Money, Banking, and International Finance

An investor values his stock, P 0 , at time 0 that equals the discounted dividend he receives
next year and the market price the investor receives if he sells the stock. Furthermore, if the
investor is in the first time period, then the investor faces the same choice for Period 2 in
Equation 13. Thus, we moved the time subscripts ahead by one period.

  +r

P

+

+r

D

P=

1 1

2 2

1 (^13 )^

We obtain Equation 14 by substituting Equation 13 into Equation 12.

     ^2

2

2

1 2

0

(^111) +r

P

+

+r

D

+

+r

D

P= ( 14 )

Then we build our sequence by examining an investor’s decision for Period 3, and
substitute that equation into Equation 14 for variable P 2. We continue to examine an investor’s
future decision for each time period until we derive an infinite sequence in Equation 15.

     

+

+r

D

+

+r

D

+

+r

D

P 0 =^12233

(^111)

( 15 )

If the corporation pays the same dividends, then D=D 1 =D 2 =, subsequently, the
market price becomes a perpetuity, where we simplify a stock’s value to Equation 16.

r

D

P 0 =^ (^16 )^

As an illustration, you purchase stock as a long-term investment. Your annual rate of return
is 5%, and you expect the corporation to pay $2 per share indefinitely. Consequently, you
compute the market value of this stock of $40 per share in Equation 17.

40.00

0.05

2

0 =$

$

=

r

D

P=^ (^17 )^

If you want to know the market value of this stock for one year, then this becomes a trick
question. Since you expect to earn the same dividend year after year, subsequently the market
price is still $40.00. Thus, the investor does not experience any capital gains or losses.
Many investors want their dividends to grow over time, and Equation 16 can include a
dividend growth rate. If the dividend grows at g percent per year, then we update the present