Question

The Duo Growth Company just paid a dividend of $1.2 per share. The dividend is expected to grow at a rate of 24% per year for the next 3 years and then to level off to 6% per year forever. You think the appropriate market capitalization rate is 21% per year.

a. What is your estimate of the intrinsic value of a share of the stock?

b. If the market price of a share is equal to this intrinsic value, what is the expected dividend yield?

c. What do you expect its price to be 1 year from now? Is the implied capital gain consistent with your estimate of the dividend yield and the market capitalization rate?

Answer 1

Answer a.

D0 = $1.2

Growth rate for first 3 years is 24%, followed by a constant growth rate (g) of 6% forever

D1 = $1.200 * 1.24 = $1.488
D2 = $1.488 * 1.24 = $1.84512
D3 = $1.84512 * 1.24 = $2.28795
D4 = $2.287955 * 1.06 = $2.42523

Market Capitalization Rate, k = 21%

P3 = D4 / (k - g)
P3 = $2.42523 / (0.21 - 0.06)
P3 = $16.1682

P0 = $1.488/1.21 + $1.84512/1.21^2 + $2.28795/1.21^3 + $16.1682/1.21^3
P0 = $12.91

Intrinsic Value of Stock is $12.91

Answer b.

Expected Dividend Yield = D1 / P0
Expected Dividend Yield = $1.488 / $12.91
Expected Dividend Yield = 0.115277 or 11.53%

P1 = $1.84512/1.21 + $2.28795/1.21^2 + $16.1682/1.21^2
P1 = $14.1307

Implied Capital Gain Yield = (P1 - P0) / P0
Implied Capital Gain Yield = ($14.1307 - $12.91) / $12.91
Implied Capital Gain Yield = 0.09455 or 9.455%

Market Capitalization Rate = Implied Capital Gain Yield + Expected Dividend Yield
Market Capitalization Rate = 9.455% + 11.53%
Market Capitalization Rate = 20.985 or 21%

So, this is consistent with DDM.