Question

Suppose a stock will pay $12 per share dividend in one year's time. The dividend is projected to grow at 8% the following year, and then 4% per year indefinitely after that.

To clarify, dividend at beginning of year 1 (that is, one year from today) is:

$12

Beginning of year 2 (2 years from today) is:

$12 * 1.08

Beginning of year 3 (3 years from today) is:

$12 * 1.08 * 1.04

and a 4% rate of growth every year after that.

The required return is 8%. What is the stock’s price today?

Answer 1

Stock’s price today (P0)

The Price of the stock today is the Present Value of the Future Dividends plus the present value of the share price in year 2 (P2)

Dividend per share Year 1 (D1) = $12.00 per share

Dividend per share Year 2 (D2) = $12.96 per share [$12.00 x 1.08]

Price of the share at the end of year 2 (P2)

Price of the share at the end of year 2 (P2) = D2(1 + g) / (Ke – g)

= $12.96(1 + 0.04) / (0.08 – 0.04)

= $13.48 / 0.04

= $336.96 per share

The Stock’s price today (P0)

The Price of the stock today is the Present Value of the Future Dividends plus the present value of the share price in year 2 (P2)

Therefore, the Price of the stock today (P0) = D1/(1 + r)¹ + D2/(1 + r)² + P2/(1 + r)²

= [$12.00/(1 + 0.08)¹] + [$12.96/(1 + 0.08)²] + [$336.96/(1 + 0.06)²]

= [$12.00 / 1.08] + [$12.96 / 1.16640] + [$336.96 / 1.16640]

= $11.11 + $11.11 + $288.89

= $311.11 per share

“Hence, the stock’s price today would be $311.11 per share”