Homework I

All payments occur at the end of the period unless stated otherwise. Interest is compounded annually unless stated otherwise. Face value of all bonds is $1000.

Short Answer: You should be able to answer these in 2 to 3 sentences.

1. A firm has an asset beta of 1 and a company cost of capital of 15%. A new project comes along with a beta of .2 and an expected return (IRR) of 10%. Putting the project's beta into the CAPM gives the project a return of 5% based on project risk. Should the firm accept or reject the project? Explain. 

2. Regression provides both a beta (used in the CAPM) and an alpha.  There is an interest in "chasing alpha".  What is alpha? Why would investors "chase alpha"?   HINT: Putting "alpha risk investment" into any search engine will give you additional information.    Be sure to put the information in your own words. 

Worked Problems for Partial Credit

1. You invest 30% in Ham and 70% in Cheese.   

Find the return and variance on the portfolio.  You must calculate: expected return for both firms; standard deviation or variance (assume it is a population (n observations)) for both firms; correlation or covariance between Ham and Cheese.

2. Suppose stock returns can be explained by the following three factor model:

R_i = R_F + β₁F₁ + β₂F₂ - β₃F₃

Assume there is no firm-specific risk.  The information for each stock is presented here:

The risk premiums for the factors are 5.3 percent, 3.9 percent, and 4.2 percent, respectively. If you create a portfolio with 60 percent invested in stock A and the remainder in stock B, and the risk-free rate is 2 percent, what is the expected return of your portfolio?

3. Ember is considering an investment of $40 million in plant and machinery.  This is expected to produce free cash flows of $13 million in year 1, $14 million in year 2, $15 million in year 3, and 25 million in year 4.  The tax rate is 35%.  You don't know the target capital structure, but you do have the following information:

• Bonds: There are 37,000 bonds with a 5.5% coupon outstanding. The coupons are paid annually. The bonds have a 1000 face value and 8 years to maturity. They sell for 96.7% of par.
• Retained Earnings (Internal Equity): There are 950,000 shares outstanding with a price of $55 per share. The beta on the stock is 1.25. The risk-free rate is 2% and the market risk premium is 6%.

a) Calculate the weighted average cost of capital.  Hint: To get the weights, you will need to solve for the market value of the debt and equity. 

b) Calculate the net present value (NPV) with the WACC.

c) Should they invest? Why or why not?

4. This is an M&M world with corporate taxes.  Sci-fi is financed with $100,000,000 in debt at 6% and has a stock price of $42 per share.  All earnings are paid out as dividends, and the growth rate is zero.  The firm decides to issue more stock and use the proceeds to repay all debt.  The capital structure change is permanent (so they will be entirely unlevered).  Fill in all of the missing information in the table below.

5. Ajax currently has 20% debt and 80% equity.  Their weighted average cost of capital is 12%, and the cost of debt is 4%.  The tax rate is 40%.  The firm is considering a new project.  The initial investment is $150,000,000, and the project will generate sales of $80M per year for 8 years.  The investment can be depreciated straight-line for 8 years to a zero book value.  There are no working capital requirements.  Operating expenses (not including depreciation or interest) are $42M per year for 8 years.  They plan to fund the project using the proportions listed above and the debt's maturity will match the life of the project.   Find the value of the project using FTE (Flow to Equity).     

6. Learning University is tax-exempt.  They need a new mini-bus for the campus.  They can either buy or lease the bus.  A new bus costs $123,000.  It has a 6-year life with no salvage value.  Depreciation is straight-line over 6 years.  The interest rate (before taxes) is 8%.  If they lease, there will be 6 prepaid lease payments.  What is the maximum lease payment that LU will accept?

7. Conglomerate Company has a cost of capital, based on the CAPM, of 17%. The risk-free rate is 4% and the market risk premium is 10%.  The firm has 3 divisions:

Find the correct cost of capital for evaluating a new generation of electrical equipment.  Explain.