Question

Lohn Corporation is expected to pay the following dividends over the next four years: $16, $12, $9, and $5. Afterward, the company pledges to maintain a constant 7 percent growth rate in dividends forever. If the required return on the stock is 15 percent, what is the current share price?

Multiple Choice

(A) $75.01

(B) $70.00

(C) $67.64

(D) $66.50

(E) $72.10

Answer 1

We have following information

k = required rate of return on the stock = cost of equity =15%

g = growth rate of dividends = 7% from 5^th year onwards

The expected dividends for year 1 to 4 -

D1 = $16

D2 = $12

D3 = $9

D4 = $5

The dividends occurring in the stable growth period of 7% from 5th year's dividend:

D5 = $5*1.07 = $5.35

Now we can calculate the present value of each dividend; where required rate of return is 15%.

Present value of dividend = Dividend paid / (1+k) ^t    (where t is the time period)

PV1 = $16/ 1.15 = $13.913

PV2 = $12/ (1.15) ^2 = $9.074

PV3 = $9/ (1.15) ^3 = $5.918

PV4 = $5/ (1.15) ^4 = $2.859

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

=D5 / (k-g)

= $5.35/ (0.15 -0.07) = $66.875

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

$66.875 / (1.15) ^4 = $38.236

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

$13.913 +$9.074 +$5.918 + $2.859 +$38.236 = $69.9999 or $70.00 (rounding off to two decimal points)

The company’s stock price is $70.00 per share.

Therefore correct answer is option (B) $70.00