Beta and Value A firm is expected to pay an annual dividend of $.80 next year. A

ID: 2805089 • Letter: B

Question

Beta and Value A firm is expected to pay an annual dividend of $.80 next year. After next year the firm’s dividends will grow at a steady state rate of 6% per year. You are trying to value the stock and Value Line lists a stock beta of 1.42 while Yahoo is reporting a beta of 1.37. The stock is currently priced at $11.40. If E(RM) – Rf = 9.3% and the risk free rate is 2.6% the stock is ____________________ if you use the Value Line beta and is ____________________ if you use the Yahoo beta.

overpriced by $3.24; overpriced by $2.84

underpriced by $1.14; underpriced by $1.44

underpriced by $1.44; underpriced by $1.14

overpriced by $2.84; overpriced by $3.24

Explanation / Answer

First we use the CAPM method to calculate the required return or cost of capital -

ER = Rf + Beta x (E(Rm) - Rf)

Then, we compute the stock price as follows using dividend discount model in case of constant growth -

P0 = Expected dividend (D1) / (Ke - g)

where, Ke = Required return / cost of capital, g = growth rate, P0 = price of stock today

Value line

ER = 2.6% + 1.42 x 9.3% = 15.806% or 0.15806

P0 = $0.80 / (0.15806 - 0.06) = $8.16 (rounded off)

Yahoo

ER = 2.6% + 1.37 x 9.3% = 15.341% or 0.15341

P0 = $0.80 / (0.15341 - 0.06) = $8.56 (rounded off)

From both the prices and comparing it to the current stock price, we can see that the stock in overpriced by $3.24 ($11.40 - $8.16) if you use the value line beta and is overpriced by $2.84 ($11.40 - $8.56) if you se the yahoo beta.

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Beta and Value A firm is expected to pay an annual dividend of $.80 next year. A

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