Exercise Bicycle Company is expected to pay a dividend in year 1 of $1.20, a dividend in year 2 of $1.50, and a dividend in year 3 of $2.00. After year 3, dividends are expected to grow at the rate of 10% per year. An appropriate required return for the stock is 14%. The stock should be worth _______ today.
A) $33.00
B) $39.86
C) $55.00
D) $66.00
E) $40.68

Question

Quizplus · Accepted Answer

To find the present value of the stock, we use the dividend discount model for a stock with dividends growing at a constant rate after a certain period. The present value (PV) of each dividend is calculated using the formula $\frac{D}{(1+r)^t}$, where $D$ is the dividend, $r$ is the required return, and $t$ is the time in years. After year 3, the stock's value can be calculated using the Gordon Growth Model: $P = \frac{D_0 \times (1+g)}{r - g}$, where $P$ is the price, $D_0$ is the dividend just before starting the constant growth, $g$ is the growth rate, and $r$ is the required return.1. Calculate the present value of the dividends for the first three years:   - Year 1: $\frac{$1.20}{(1+0.14)^1} = $1.05$   - Year 2: $\frac{$1.50}{(1+0.14)^2} = $1.15$   - Year 3: $\frac{$2.00}{(1+0.14)^3} = $1.43$2. Calculate the stock price at the end of year 3 using the Gordon Growth Model:   - $P_3 = \frac{$2.00 \times (1+0.10)}{0.14 - 0.10} = \frac{$2.20}{0.04} = $55.00$3. Discount $P_3$ back to present value:   - $PV = \frac{$55.00}{(1+0.14)^3} = $37.05$4. Add the present values of the dividends and the discounted $P_3$:   - Total value = $1.05 + $1.15 + $1.43 + $37.05 = $40.68Therefore, the stock should be worth $40.68 today.

Exercise Bicycle Company Is Expected to Pay a Dividend in Year