EXERCISES FOR CHAPTER 1With Solutions

Exercise 1.

At the beginning of 2002, the shares of General Motors Corporation traded at $60 each, and closed the year in December at $40. GM paid a $2.00 dividend on each share during the year.

a. What was the rate of return that shareholders earned on GM shares during 2002?

b. The yield on long-term US Treasuries at the beginning of 2002 was 5% and you require a 5% risk premium for this stock. What is your required rate of return (the beta return)?

c. Using this required rate of return, what is the abnormal rate of return return (alpha) for the year?

(Refer to Box 1.1. See also p. 44)

Solution

a. Return = (40 – 60 + 2) = -18 (returns are capital gain (loss) plus dividends)

Rate of return = -18/60 = -30%

b. Required return = Risk free return + risk premium = 5% + 5% = 10%

The risk premium might be calculated with an “asset pricing model” (a beta technology), like the Capital Asset Pricing Model.

c. Abnormal rate of return = Rate of return – Required rate of return = -30% - 10% = -40%

Exercise 2.

At one point during the internet and telcom bubble of the late 1990s, Cisco Systems, the manufacturer of routers for communications networks, traded at a market capitalization of over half a trillion dollars, the largest market capitalization for any firm ever. Its P/E was 130. Analysts said that Cisco was such a good company that investors should buy it at any price.

Comment on the analyst recommendation.

(Refer to pp. 7-9)

Solution

Good companies can be overpriced. A P/E of 130 has rarely been observed for a firm with large market capitalization: the historical P/E for the S&P 500 is 14. These observations suggest that Cisco’s price should be challenged with some fundamental analysis. Price is what you pay, value is what you get.

Exercise 3.

With its shares trading at $89 in September 2003, the market capitalization of IBM’s common equity was $153.97 billion. IBM listed $14 billion of debt on its most recent balance sheet.

a. How many common shares were outstanding?

b. What value was the market placing on IBM’s enterprise value (the value of the firm)?

c. IBM listed 199 million shares in treasury stock on its balance sheet. How many issues shares were there?

(Refer to page 11)

Solution

a. Shares outstanding = Market cap/price per share = $153.97/89 = 1,730 million

b. Enterprise value = Value of Equity + Value of debt

= $153.97 + 14 = $167.97

This calculation assumes that the debt is carried on the balance sheet at an amount close to its value (which it usually is).

c. Shares outstanding = issues shares – shares (repurchased) in treasurySo, issued shares = 1,730 million + 199 million

= 1,929 million