The required return for Williamson Heating's stock is 12%, and the stock sells for $40 per share. The firm just paid a dividend of $1.00, and the dividend is expected to grow by 30% per year for the next 4 years, so D4 = $1.00(1.30)4 = $2.8561. After t = 4, the dividend is expected to grow at a constant rate of X% per year forever. What is the stock's expected constant growth rate after t = 4, i.e., what is X?
A) 5.17%
B) 5.44%
C) 5.72%
D) 6.02%
E) 6.34%

Question

Quizplus · Accepted Answer

$\begin{array}{lc}
\text { Stock price } & \$ 40.00 \
\text { Paid dividend }\left(\mathrm{D}_{0}\right) & \$ 1.00 \
\text { Short-run growth rate } & 30.0 \% \
\text { Required return } & 12.0 \% \
\text { Forecasted LR growth rate, } \mathrm{X} & 6.34 \% \text { Arbitrarily set at } 5 \% \text { initially }
\end{array}$ 
 $\begin{array} { l c c c c c c c c } 
\text { Year } & 0 & 1 & 2 & 3 & 4 & 5  \
\hline & &30.0\% &30.0\% & 30.0\%& 30.0\% & 6.34\% \
\text { Dividend } & \$ 1.0000 & \$ 1.3000 & \$ 1.6900 & \$ 2.1970 & \$ 2.8561 & \$ 3.0372  \
\text { Harizan value } = P _ { 5 } = D _ { 6 } / \left( r _ { 5 } \right. & & & & & & & & \
- \text { g5 } ) = & & &53.6777  & & & \
\hline \text { Total CFs } & &\$ 1.3000 & \$ 1.6900 & \$ 2.1970 & \$ 56.5338 \
\text { PV of CFs } & & \$ 1.1607 & \$ 12472 & \$ 15628 & \$ 25.0280
\end{array}$ 
Stock price = $40.00. Must equal $40. Change the forecasted growth rate till reach $40. We must solve for the long-run growth rate. We can forecast the dividends in Years 1-4, so they are inserted in the time line. We need a growth rate to find D5 and the TV. We begin with a guess of say 5.0%, which we insert in the forecast cell. We then find the PV of the forecasted CFs and sum them. If the sum equals the given price, then our growth rate would be correct. If not, we need to substitute in different g's until we find the one that works. We used Excel's Goal Seek function to simplify the process, but one could use trial and error.

The Required Return for Williamson Heating's Stock Is 12%, and the Stock