Question 2 You are an original owner of a publicly traded food service company named 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 equity today to open a new fast food division (FF). Opening this new division costs $15M today, which you will fund by issuing equity. Revenues from this new division are expected to be $8M next year and are projected to grow by 2.5 percent per year. Costs from this new division are expected to be $6M next year and are projected to grow by 2 percent per year. The life of this project is 15 years. Analyses of other fast food businesses suggest that the beta of a typical 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 5 percent. a) What is the NPV of this new investment? Is the investment worthwhile? (Hint: you will first need to use the CAPM to find the correct discount rate. Then 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 five years tells you that the beta of the high-end division equals 1.5. Directly before the investment in the fast food division, the assets of SF were worth $50M. 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 Vos Voi + Voz -BD1 + V02 Voi+Vp2 -BD2 where D1 represents "Division 1" and D2 represents "Division 2" (in this case, the high-end division and the fast food division). The value of the new division equals the present value of its future net cash flows. When calculating the value of the fast food division, do not subtract the initial $15M cost, as this was paid for using newly-issued equity. c) The value of the existing debt on the balance sheet of Smith's Foods is $25M. Assume that the beta of this debt equals 0.05. What is the beta of the firm's equity after the announcement of the new division? (Hint: use the BE equation on slide 26 in the Week 2 lecture slides. To calculate E, add the values of the two divisions to get the value of assets, and then subtract the value of debt.) d) The equity beta of the firm decreased as a result of the announcement. Discuss the two ways in which the announcement decreased the equity beta. (Hint: refer again to slide 26 in the Week 2 lecture slides.)