Assume a stock just paid an annual dividend of $1.20 per share. The required return on the stock is 14 percent. If the dividends are expected to grow at 12 percent for 4 years and 2 percent thereafter, what is the price of the stock?

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Quizplus · Accepted Answer

To find the price of the stock, we use the Dividend Discount Model (DDM) for a multi-stage growth scenario. First, calculate the dividends for the first 4 years, which grow at 12%, and then find the price at the end of year 4 using the perpetuity formula with a 2% growth rate. Finally, discount all future dividends and the price back to the present value using the required return of 14%.1. Calculate dividends for the first 4 years:- D1 = $1.20 * (1 + 0.12) = $1.344- D2 = $1.344 * (1 + 0.12) = $1.50528- D3 = $1.50528 * (1 + 0.12) = $1.68632- D4 = $1.68632 * (1 + 0.12) = $1.888682. Calculate the stock price at the end of year 4 using the Gordon Growth Model (perpetuity formula with growth):- P4 = D5 / (r - g) = D4 * (1 + g2) / (r - g2)- P4 = $1.88868 * (1 + 0.02) / (0.14 - 0.02) = $1.92845 / 0.12 = $16.070423. Discount dividends and P4 back to present value:- PV = D1 / (1 + r)^1 + D2 / (1 + r)^2 + D3 / (1 + r)^3 + D4 / (1 + r)^4 + P4 / (1 + r)^4- PV = $1.344 / (1.14)^1 + $1.50528 / (1.14)^2 + $1.68632 / (1.14)^3 + $1.88868 / (1.14)^4 + $16.07042 / (1.14)^4- PV ≈ $1.17947 + $1.16162 + $1.14421 + $1.12722 + $11.49748 = $14.10Therefore, the correct answer is E) $14.10.

Assume a Stock Just Paid an Annual Dividend of $1