Question

Apocalyptica Corporation is expected to pay the following dividends over the next four years: $3, $15, $10, and $3.08. Afterwards, the company pledges to maintain a constant 5 percent growth rate in dividends, forever.
 Required:
If the required return on the stock is 10 percent, what is the current share price

Answer 1

With nonconstant dividends, we find the price of the stock when the dividends level off at a constant growth rate, and then find the present value of the future stock price, plus the present value of all dividends during the nonconstant growth period. The stock begins constant growth after the fourth dividend is paid, so we can find the price of the stock at Year 4, when the constant dividend growth begins, as:

P₄ = D₄(1 + g) / (R – g)

P₄ = $3.08(1.05) / (.10 – .05)

P₄ = $64.68

The price of the stock today is the present value of the first four dividends, plus the present value of the Year 4 stock price. So, the price of the stock today will be:

P₀ = $3 / 1.10 + $15 / 1.10² + $10 / 1.10³ + $3.08 / 1.10⁴ + $64.68 / 1.10⁴

P₀ = $68.92