Crisp Cookware'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 0.6. The risk-free rate is 5.8% and the market risk premium is 5%. The dividend is expected to grow at some constant rate, gL, and the stock currently sells for $80 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 calculations. Round your answer to the nearest cent.

P3 = $96.9425 rounded off to $96.94

Explanation:

To calculate the market price of the stock three years from today (P3), we will use the constant growth model of DDM. The constant growth model calculates the values of the stock based on the present value of the expected future dividends from the stock. The formula for price today under this model is,

P0 = D1)  /  (r - g)

Where,

To calculate the price of the stock today (P0), we use the dividend expected for the next period (D1). So, to calculate the price at the end of 3 years (P3) we will use D4.

We first need to calculate r using the CAPM equation. The equation is,

r = rRF + Beta * rpM

Where,

r = 0.058 + 0.6 * 0.05  

r = 0.088 or 8.8%

Using the price formula for DDM above and the values for P0, D1 and r, we can calculate the g to be,

80 = 1.75 / (0.088 - g)

80 * (0.088 - g) = 1.75

7.04 - 80g = 1.75

7.04 - 1.75 = 80g

5.29/80 = g

g = 0.066125 or 6.6125%

We first need to calculate D4.

D4 = D1 * (1+g)^3

D4 = 1.75 * (1+0.066125)^3

D4 = 2.12061793907

Using the formula from DDM for P3, we can calculate P3 to be,

P3 =  2.12061793907 / (0.088 - 0.066125)

P3 = $96.9425 rounded off to $96.94

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