Question

A company will pay a $2 per share dividend in 1 year. The dividend in 2 years will be $4 per share, and it is expected that dividends will grow at 5% per year thereafter. The expected rate of return on the stock is 12%. a. What is the current price of the stock? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Current price b. What is the expected price of the stock in a year? (Do not round Intermediate calculations. Round your answer to 2 decimal places.) Expected price

Answer 1

a. Current price calculation:

The expected dividends for year 1 and year 2 -

D1 = $2

D2 = $4

The dividends occurring in the stable growth period of 5% after year 2

g = growth rate of dividends = 5% after year 2

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

Now we can calculate the present value of each dividend;

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

PV1 = $2/ 1.12 = $1.79

PV2 = $4/ (1.12) ^2 = $3.19

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

=D2 *(1+g) / (k-g)

= $4 * (1+5%)/ (12% - 5%) = $60.00

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

$60 / (1.12) ^2 = $47.83

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

P0 = $1.79 + $3.19 + $47.83

= $52.81 (rounding off to two decimal points)

The company’s stock price today is $52.81 per share.

b. Expected price calculation in a year

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

P1 = stock price after 1 year =?

D2 = dividend for year 2 = $4 per share

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

g = growth rate of dividends = 5% after year 2

The dividends occurring in the stable growth period of 5%, 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 = D2 * (1+g) / (k –g) = $4 *(1+5%) / (12%- 5%) = $60.00

Now we can calculate the present value at the end of year 1 of dividend and terminal value and add the present values of future dividends and terminal value to get current stock price;

P1 = $4 / (1+12%) ^1 + $60 / (1+12%) ^1

= $3.57 +$53.57

= $57.14

Therefore stock price after 1 year will be $57.14 per share