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? $$\begin{array} { | c | c | c | c | c | }
\hline \mathbf { D } _ { \mathbf { 1 } } & \mathbf { D } _ { \mathbf { 2 } } & \mathbf { D } _ { \mathbf { 1 } } & \mathbf { D } _ { \mathbf { 4 } } & \text { Later } \
\hline \$ 2.00 & \$ 2.40 & \$ 2.76 & \$ 3.17 & \mathbf { 6 \% } \text { prowth } \
\hline
\end{array}$$
A) $60.20
B) $63.25
C) $65.42
D) $84.01

Question

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? $$\begin{array} { | c | c | c | c | c | } 
\hline \mathbf { D } _ { \mathbf { 1 } } & \mathbf { D } _ { \mathbf { 2 } } & \mathbf { D } _ { \mathbf { 1 } } & \mathbf { D } _ { \mathbf { 4 } } & \text { Later } \
\hline \$ 2.00 & \$ 2.40 & \$ 2.76 & \$ 3.17 & \mathbf { 6 \% } \text { prowth } \
\hline
\end{array}$$
A) $60.20
B) $63.25
C) $65.42
D) $84.01

Quizplus · Accepted Answer

The stock price is calculated using the dividend discount model: P = D1/(1+r) + D2/(1+r)^2 + D3/(1+r)^3 + D4/(1+r)^4 + D4*(1+g)/(r-g)/(1+r)^4. Plugging in the values, P = 2/(1.1) + 2.4/(1.1)^2 + 2.76/(1.1)^3 + 3.17/(1.1)^4 + 3.17*1.06/(0.1-0.06)/(1.1)^4 = $65.42.

Charlie Is Valuing a Common Stock with Forecast Dividends as Shown