Solutions to Homework 3,
Topic 6: Equity Valuation
1. Suppose that the consensus forecast of security analysts of your favorite company is that earnings
next year will be
E1 = $5.00
per share. Sup-
pose that the company tends to plow back 50% of its earnings and pay the rest as dividends. If the Chief Financial Ocer (CFO) estimates that the company's growth rate will be 8% from now onwards, answer the following questions.
(a) If your estimate of the company's required rate of return on its stock is 10%, what is the equilibrium price of the stock? The equilibrium price of a stock can be determined using Gordon's growth formula as follows:
5) .10 − g
g = 0.05.
2. This question requires data collection.
You can nd all numbers on
The questions concern Microsoft (ticker: MSFT).
The answers are for the numbers as of August 5, 2013.
[Figure 1 about here.]
(a) What is the current price and the current price-earnings ratio?
The current price is $31.74, the current earnings per share (EPS) are $2.58, and the current price-earnings ratio is 31.74/2.58=12.30. All these statistics are in the table under Summary". (b) What is the current plow-back ratio? The earnings per share are $2.58, and the dividends per share are $0.92, so that the plow-back ratio is (2.58-0.92)/2.58 = 0.6434 or 64.34%. Microsoft reinvests (plows back) almost 64% of its
earnings and pays out the other 36% to its shareholders. (c) What is the growth rate of earnings for the next 5 years according to the analysts? Hint: look for annual growth rates under analyst estimates" The consensus forecast for the next 5 years is an average annual earnings growth rate of 8.63% (d) What is the beta of MSFT? Hint: look for key statistics". If the risk-free rate (Rf ) is 4% and the market risk premium
E[RM −Rf ]
is 6%, what is the required rate of return on MSF according to the CAPM? The beta of MSF is 0.90. The security market line of the CAPM tells us that the required rate of return is given by:
E[RM SF ] = Rf + βM SF (E[RM − Rf ]) = .04 + 0.90 ∗ .06 = 0.0940
(e) Assume that Microsoft will have earnings and dividends that will grow at the analysts forecasted rate forever after; i.e., the Gordon growth model (GGM) applies. What is the price-earnings ratio
that the GGM predicts for Microsoft? The price-earnings ratio in the GGM is given by:
(1 − b)(1 + g) (1 − .6434)(1 + .0863) P0 = = = 50.3084 E0 (R − g) (.0940 − .0863)
(f ) What growth rate does the market price-earnings ratio price in/imply? The market price-earnings ratio is 12.30.
(1 − b)(1 + g) P0 = E0 (R − g) (1 − b) 12.30 ⇔ = (1 − .6434) ⇔ 34.4924 = ⇔ 34.4924R − 34.4924 ∗ g = ⇔g = = ⇔
(1 + g) (R − g) (1 + g) (R − g) (1 + g) (R − g) 1+g 34.4924R − 1 1 + 34.4924 34.4924 ∗ 0.0940 − 1 = 0.0632 1 + 34.4924
The market prices in a 6.32% earnings growth rate, which is lower than the 8.63% growth rate of the analysts. This makes sense
because the price-earnings ratios in the data is much lower than the price-earnings ratios in the GGM.
Topic 7: Arbitrage
3. The stock PolarBear.com trades on both the South Pole Stock Exchange and the North Pole Stock Exchange.
(a) Suppose the price on the North Pole is $18. What does the NoArbitrage Condition say about the price on the South Pole? (Assume no trading costs.) To rule out arbitrage, the price on the South Pole must be the same as on the North Pole, $18.
(b) Suppose the price on the North Pole is $18 and the price on the the South Pole is $17? How can you make an arbitrage prot?
(Assume no trading costs.) You can make...