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Lecture 1: Introduction and Review on Time Value of Money, Cost of Capital

Note:

This topic has more questions than can be covered in a 2 hour session. The questions to be covered by your tutor are indicated by an asterisk (*); the rest should be viewed as extra practice problems.

Time Value of Money

4-3. Calculate the future value of $4000 in:

a. Three years at an interest rate of 6% per year.

b. Six years at an interest rate of 6% per year.

c. Three years at an interest rate of 12% per year.

d. Why is the amount of interest earned in part (a) less than half the amount of interest earned in part (b)?

4-4. What is the present value of $13,000 received:

a. Ten years from today when the interest rate is 4% per year?

b. Twenty years from today when the interest rate is 8% per year?

c. Five years from today when the interest rate is 2% per year?

4-5*. Your brother has offered to give you either $60,000 today or $100,000 in 12 years. If the interest rate is 6% per year, which option is preferable?

4-15*. Marian Plunket owns her own business and is considering an investment. If she undertakes the investment, it will pay $40,000 at the end of each of the next three years. The opportunity requires an initial investment of $10,000 plus an additional investment at the end of the second year of $50,000. What is the NPV of this opportunity if the interest rate is 9% per year? Should Marian take it?

4-48. Suppose you invest $3500 today and receive $9500 in five years.

a. What is the IRR of this opportunity?

b. Suppose another investment opportunity also requires $3500 upfront, but pays an equal amount at the end of each year for the next five years. If this investment has the same IRR as the first one, what is the amount you will receive each year?2

Cost of Capital

12-1. Suppose Pepsico’s stock has a beta of 0.59. If the risk-free rate is 3% and the expected return of the market portfolio is 7%, what is Pepsico’s equity cost of capital?

12-2*. Suppose the market portfolio has an expected return of 10% and a volatility of 20%, while Microsoft’s stock has a volatility of 30%.

a. Given its higher volatility, should we expect Microsoft to have an equity cost of capital that is higher than 10%?

b. What would have to be true for Microsoft’s equity cost of capital to be equal to 10%?

12-10*.You need to estimate the equity cost of capital for XYZ Corp. You have the following data available regarding past returns:

a. What was XYZ’s average historical return?

b. Compute the market’s and XYZ’s excess returns for each year. Estimate XYZ’s beta.

c. Suppose the current risk-free rate is 3%, and you expect the market’s return to be 8%. Use the CAPM to estimate an expected return for XYZ Corp.’s stock.

d. Would you base your estimate of XYZ’s equity cost of capital on your answer in part (a) or in part (c)?

12.11*. Use the regression analysis and the data provided in the spreadsheet provided to estimate the beta of HP Inc. (ticker HPQ) stock based on their monthly returns from 2011-2015.

12-15.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 2%. Suppose the market risk premium is 4% and you believe Rite Aid’s bonds have a beta of 0.39. If the expected loss rate of these bonds in the event of default is 52%.

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

b. In mid-2015, Rite-Aid’s bonds had a yield of 8.8%, while similar maturity Treasuries had a yield of 0.8%. What probability of default would you estimate now? Assume Rite Aid’s debt beta, market risk premium and expected loss rate did not change.

12-16*.During the recession in mid-2009, homebuilder KB Home had outstanding 7-year bonds with a yield to maturity of 8.7% and a BB rating. If corresponding risk-free rates3 were 3.5%, and the market risk premium was 5.1%, estimate the expected return of KB Home’s debt using two different methods. How do your results compare? Use the recession estimates in Table 12.2 and an expected loss rate of 60% (provided by the textbook).

12-17. The Dunley Corp. plans to issue 5-year bonds. It believes the bonds will have a BBB rating. Suppose AAA bonds with the same maturity have a 4% yield. Assume the market risk premium is 5% and use the data in Table 12.2 and Table 12.3.

a. Estimate Dunley’s cost of debt, the yield Dunley will have to pay, assuming an expected 50% loss rate in the event of default during average economic times.

b. Estimate the yield Dunley would have to pay if it were a recession, assuming the expected loss rate is 71% at that time, but the beta of debt and market risk premium are the same as in average economic times.

12-26*. Unida Systems has 42 million shares outstanding trading for $10 per share. In addition, Unida has $94 million in outstanding debt. Suppose Unida’s equity cost of capital is 16%, its debt cost of capital is 8%, and the corporate tax rate is 35%.

a. What is Unida’s asset cost of capital or unleveraged cost of capital?

b. What is Unida’s after-tax debt cost of capital?

c. What is Unida’s weighted average cost of capital?

d. If you are evaluating a project and consider that that project has the similar risk as Unida System, estimate the project’s cost of capital if the project is financed by all equity? If the project is financed by both debt and equity as similar to Unida, is the project’s cost of capital higher or lower?