FIN 405 Homework Assignment 2
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FIN 405
Homework Assignment 2
Due: February 16, 2023, before class, via Canvas
1 Short DCF valuation problems [30 points]
(a) Suppose you have obtained the following information on Pierogi Perfection, Inc. The firm’s equity beta is 1.0, the firm’s debt beta is 0.2, the risk-free rate is 3%, and the market risk premium is 6%. Next year’s free cash flow to the firm is $600,000 and the growth rate of cash flows going forward is expected to be zero. The current market value of debt is $10,000,000 and the current market value of equity is $2,000,000. The tax rate is 0%, so there is no tax shield on debt. What is the value of the firm? [5 points]
(b) Suppose you have obtained the following information on Pierogi Perfection. The firm’s equity beta is 1.5, the firm’s debt beta is 0.5, the risk-free rate is 3%, and the market risk premium is 6%. Next year’s free cash flow to the firm is $600,000 and the growth rate of cash flows going forward is 2%. The current market value of debt is $10,000,000 and the current market value of equity is $4,400,000. The tax rate is 40%. The growth rate of the tax shield is expected to be 2%. What is the value of the firm using WACC (i.e. the MM-with-taxes WACC formula)? [5 points]
(c) Suppose you have obtained the following information on Pierogi Perfection. The firm’s equity beta is 1.5, the firm’s debt beta is 0.5, the risk-free rate is 3%, and the market risk premium is 6%. Next year, EBIT is expected to be $1,600,000. The firm’s tax rate is 40%, the firm’s capex is expected to be $600,000, depreciation and amortization are expected to be $300,000, and net working capital is expected to increase by $60,000. The growth rate of cash flows going forward is 2%, while the growth rate of the tax shield is expected to be 1%. The current market value of debt is $10,000,000 and the current market value of equity is $4,400,000. Please solve for the value of the firm using APV. [5 points]
(d) Can we solve for the value of the firm using WACC if the tax shield grows at a different growth rate than the rest of the firm’s cash flows? Why or why not? [5 points]
Now suppose you have obtained the following information on Pierogi Perfection. The firm’s equity beta is 1.5, the firm’s debt beta is 0.5, the risk-free rate is 3%, and the market risk premium is 6%. Next year, EBIT is expected to be $1,600,000. The firm’s interest expense is expected to be $600,000, the firm’s tax expense is expected to be $400,000, the firm’s capex is expected to be $600,000, depreciation and amortization are expected to be $300,000, and net working capital is expected to increase by $60,000. The growth rate of cash flows going forward is 2%, while the growth rate of the tax shield is also expected to be 2%. The cur- rent market value of debt is $10,000,000 and the current market value of equity is $4,400,000.
(e) What is the value of the firm using APV under the assumption that the risk of the tax shield equals the risk of the firm’s debt? [5 points]
(f) What is the value of the firm using APV under the assumption that the risk of the tax shield equals the risk of the firm’s assets? [5 points]
2 Is AAL’s valuation in the clouds? [40 points]
The “AAL Valuation.xlsx” spreadsheet on Canvas contains some future financial projections for American Airlines Group, Inc. (NASDAQ: AAL) that I have taken from recent analyst reports.
(a) Based solely on the information in the spreadsheet, what is a reasonable valuation for American Airlines? To answer this question, please construct a DCF valuation model for American using both the WACC and APV methodologies. I would like you to compute two different terminal values for American: one using the long-term FCF growth rate as stated in the spreadsheet and one using a presumed price multiple of 7x 2027 EBITDA. Please note that I expect you to produce a total of four valuations for American (WACC and APV, each with two different terminal value assumptions). [30 points]
(b) Compute the average of the four numbers you calculated in part (a). You may assume
that this average is the “correct” valuation for American Airlines as a company. The current market value of American Airlines stock is approximately $10.4 billion (as of January 27th). How does your valuation compare with the market’s valuation of American? Why might your valuation differ from the market’s valuation? Please be specific in your answers. [10 points]
3 Bottom-up beta for Dollar Tree [30 points]
Please compute bottom-up asset and equity betas for Dollar Tree, Inc. (NASDAQ: DLTR) as of today. For simplicity, please assume that Dollar Tree and its competitors all have debt betas of zero (which would almost certainly not be true in reality). To compute equity betas, please run a regression of eaCeSS stock returns on eaCeSS market returns using 36 months of monthly stock returns. That is, please run the regression Ti − Tf = a + 8(Tm − Tf ) + e, where Ti is the monthly total return (including dividends) on the stock you are evalu- ating, Tf is the risk-free rate, and Tm − Tf is the market risk premium. You can ob- tain data on the risk-free rate (“RF”) and market risk premium (“MKTRF”) from Ken French’s website (visit https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/ data_library.html and click on the “CSV” link next to “Fama/French 3 Factors”; please also note that reported returns are multiplied by 100 so an entry of 0.22 means 0.22%, not 22%).
Please discuss each peer firm that you have chosen for your bottom-up beta calculations and indicate why you selected that firm. Please also show all of your calculations. If you submit an Excel table or tables, please write out the formulas you used to compute each column. Please also be sure to provide sources for the data that you use in your calculations. Good luck! [30 points]
2023-02-15