Question

Ainsley Adams would like to purchase the stock of Abercrombie and Switch and plans to hold the stock for four years. The projected annual dividends for the next four years are $2.15, $2.28, $2.47 and $2.60, respectively. Ainsley believes that at the end of the holding period, the stock will be selling for $45.68. If Ainsley requires an annual rate of return of 19.25% on this investment, what would he be willing to pay for the stock today ?

Answer 1

Solution:

Annualised Holding period return of Ainsley is 19.25% or 0.1925,thus we need to find out the total holding period return;

Annualised Holding Period Return=[(1+Total Return)^1/years]-1

0.1925+1=(1+Total return)^1/4

(1.1925)^4=1+Total Return

Total Return=2.0222-1

=1.0222 or 102.22%

Thus holding period return is 102.22%

Holding Period return=[Income+(V1-V0)]/V0

Here,

Income=Annual dividends

=$2.15+$2.28+$2.47+$2.60

=$9.5

V1(Value of Investment at the end of holding period)=$45.68

V0=Let it be X

Now,putting the value,

1.0222=$9.5+($45.68-X)/X

1.0222X=$9.5+$45.68-X

2.0222X=55.18

X=$55.18/2.0222

=$27.29(approx)

Thus,the price Ainsley would he be willing to pay for the stock today is $27.29