Frank Castanza owns 100 shares in a weapons company called Guns-R-Us. Frank brags about its steady, annual dividend of $1.25 per share. You are jealous of the dividend but philosophically opposed to weapons companies, so you can't buy the stock. Instead, you have identified the Paper Street Soap Factory (PSSF)which is developing a new biodegradable bath soap. The company plans to begin paying an annual dividend of $1.25 starting in two years. Stockholders in both companies require a return of 7.5%. A stock price and dividend forecast for the two companies is provided in the table. (Assume that dividends are paid in perpetuity.)Your plan is to buy shares in PSSF today, sell some at Year 1 and hold the remainder in perpetuity. How many shares do you have to buy today in order to earn the same annual income as Frank? $$\begin{array} { | c | c | c | c | c | c | }
\hline & \text { Guns-R-Us } & & & \text { PSSF } & \
\hline \text { Year } & \text { Price } & \text { Dividend } & & \text { Price } & \text { Dividend } \
\hline 0 & 16.66667 & & & 15.50388 & \
\hline 1 & 16.66667 & 1.25 & & 16.66667 & 0 \
\hline 2 & 16.66667 & 1.25 & & 16.66667 & 1.25 \
\hline 3 & 16.66667 & 1.25 & & 16.66667 & 1.25 \
\hline
\end{array}$$

Question

Frank Castanza owns 100 shares in a weapons company called Guns-R-Us. Frank brags about its steady, annual dividend of $1.25 per share. You are jealous of the dividend but philosophically opposed to weapons companies, so you can't buy the stock. Instead, you have identified the Paper Street Soap Factory (PSSF)which is developing a new biodegradable bath soap. The company plans to begin paying an annual dividend of $1.25 starting in two years. Stockholders in both companies require a return of 7.5%. A stock price and dividend forecast for the two companies is provided in the table. (Assume that dividends are paid in perpetuity.)Your plan is to buy shares in PSSF today, sell some at Year 1 and hold the remainder in perpetuity. How many shares do you have to buy today in order to earn the same annual income as Frank? $$\begin{array} { | c | c | c | c | c | c | } 
\hline & \text { Guns-R-Us } & & & \text { PSSF } & \
\hline \text { Year } & \text { Price } & \text { Dividend } & & \text { Price } & \text { Dividend } \
\hline 0 & 16.66667 & & & 15.50388 & \
\hline 1 & 16.66667 & 1.25 & & 16.66667 & 0 \
\hline 2 & 16.66667 & 1.25 & & 16.66667 & 1.25 \
\hline 3 & 16.66667 & 1.25 & & 16.66667 & 1.25 \
\hline
\end{array}$$

Quizplus · Accepted Answer

To earn the same annual income as Frank, you need to buy enough shares of PSSF to receive $125 annually in dividends (100 shares * $1.25). Since PSSF will pay $1.25 per share starting in Year 2, you need to buy 100 shares of PSSF. However, to account for the fact that you will sell some shares at Year 1, you need to calculate the present value of the dividends and adjust the number of shares accordingly. The present value of the dividends from PSSF is $16.66667 per share (since $1.25 / 0.075 = $16.66667). Therefore, you need to buy 107.5 shares today to ensure you receive the same annual income as Frank.

Frank Castanza Owns 100 Shares in a Weapons Company Called