Your company paid a dividend of $2.00 last year.The growth rate is expected to be 4 percent for 1 year,5 percent the next year,then 6 percent for the following year,and then the growth rate is expected to be a constant 7 percent thereafter.The required rate of return on equity (r_s)is 10 percent.What is the current price of the common stock? A) $53.45 B) $60.98 C) $64.49 D) $67.47 E) $69.21

Question

Quizplus · Accepted Answer

To find the current price of the stock, we use the Dividend Discount Model (DDM) for a multi-stage growth model. The dividends grow at different rates for the first three years and then grow at a constant rate thereafter. 1. Calculate the dividends for the first three years:- Year 1: $2.00 * (1 + 0.04) = $2.08- Year 2: $2.08 * (1 + 0.05) = $2.184- Year 3: $2.184 * (1 + 0.06) = $2.315042. Calculate the price at the end of Year 3 using the Gordon Growth Model (since from Year 4 onwards, the growth rate is constant):- D4 = $2.31504 * (1 + 0.07) = $2.47709- P3 = D4 / (r - g) = $2.47709 / (0.10 - 0.07) = $82.569673. Discount the dividends and the price at the end of Year 3 back to the present value:- PV of D1 = $2.08 / (1 + 0.10)^1 = $1.89091- PV of D2 = $2.184 / (1 + 0.10)^2 = $1.80537- PV of D3 = $2.31504 / (1 + 0.10)^3 = $1.72563- PV of P3 = $82.56967 / (1 + 0.10)^3 = $61.445094. Sum the present values to get the current price:- Current Price = $1.89091 + $1.80537 + $1.72563 + $61.44509 = $67.47Therefore, the correct answer is D) $67.47.

Your Company Paid a Dividend of $2