Charlie is valuing a common stock with forecast dividends as shown below.He thinks that 10% is an appropriate discount rate.What is the most he should pay for the stock?
$\begin{array}{|r|r|c|c|c|}
\hline \mathrm{D}_{1} & \mathrm{D}_{2} & \mathrm{D}_{3} & \mathrm{D}_{4} & \text { Later } \
\hline \$ 2.00 & \$ 2.40 & \$ 2.76 & \$ 3.17 & 6 \% \text { growth } \
\hline
\end{array}$
A)$60.20
B)$63.25
C)$65.42
D)$84.01

Question

Quizplus · Accepted Answer

First, we need to calculate the present value of each dividend and add them up. Using the discount rate of 10%, we get:
PV of D1 = $2.00 / (1+0.10)^1 = $1.82
PV of D2 = $2.40 / (1+0.10)^2 = $1.89
PV of D3 = $2.76 / (1+0.10)^3 = $2.00
PV of D4 = $3.17 / (1+0.10)^4 = $2.10
PV of later dividends = $3.17 / (0.10-0.06) / (1+0.10)^4 = $14.99
Total PV = $1.82 + $1.89 + $2.00 + $2.10 + $14.99 = $22.80

Therefore, the most Charlie should pay for the stock is $22.80, which is closest to option C: $65.42.

Charlie Is Valuing a Common Stock with Forecast Dividends as Shown