Question

Refer to Problem 91. Suppose that a stock pays an annual dividend of $2.50 and, historically, the dividend has increased 4% per year. You desire an annual rate of return of 11%. What is the most that you should pay for the stock?

Short answer

One should pa at most $39.7.

Step-by-step solution

Given information

We are given$P=2.5,i=0.04,r=0.11$

Find the geometric sequence

We have,

$$\begin{gathered} P_n=\frac{1+i}{1+r}{a}_{n-1} \\ {P}_n=\frac{1+0.04}{1+0.11}{a}_{n-1} \\ {P}_n=0.937a_{n-1} \end{gathered}$$

Calculate The value of S

We use the formula $$\begin{gathered} S=\frac{a_1}{1-r} \\ Withr=0.937 \end{gathered}$$We get,

$$\begin{gathered} S=\frac{2.5}{1-0.937} \\ S=39.7 \end{gathered}$$

Conclusion

One should pa at most $39.7.