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Chapter 12: Q. 91 (page 825)

One method of pricing a stock is to discount the stream of future dividends of the stock. Suppose that a stock pays \(P per year in dividends and, historically, the dividend has been increased i% per year. If you desire an annual rate of return of r%, this method of pricing a stock states that the price that you should pay is the present value of an infinite stream of payments:

Price=P+P(1+i1+r)+P(1+i1+r)2+.....

The price of the stock is the sum of an infinite geometric series. Suppose that a stock pays an annual dividend of \)4.00 and, historically, the dividend has been increased 3% per year. You desire an annual rate of return of 9%. What is the most you should pay for the stock?

Short Answer

Expert verified

One should pay at most $72.7 .

Step by step solution

01

Given information

We are givenP=5,i=0.03,r=0.09

02

Find the geometric sequence

We have

P1=P=4Pn=1+i1+ran-1Pn=1+0.031+0.09an-1Pn=0.945an-1

03

Calculate the value of S

We use the formula

S=a11-0.945S=41-0.945S=72.2
04

Conclusion

One should pay at most $72.7

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