# Calculating Final Payoffs

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You would like to estimate the weighted average cost of capital for a new airline business. Based on its industry asset beta, you have already estimated an unlevered cost of capital for the firm of 9%. However, the new business will be 25% debt financed, and you anticipate its debt cost of capital will be 6%. If its corporate tax rate is 40%, what is your estimate of its WACC?

Weston Enterprises is an all-equity firm with two divisions. The soft drink division has an asset beta of 0.60, expects to generate free cash flow of $50 million this year, and anticipates a 3% perpetual growth rate. The industrial chemicals division has an asset beta of 1.20, expects to generate free cash flow of $70 million this year, and anticipates a 2% perpetual growth rate.

Suppose the risk-free rate is 4% and the market risk premium is 5%.

a. Estimate the value of each division.

b. Estimate Weston's current equity beta and cost of capital. Is this cost of capital useful for valuing Weston's projects? How is Weston's equity beta likely to change over time?

IDX Tech is looking to expand its investment in advanced security systems. The project will be financed with equity. You are trying to assess the value of the investment, and must estimate its cost of capital. You find the following data for a publicly traded firm in the same line of business:

Debt Outstanding $400 million

No. of Share 80 million

Stock Price $15.00

Book Value $6.00

Beta of Equity 1.2

What is your estimate of the project's beta? What assumptions do you need to make?

In mid-2009, Rite Aid had CCC-rated, 6-year bonds outstanding with a yield to maturity of 17.3%. At the time, similar maturity Treasuries had a yield of 3%. Suppose the market risk premium is 5% and you believe Rite Aid's bonds have a beta of 0.31. The expected loss rate of these bonds in the event of default is 60%.

a. What annual probability of default would be consistent with the yield to maturity of these bonds in mid-2009?

b. In mid-2012, Rite-Aid's bonds had a yield of 8.3%, while similar maturity Treasuries had a yield of 1%. What probability of default would you estimate now?

Suppose the risk-free interest rate is 5%, and the stock market will return either 40% or -20%

each year, with each outcome equally likely. Compare the following two investment strategies:

(1) invest for one year in the risk-free investment, and one year in the market, or (2) invest for

both years in the market.

a. Which strategy has the highest expected final payoff?

b. Which strategy has the highest standard deviation for the final payoff?

c. Does holding stocks for a longer period decrease your risk?

Consider two local banks. Bank A has 100 loans outstanding, each for $1 million, that it expects will be repaid today. Each loan has a 5% probability of default, in which case the bank is not repaid anything. The chance of default is independent across all the loans. Bank B has only one loan of $100 million outstanding, which it also expects will be repaid today. It also has a 5% probability of not being repaid. Explain the difference between the type of risk each bank faces.

Which bank faces less risk? Why?

The following table shows the one-year return distribution of Startup, Inc. Calculate

a. The expected return.

b. The standard deviation of the return.

Probability 40% 20% 20% 10% 10%

Return -100% -75% -50% -25% -1000%.

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#### Solution Summary

The solution assists with calculating final payoffs.

Quantitative Methods

The owner of the Columbia Construction Company must decide between building a housing development, constructing a shopping center, or leasing all of the company's equipment to another company. The profit that will result from each alternative will be determined by whether material costs remain stable or increase. The profit from each alternative given the two possibilities for material costs is shown in the following payoff table.

Material Costs

Decision Stable Increase

Houses $70,000 $30,000

Shopping Center $105,000 20,000

Leasing $ 40,000 40,000

Determine the best decision using the following decision criteria.

A. Maximax

B. Maximin

C. Minimax Regret

D. Hurwicz (x=.2)

E. Equal likelihood

Please show the work for each problem.

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