Question

Company X has 100 shares outstanding. It earns $1,000 per year and announces that it will use all $1,000 to repurchase its shares in the open market instead of paying dividends. Calculate the number of shares outstanding at the end of year 1, after the first share repurchase, if the required rate of return is 10 percent.a) 110.0
b) 100.0
c) 90.91
d) 89.0

Answer 1

Answer:

d) 89.0

Explanation:

The value of the company today is the present value of its cash flows in perpetuity which is the cash flows divided by the required rate of return.

value of the firm=$1000/10%=$10,000

share price=value of the firm/shares outstanding

share price=$10,000/100=$100

number of shares to be repurchased=$1000/$100=10

number of shares after repurchase=100-10=90

note that when 90.91 is rounded to a whole, it turns out to be 92 while 89 is rounded to 90