Question

Brooks Corp is expected to pay the following dividends over the next four years: $2, $2, $14, and $4. Afterward, the company pledges to maintain a constant 0.02 growth rate in dividends forever. If the required return on the stock is 0.11, what is the current share price?

Answer 1

With supernormal dividends, we find the price of the stock when the dividends level off at a constant growth rate, and then find the PV of the future stock price, plus the PV of all dividends during the supernormal growth period. The stock begins constant growth in Year 4, so we can find the price of the stock in Year 4, at the beginning of the constant dividend growth, as:

P₄ = D₄(1 + g) / (R − g)

P₄ = $4(1.02) / (0.11 − 0.02)

P₄ = $45.33

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

P₀ = $2 / 1.11 + $2 / 1.11² + $14 / 1.11³ + $4 / 1.11⁴ + $45.33 / 1.11⁴

P₀ = $46.16