Jen's Fashions is growing quickly.Dividends are expected to grow at a 19 percent rate for the next 3 years,with the growth rate falling off to a constant 8 percent thereafter.The required return is 12 percent and the company just paid a $3.80 annual dividend.What is the current share price?
A)$128.96
B)$131.11
C)$135.95
D)$148.87
E)$152.20

Question

Quizplus · Accepted Answer

The current share price can be calculated using the dividend discount model for a stock with dividends growing at different rates. First, calculate the dividends for the next three years using the 19% growth rate, then calculate the price at the end of year 3 using the constant growth formula, and finally discount those future values back to the present.1. Calculate future dividends:- D1 = $3.80 * (1 + 0.19) = $4.522- D2 = $4.522 * (1 + 0.19) = $5.38118- D3 = $5.38118 * (1 + 0.19) = $6.40362. Calculate the price at the end of year 3 using the Gordon Growth Model (constant growth from year 4 onwards):- P3 = D4 / (r - g) = D3 * (1 + g) / (r - g) = $6.4036 * (1 + 0.08) / (0.12 - 0.08) = $6.915888 / 0.04 = $172.89723. Discount future dividends and P3 back to the present:- PV = D1 / (1 + r)^1 + D2 / (1 + r)^2 + D3 / (1 + r)^3 + P3 / (1 + r)^3- PV = $4.522 / (1 + 0.12)^1 + $5.38118 / (1 + 0.12)^2 + $6.4036 / (1 + 0.12)^3 + $172.8972 / (1 + 0.12)^3- PV ≈ $4.03 + $4.29 + $4.56 + $122.78 ≈ $135.95Therefore, the current share price is approximately $135.95.

Jen's Fashions Is Growing Quickly