Constant Growth Valuation: Krispy Inc.\'s common stock is expected to pay a divi

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

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