# Finance:CAPM, Time value of money etc.

1) Stocks A and B have the following distributions:

State Probability of state Return on Stock A Return on Stock B

Boom 30% 12% -2%

Normal 60% 8% 2%

Bust 10% 4% 6%

a) Calculate each stock's expected return, standard deviation and coefficient of variation.

b) Calculate the expected return, standard deviation and coefficient of variation for a portfolio invested $14,000 in Stock A and $6,000 in Stock B.

2) Consider the following two stocks:

Beta Expected Return

Merck Pharmaceutical 1.4 25%

Pizer Drug Corp. 0.7 14%

Assume the CAPM holds. Based on the CAPM, what is the return on the market? What is the risk free rate?

3) Calculate the weighted average cost of capital for the Luxury Porcelain Company. The book value of Luxury's outstanding debt is $60 million. Currently, the debt is trading at 120 percent of book value and is priced to yield 12%. The 5 million outstanding shares of Luxury stock are selling for $20 per share. The required return on Luxury's stock is 18 percent. The tax rate is 25 percent.

4) Shortroad Inc. has the following target capital structure:

Debt 30%

Preferred stock 15%

Common stock 55%

Total capital 100%

Stockholders expect earnings and dividends to grow at a constant rate of 8 percent in the future. Shortroad's tax rate is 34 percent. Treasury bonds yield 5 percent and the market risk premium is 8 percent. Shortroad has a beta of 1.4. The following information is also available:

Common stock: It is assumed that no new common stock would be issued.

Preferred stock: New preferred stock could be sold to the public at a price of $100 per share, with a dividend of $10. Flotation costs of $5 per share would be incurred.

Debt: Shortroad's 15-year 10% semiannual coupon bonds ($1,000 par value) are currently selling for $1,207.50.

a) Find the component cost of debt

b) Find the component cost of preferred stock

c) Find the component cost of common equity using the CAPM model

d) Find the firm's WACC

5) The WSJ of September 4 had an article titled " Is it time to scrap the P/E Ratio". Define P/E and explain how one may interpret that ratio. What information does it convey. Why does the WSJ think that perhaps it is time to scrap that ratio.

6) Consider a bond with a par value of $1,000. The coupon is paid semi-annually and the market interest rate (effective interest rate) is 10 percent. How much would you pay for the bond if:

a) The coupon rate is 8% and the remaining time to maturity is 20 years?

b) The coupon rate is 12% and the remaining time to maturity is 15 years?

7) A 20-year maturity 9% coupon bond paying coupons semiannually is callable in 5 years at a call price of $1,060. The bond currently sells at a yield to maturity of 7%. What is the yield to call? Would the firm likely call this bond and if so, why?

8) Assume NetWonders is operating in a new industry that has recently caught on with the public. The latest annual dividend, paid yesterday, was $1. Due to high growth in sales, a 25% growth rate in cash dividends is expected over the next four years. Thereafter, the growth rate is expected to be 5% forever. The required rate of return on the stock is 22%. What is a share of NetWonders common stock worth?

9) You are saving for the college education of your two children. One child will enter college in 5 years, while the other child will enter college in 7 years. College costs are currently $20,000 per year and are expected to grow at a rate of 5 percent per year. All college costs are paid at the beginning of the year. You assume that each child will be in college for four years. You currently have $50,000 in your educational fund. Your plan is to contribute a fixed amount to the fund over each of the next 5 years. Your first contribution will come at the end of this year, and your final contribution will come at the date at which you make the first tuition payment for your oldest child. You expect to invest your contributions into various investments which are expected to earn 8 percent per year. How much should you contribute each year in order to meet the expected cost of your children's education?

10) Today is Rachel's 30th birthday. Five years ago, Rachel opened a brokerage account when her grandmother gave her $25,000 for her 25th birthday. Rachel added $2,000 to this account on her 26th birthday, $3,000 on her 27th birthday, $4,000 on her 28th birthday, and $5,000 on her 29th birthday. Rachel's goal is to have $400,000 in the account by her 40th birthday. Starting today, she plans to contribute a fixed amount to the account each year on her birthday. She will make 11 contributions, the first one will occur today, and the final contribution will occur on her 40th birthday. Complicating things somewhat is the fact that Rachel plans to withdraw $20,000 from the account on her 35th birthday to finance the down payment on a home. How large does each of these 11 contributions have to be for Rachel to reach her goal? Assume that the account has earned (and will continue to earn) an effective return of 12 percent a year.

11) Consider a pharmaceutical firm that is developing a new drug that it expects will have a significant effect. The firm has anticipated that the cash flows from this drug will begin at t=11 after FDA approval and continue for 15 years. Assume further that the cash flows beginning at t=11 will equal $1,800,000 per year and will remain constant for fifteen years. Assuming that the firm wishes to earn a minimum of 16%, what would be the present value as of today, t=0, of these cash flows?

12) In this problem, you will need to go to yahoo finance. Find the information for Ford Motor Company, and then click on statistics. Get the current beta value, current stock price, dividend information and next five years PEG growth rate. The current 10 year US treasury rate is about 2.5%. Use this as your risk-free rate and determine the current required rate of return for Ford. Then, determine the expected rate. Is Ford overpriced or underpriced based on your analysis? Be sure to show all work and discuss. Also, make sure you note the date from which you draw your information from yahoo and include a copy of those pages.

13) Why would someone purchase one share of Berkshire-Hathaway stock which is currently priced at around $123,914 per share when they could easily purchase far more shares of ATT which is selling for around $29 per share? Explain. Does price per share matter?

14) The Wall Street Journal and other publications have had a number of articles about the issues with pension funds. See WSJ of 9-18-2010, front page. Discuss the issues concerning pension funds and their safety. In general, how do they determine if a pension is underfunded or overfunded.

15) How would the price of a share of stock vary with the time an investor prefers to hold the stock? That is, suppose you have a planned holding period of 3 years and someone else has a planned holding period of 5 years. How would that affect the current price of the stock? Explain.

#### Solution Summary

The problem set deal with issues in finance: Capital asset pricing model (CAPM), stock returns, standard deviation, coefficient of variation and weight of capital sources.