Question 3 You are an original owner of a publicly traded food service company c

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Question 3
You are an original owner of a publicly traded food service company called Smith’s Foods (SF). Your company has been in the high-end restaurant business (HE) for the past ten years. You announced today that the company will be issuing debt today to open a new fast food division (FF).
Opening this new division costs $10M today, which you will fund by issuing debt. Revenues from this new division are expected to be $3M next year and are projected to grow by 4 percent per year. Costs from this new division are expected to be $2M next year and are projected to grow by 2 percent per year. The life of this project is 15 years.
Analysis of other fast food businesses suggests that the beta of a fast food division equals 0.70. Assume that the revenues and costs have similar risk. Throughout this problem, assume a risk-free rate of 3 percent and a market risk premium of 6 percent.
a) What is the NPV of this new investment? Is it a good investment? Hint: you will need to use the growing annuity formula twice. Once for revenues and once for costs.
A regression of monthly SF excess stock returns on monthly S&P 500 excess returns from the past ten years tells you that the beta of the high-end division equals 1.5. Directly before the investment in the fast food division, SF was an all-equity firm with 1M shares outstanding trading at $25 per share. Assume that the announcement of the new division does not affect the value or beta of the high-end division.
b) What is the beta of the firm after the announcement of the new division? The beta of a firm can be calculated as the value-weighted average of the division betas:
Bfirm = (Vd1/(Vd1+Vd2)Bd1 + (Vd2/(Vd1+Vd2))Bd2
where the value of a division (VD1 or VD2) equals the present value of its future net cash flows.
c) Assume that the beta of the new debt (valued at $10M) is equal to 0.1. What is the beta of the firm’s equity after the announcement of the new division?
d) The beta of your firm’s equity was originally 1.6. There are two reasons why the announcement caused the beta of your firm’s equity to slightly change – one reason causes the original beta to decrease while the other causes it to increase. Briefly explain these reasons.
e) What is the change in the expected return of the firm due to the announcement?

Explanation / Answer

5.36

a) NPV of Fast Food Division (NPV) Year Cash Inflow Cash Outflow Net Cash Inflow Dis. Factor NPV (CIF X (1+.04)) (COF X (1+.02)) 1/(1+r)=(1/1.06) (a) (b) (c ) (d)= (b)-(c ) (e) (f)=(d) X (e) 0 10.00 (10.00) 1.00 (10.00) 1 3.00 2.00 1.00 0.94 0.94 2 3.12 2.04 1.08 0.89 0.96 3 3.24 2.08 1.16 0.84 0.98 4 3.37 2.12 1.25 0.79 0.99 5 3.51 2.16 1.34 0.75 1.00 6 3.65 2.21 1.44 0.70 1.02 7 3.80 2.25 1.54 0.67 1.03 8 3.95 2.30 1.65 0.63 1.04 9 4.11 2.34 1.76 0.59 1.04 10 4.27 2.39 1.88 0.56 1.05 11 4.44 2.44 2.00 0.53 1.06 12 4.62 2.49 2.13 0.50 1.06 13 4.80 2.54 2.27 0.47 1.06 14 5.00 2.59 2.41 0.44 1.07 15 5.20 2.64 2.56 0.42 1.07 60.07 44.59 15.48 NPV of FF

5.36

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Question 3 You are an original owner of a publicly traded food service company c

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