Question

A stock just paid an annual dividend of $1.6. The dividend is expected to grow by 9% per year for the next 4 years. The growth rate of dividends will then fall steadily from 9% after 4 years to 4% in year 8.

The required rate of return is 12%.

What is the stock price if the dividend growth rate will stay 4% forever after 8 years?

Answer 1

We have following information

D0 = current dividend paid = $1.60 per share

k = required rate of return = cost of equity =12%

g = growth rate of dividends = 9% for year 1, year 2, year 3 and year 4

The growth rate of dividends will then fall steadily from 9% after 4 years to 4% in year 8

Therefore, (9% - 4%) / 4 = 5%/4 = 1.25% fall in growth rate every year; 7.75% in year 5, 6.50% in year 6, 5.25% in year 7 and 4% in year 8

Stable growth rate after year 8 is 4% forever.

With the given dividend growth rate, we can calculate the actual dividends for year 1 to 8.

			Dividend paid
D1	=	D0 * (1+9%)	$       1.74
D2	=	D1 * (1+9%)	$       1.90
D3	=	D2 * (1+9%)	$       2.07
D4	=	D3 * (1+9%)	$       2.26
D5	=	D4 * (1+7.75%)	$       2.43
D6	=	D5 * (1+6.50%)	$       2.59
D7	=	D6 * (1+5.25%)	$       2.72
D8	=	D7 * (1+4%)	$       2.83

The dividends occurring in the stable growth period of 4% from eight year's dividend:

D8 = D7 * (1+4%) = $2.72 *1.04 = $2.83

Now we can calculate the present value of each dividend; where required rate of return is 12%.

Dividend paid	Present value (PV) = Dividend/ (1+12%)
$       1.74	$                      1.56
$       1.90	$                      1.70
$       2.07	$                      1.85
$       2.26	$                      2.02
$       2.43	$                      2.17
$       2.59	$                      2.31
$       2.72	$                      2.43

We can apply the stable-growth Gordon Growth Model formula to these dividends to determine the residual value in the terminal year

=D8 / (k-g)

= $2.83/ (0.12 -0.04) = $35.38

The present value of these stable growth period dividends (residual value) are

$35.38 / (1.12) ^7 = $16.00

Now add the present values of future dividends to get current stock price

$1.56 + $1.70 + $1.85 + $2.02 + $2.17 + $2.31 + $2.43 + $16.00

= $30.03 (rounding off to two decimal points)

The company’s stock is worth $30.03 per share.