8. If the risk-free rate is currently 5.6% and the market rate of return is 11.5

Question

8. If the risk-free rate is currently 5.6% and the market rate of return is 11.5%, what would be the required rate of return on a stock with a beta of 1.3? Now suppose that the stock is selling for $32 per share and just recently paid a dividend of $1.80 and it has an expected growth rate of 6.2%. Is the price of this stock too high or too low? Explain. Also explain what would happen to the required return of this stock if inflationary expectations increase by 2%, or the rate of return on the market decreases to 10% or the beta of the stock decreases to 1.1. Analyze each of these changes independently. (7 pts.)

Explanation / Answer

Risk-free rate (Rf) = 5.6% = 0.056

Market rate of return (Rm) = 11.5% = 0.115

Beta (B) = 1.3

Required rate of return (k) = Rf  + B * (Rm - Rf) (According to Capital Asset Pricing Model)

i.e. k = 0.056 + 1.3 (0.115 - 0.056) = 13.27%

According to Gordon Dividend Growth Model;

Value of stock = D1/ (k - g)
where:
D1 = next year's expected annual dividend per share = $1.80 (1 + 0.062) = $1.9116
k = the required rate of return (as estimated using the Capital Asset Pricing Model) = 13.27% = 0.1327
g = the expected dividend growth rate = 6.2% = 0.062

So, Value of Stock = $1.9116 / (0.1327 - 0.062) = $27.04 per share

Market Price of Stock = $32 per share, which is too high of the actual value of the stock ($27.04) as determined above.

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