Constant Growth Valuation Crisp Cookware\'s common stock is expected to pay a di
ID: 2613499 • Letter: C
Question
Constant Growth Valuation
Crisp Cookware's common stock is expected to pay a dividend of $1.5 a share at the end of this year (D1 = $1.50); its beta is 1.15; the risk-free rate is 5.2%; and the market risk premium is 5%. The dividend is expected to grow at some constant rate g, and the stock currently sells for $47 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.
$
Constant Growth Valuation
Crisp Cookware's common stock is expected to pay a dividend of $1.5 a share at the end of this year (D1 = $1.50); its beta is 1.15; the risk-free rate is 5.2%; and the market risk premium is 5%. The dividend is expected to grow at some constant rate g, and the stock currently sells for $47 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
Solution:
Calculation of Required rate using CAPM model:
Required rate = Risk free rate + (Beta * market risk premium)
=5.2% + (1.15*5%)
= 10.95%
Calculation of Growth rate using Dividend Growth formula :
Growth rate = Required rate - (Expected dividend D1 / Current Price )
=10.95% - (1.50 / 47)
= 0.1095 – 0.03191
= 0.077585
Calculation of stock's price at the end of 3 years:
Price (Year 3) = Dividend (Year 4) / (required rate – growth rate )
Dividend (Year 4) = Dividend (Year 1) D1 * (1+ growth rate )^3
=1.50 * (1+0.077585)^3
= 1.50 * 1.251280314
= $1.87692
Hence Price (Year 3) = 1.87692 / (0.1095 – 0.077585)
= 1.87692 / 0.031915
= $58.81