Question

BlueCorp. is growing quickly. Dividends are expected to grow at a rate of 16 percent for the next three years, with the growth rate falling off to a constant 4.3 percent thereafter. If the required return is 12.59 percent and the company just paid a $3.78 dividend, what is the current share price? Answer to two decimals.

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 third dividend is paid, so we can find the price of the stock in Year 3, when the constant dividend growth begins as:

P₃ = D₃(1 + g₂) / (R – g₂)

P₃ = D₀(1 + g₁)³(1 + g₂) / (R– g₂)

P₃ = $3.78(1.16)³(1.043) / (.1259 – .043)

P₃ = $74.23

The price of the stock today is the present value of the first three dividends, plus the present value of the Year 3 stock price. The price of the stock today will be:

P₀ = $3.78(1.16) / 1.1259 + $3.78(1.16)² / 1.1259²+ $3.78(1.16)³ / 1.1259³ + $74.23 / 1.1259³

P₀ = $64.05