Corporate and Entrepreneurial Finance Professor Richard T. Thakor Spring 2024 Problem Set 2 Due by 11:59pm on 3/28/2024 IMPORTANT: Be sure to show your work, in order to receive partial credit. 1. Provide an estimate of Target Corporation’s (TGT) equity cost of capital using the steps below. This exercise will require that you make a number of assumptions, so make sure that you clearly state them and the rationale behind them. Download daily stock return data (Yahoo! Finance is a good free resource) for TGT between the 12/31/2021 and 12/31/2023. Download daily risk-free interest rate and factor returns (you can find them under “Fama/French 3 Factors” at the top of the downloadable files) from Ken French’s website: https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_ library.html Using the CAPM, estimate TGT’s equity cost of capital r E using the above data. You will need to make an assumption how what period of time (i.e. over 2023) you are using to estimate the beta, and what period of time you are using to estimate expected returns for the market risk premium and the riskfree rate (I suggest a long period, such as from 12/31/1949 to 12/31/2023). Using the Fama-French 3 factor model, estimate TGT’s equity cost of capital r E using the above data. You will again need to make an assumption about how what period of time you are using to estimate the beta, and what period of time you are using to estimate expected returns. Annualize your cost of capital estimates, given 252 trading days in a year. Use r annual = (1 + r daily ) 252 − 1. Briefly compare your two estimates. 2. Suppose that a TV manufacturing company is currently financed with 50% debt and 50% equity (at market values). The required return on equity is 15%, and the required return on debt is 5%. For all parts of this question, assume that the Modigliani-Miller theorem holds (i.e., there are no frictions such as taxes, costs of financial distress, asymmetric information, etc.). (a) What is the company’s weighted-average cost of capital? 1

(b) The company decides to raise additional funds by issuing some more debt. After doing so, its capital structure changes to 60% debt and 40% equity. Assume, for now, that the issue is sufficiently small to not change the cost of debt (which therefore continues to be 5%). What is the company’s weighted-average cost of capital after the debt issuance? What is the required return on the company’s equity? (c) Assume now that the capital structure change described in part (b) did raise the cost of debt after all, from 5% to 6%. What is the company’s weighted-average cost of capital after the debt issuance, given that the cost of debt has risen to 6%? What is the required return on the company’s equity? 3. You are in the midst of valuing a large, risky investment in an offshore windfarm. You are faced with two options: using generic turbines or using new-technology turbines. Building the wind farm with generic technology is cheaper: a generic wind farm costs 20M while a new technology wind farm has a price tag of 30M. Either option will create 3M in FCF next year that will grow at a rate of 3.2% in perpetuity. To evaluate your project, you find two comparable companies. Your generic technology comparable has an expected equity return of 15%, a constant leverage ratio ( D/V ) of 50%, and a credit rating of BB. The yield on its debt is 12%, but debtholders only expect to lose 10% of what they are owed if the bonds default. Your new technology comparable has an expected equity return of 17%, a constant leverage ratio ( D/V ) of 40%, a yield of 23%, and a credit rating of B+. Addition- ally, since the technology is completely new it is less easy to sell in the aftermarket, debtholders will only recover 45 cents on the dollar in case of default. The average default probability of firms with a BB rating is 10% and the equivalent default probability for firms with a B+ rating is 20%. You are extremely averse to taking on any debt and so, regardless of your choice of technology, you plan on financing your windfarm with no debt whatsoever. Assume a 30% tax rate. Answer the following questions: (a) What is the unlevered cost of capital for the generic technology comp? (b) What is the unlevered cost of capital for the new technology comp? (c) Which technology would you choose for your windfarm? 4. Tablet Company is looking to set up a wholly owned subsidiary firm, which will sell cheap, rugged computers in developing countries. The firm will raise 900M in debt for the initial investment—the debt schedule for the firm is predetermined and shown below for years 0, 1, and 2. After year 2, the firm will maintain a fixed level of debt equal to 700. The free cash flows of the firm for years 0 to 2 are as follows: Year 0 1 2 FCF - 150 200 Debt 900 800 700 2

Assume that after year 2 the FCFs grow at a rate of 2% each year. The unlevered cost of capital is 17%, the return on debt is 8%, and the tax rate is 40%. (a) Calculate the terminal value of the project as of year 2 using the APV method. Be sure to include the value of the tax shield in your calculations. (b) Use the Adjusted Present Value (APV) method to calculate the levered value of the firm as of year 0 and year 1. (c) What is the value of the firm’s equity as of years 0, 1, and 2? (Hint: Remember that V = D + E ) (d) Using your answers from the previous parts, what is the cost of equity capital as of years 0, 1, and 2? (e) Calculate the after-tax WACC for each year. (f) Now re-calculate the total value of the firm as of years 0, 1, and 2 by discounting the subsequent free cash flows/firm values using the after-tax WACC. Use your answers from the previous parts as inputs into your calculations. Why are your answers different from parts (a) and (b)? Which method would be more correct to use in this situation—APV or after-tax WACC? 3

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