Question

Constant Dividend Growth Valuation

Crisp Cookware's common stock is expected to pay a dividend of $2.25 a share at the end of this year (D₁ = $2.25); its beta is 0.6. The risk-free rate is 6% and the market risk premium is 6%. The dividend is expected to grow at some constant rate, g_L, and the stock currently sells for $40 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

Answer 1

Answer :

We are given that,

Risk-free rate = 6%

Market risk premium = 6%

Beta of stock = 0.6

The Required rate of return on the stock as per CAPM

= Risk-free rate + ( Beta * Market risk premium )

= 6% + ( 0.6 * 6% )

= 9.6%

Now, Current stock price = D1 / ( Required return - Growth rate )

$40 = $2.25 / ( 0.096 - Growth rate )

0.096 - Growth rate = $2.25 / $40 = 0.05625

Growth rate = 0.096 - 0.05625 = 0.03975 (or) 0.04 (Approx.)

Hence, Growth rate of dividend = 4%

D4 = D1 * ( 1 + Growth rate )^3 = $2.25 * 1.04^3 = $2.53

Stock price at the end of year 3 = D4 / ( Required return - Growth rate )

= $2.53 / ( 0.096 - 0.04 )

Stock price at the end of year 3 = $45.18