The following information is available in general and about investments in stock
ID: 2673086 • Letter: T
Question
The following information is available in general and about investments in stocks J and K.The market return (kM) = 9%
The risk free rate (kRF) = 5%
Stock J's beta = 0.8
Expected constant growth rate for Stock J = 6%
Investment in Stock J = $80,000
Stock K's beta = 1.4
Expected constant growth rate for Stock K = 7%
Investment in Stock K = $120,000
a. What are the expected returns on Stock J and Stock K individually?
b. What is the expected return on the portfolio?
c. If Stock K just paid a dividend of $2.50, what is Stock K's intrinsic value?
Explanation / Answer
The following information is available in general and about investments in stocks J and K.
The market return (kM) = 9%
The risk free rate (kRF) = 5%
Stock J's beta = 0.8
Expected constant growth rate for Stock J = 6%
Investment in Stock J = $80,000
Stock K's beta = 1.4
Expected constant growth rate for Stock K = 7%
Investment in Stock K = $120,000
a. What are the expected returns on Stock J and Stock K individually?
Stock-J and Stock-K using CAPM equation.
Rj = Rf + [ E(Rm) - Rf]
Rj = Expected return on Stock-J
= beta of stock-J = 0.8
E(Rm) = Expected market return = 9%
Rf = Risk free rate = 5%
Rj = 0.05 + 0.8 [0.09 - 0.05]
= 0.05 + 0.8 [ 0.04]= = 0.05 + 0.032
= 0.082 or 8.2%
, the expected return on Stock-J is 8.2%
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the expected return on Stock-K:
Rk = Rf + [ E(Rm) - Rf]
= beta of Stock-K = 1.4
E(Rm) = Expected market return = 9%
Rf = Risk free rate = 5%
Rk = 0.05 + 1.4 [ 0.09 - 0.05]
= 0.05 + 1.4 [ 0.04]
= 0.05 + 0.056= = 0.106 or 10.6%
the expected return on Stock-K is 10.6%
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b. What is the expected return on the portfolio?
Weight of Stock-J = Investment in Stock-J / Total investment
= $80,000 / ($80,000 + $120,000= $80,000 / $200,000= 0.4 or 40%
Weight of Stock-K = Investment in Stock-K / Total investment
= $120,000 / ($80,000 + $120,000)
= $120,000 / $200,000= 0.6 or 60%
Portfolio expected return
Ep = (Weight of stock-J x Expected return on Stock-J) + (Weight of stock-K x Expected return on Stock-K)
= (0.4 x 0.082) + (0.6 x 0.106)
= 0.0328 + 0.0636= = 0.0964 or 9.64%
the portfolio expected return is 9.64%
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c. If Stock K just paid a dividend of $2.50, what is Stock K's intrinsic value?
Intrinsic value = D1 / (K - g)
where D1 = Dividend in year-1 = $250
K = Required return = 10.6%
g = Expected growth rate = 7%
Intrinsic value = $250 / (0.106 - 0.07)
= $250 / 0.036= $6944.44 or $6944
the stock's intrinsic value using constant growth model is $6944.
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