Constant Growth Valuation: Krispy Inc.\'s common stock is expected to pay a divi
ID: 2653164 • Letter: C
Question
Constant Growth Valuation:
Krispy Inc.'s common stock is expected to pay a dividend of $1.75 a share at the end of this year (D1 = $1.75); its beta is 0.95; the risk-free rate is 5.2%; and the market risk premium is 4%. The dividend is expected to grow at some constant rate g, and the stock currently sells for $25 a share. Assuming the market is in equilibrium, what does the market believe will be the stock's price at the end of 3 years (i.e., what is )? Do not round intermediate steps. Round your answer to the nearest cent.
Explanation / Answer
For this First we have to calculate Required Rate of Return.
Which can be Calculated through CAPM.
Required Rate of Return according to CAPM:
R = Rf + Beta (RM - Rf)
R = Required Rate of Return, Rf = Risk Free Rate = 5.2%, (RM - Rf) = Market Risk Premium = 4%, Beta = 0.95
R = 5.2 + 0.95 (4)
R = 9%
So, Required Rate of Return = 9%
Now we can calculate Dividend Growth Rate by Constant Growth Model.
P0 = D1 / k - g
P0 = Price of the Stock = 25, D1 = Dividend next Year = 1.75, k = Cost of Capital = 9%, g = Dividend Growth Rate = X
25 = 1.75/ 0.09 - X
25(0.09 - X) = 1.75
X = 2% , So, the growth Rate is 2%
We have to Calculate Price of the Share at the End of 3 Years, so first we will calculate D4
D2 = 1.75 x 1.02 = $1.785
D3 = 1.785 x 1.02 = $1.8207
D4 = 1.8207 x 1.02 = $1.857114
Calculation of P3 = D4 / k - g
P3 = 1.857114 / 0.09 - 0.02
P3 = 26.53
So, the Stock price at the End of 3 Years is $26.53