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A share of stock with a beta of 0
A share of stock with a beta of 0.76 now sells for $51. Investors expect the stock to pay a year-end dividend of $3. The T-bill rate is 3%, and the market risk premium is 6%. If the stock is perceived to be fairly priced today, what must be investors' expectation of the price of the stock at the end of the year? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Expert Solution
Computation of Price of Stock at the End of the Year:
Ke = Rf + Beta(Rm-Rf)
Here,
Ke = Expected Return on Stock = ?
Rf = Risk-free Rate = 3%
Beta = 0.76
Rm-Rf = Market Risk Premium = 6%
Ke = 3% + 0.76*6%
= 3% + 4.56%
Ke = 7.56%
So, Expected Return on Stock (Ke) is 7.56%
P0 = (P1+D1)/(1+Ke)
Here,
P0 = Current Price of Stock = $51
P1 = Price for Next Year = ?
D1 = Dividend for Next Year = $3
Ke = Expected Return on Stock = 7.56% or 0.0756
$51 = (P1 + $3)/(1+0.0756)
$51*1.0756= P1 + $3
$54.86 = P1 + $3
P1 = $54.86 - $3
P1 = $51.86
So, Price for next year is $51.86
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