Question

A corporation will pay a $1 dividend in one year, $2.00 in two years and $3 in threee years. After that, dividends are expected to grow by 49% per year. The required rate of return is 9% a. What will be the price of the company's stock two years from now? b. What should be the price of the stock today? 1.

Answer 1

1. Price of a company’s stock is the present value of its all expected future cash flows, therefore stock price after 2 years is the sum of the present value of its all expected future cash flows after year 2

P2 = stock price after 2 years =?

D3 = dividend for year 3 = $3 per share

k = required rate of return or cost of equity = 9%

g = growth rate of dividends = 4% after year 3

The dividends occurring in the stable growth period of 4%, we then apply the stable-growth Gordon Growth Model formula to these dividends to determine their value in the terminal year

Value in the terminal year = D3 * (1+g) / (k –g) = $3 *(1+4%) / (9%- 4%) = $62.40

Now we can calculate the present value at the end of year 2 of dividend and terminal value and add the present values of future dividends and terminal value to get current stock price; where required rate of return is 9%.

Therefore,

P2 = $3 / (1+9%) ^1 + $62.40 / (1+9%) ^1

= $2.75 +$57.25

= $60.00

Therefore stock price after 2 years will be $60.00 per share

2. The expected dividends for year 1 to 3 -

D1 = $1

D2 = $2

D3 = $3

The dividends occurring in the stable growth period of 4% after year 3

Now we can calculate the present value of each dividend; where required rate of return is 9%.

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

PV1 = $1/ 1.09 = $0.92

PV2 = $2/ (1.09) ^2 = $1.68

PV3 = $3/ (1.09) ^3 = $2.32

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

=D3 *(1+g) / (k-g)

= $3 * (1+4%)/ (9% - 4%) = $62.40

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

$62.40 / (1.09) ^3 = $48.18

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

= $0.92 + $1.68 + $2.32 + $48.18

= $53.10 (rounding off to two decimal points)

The company’s stock price today is $53.10 per share.