Calculate the betas of t-bills

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Reference no: EM134659

You recently joined "Arigato", a Japanese company that owns a chain of sushi restaurants across the state.

The company's stock is hundred percent owned by its two cofounders and the current market price of each of the 1 million shares of stock is \$20.

One of your first big assignments at work was working in a team with a few other employees of the company on evaluating the level of risk of the company, and compare it with that of its competitors in the restaurant business. Your team identified four main competitors, also owned fully by their respective cofounders: Todai, Yamashiro, Sakana, and Mika. The sizes of the four competing companies are comparable to the size of your company. You have found out that the risk of "Arigato" reflects the average risk of the competitors. In your role of financial analysts, you applied your sophisticated finance knowledge and obtained the following information regarding various financial investments:

 Actual expected annual return (%) Variance of annual returns Covariance of annual returns with those of the market portfolio Treasury bills 5 0 0 S&P 500 (proxy for the market portfolio) 15 20 20 Todai 5.5 80 8 Yamashiro 8 49 11 Sakana 11 36 11 Mika 18.5 65 10

Your most recent assignment is to evaluate the profitability of a new investment project: opening a new sushi restaurant in Pomona. You were asked to analyze the projected revenues and costs and advise the board of directors on the company's future financial planning. Below is the information regarding the project:

 Project life 4 years Initial investment \$2,000,000 Number of customers per year 70,000 Average price customer pays \$18 per person Vallet parking paid by 30% of customers \$3 per person Variable costs per average customer per year \$5 per person Annual increase in variable costs after the 1st year due to forecast inflation 3% Riskiness of the project measured by Beta 1.2

Corporate income tax rate is 34%. The project equipment (i.e., the initial investment) will depreciate on the straight line over 4 years to zero salvage value.

Based on the above information, answer the following questions:

Question 1. Calculate the Betas of T-bills, S&P500 and the four competitors. Which one of these has the highest total risk (explain what total risk means)? The highest systematic risk (explain what systematic risk means)? Calculate and explain all calculations.

Question 2. You analyzed the company's performance and prepared a report for your boss regarding the relative riskiness of the company's as well as of its competitors' stock returns. In this report you concluded that the expected return on the company's stock correctly reflects its systematic risk. Based on this, what is the annual rate of return on equity that investors require? Calculate and explain.

Question 3. What is the weighted average cost of capital for the proposed investment project? Is the project as risky as the company? Calculate both and explain your calculations.

Question 4. Would you recommend your boss to accept or reject the new sushi restaurant project? Calculate the net present value of the proposed project. Explain all calculations.

Question 5. How would the systematic risk of the company change if the project got accepted? For that you can use the information given earlier about the company's current capital structure, and the fact that another \$2,000,000 worth of additional equity was raised to cover the initial cost of the project. (Hint: you can view the new company with the project as a portfolio.) Calculate the answer and explain your calculations.

Question 6. You and your company's co-owners decided to do an extra research regarding the possible debt financing of the project. You did some additional calculations and came to conclusion that paying for the initial investment of the project with equity alone is not optimal. You believe that financing half of the total initial investment by debt and only half by equity would be a good target debt-equity ratio, and that using it would maximize the value of the new sushi restaurant project. The debt is risk-free and thus has the same expected return as the risk-free asset. It is interest-only loan, which means that it will require annual interest payments for four years, and the principal will be fully repaid at the end of the fourth year.

(a) What is the current value of the project using the Adjusted Present Value (APV) approach? Calculate and explain.

(b) What is the current value of the project using the Cash Flow-to-Equity (FTE) approach? Calculate and explain.

(c) Finally, what would be the current value of the project based on the Weighted Average Cost of Capital (WACC) approach? Calculate and explain.

Question 7. Would your answers to Question 6-(a), (b), (c) change if the debt instead looked like a four-year amortizing loan, with fixed total annual payments in all four years? (You can review what amortizing loans look like in Ross, Westerfield, Jordan textbook that you used in FRL300 class, or you can use other sources.) Explain and show all calculations as well as what changes in your answers to 6-(a), (b), and (c), where necessary.