Question

# Company X has 100 shares outstanding and is expected to earn \$1,000 per year in perpetuity....

Company X has 100 shares outstanding and is expected to earn \$1,000 per year in perpetuity. It announces that instead of paying year 1’s earnings as dividends, it will use the \$1,000 to repurchase shares in the open market. Calculate the number of shares outstanding at the end of year 1, after the share repurchase, if the required rate of return is 10 percent. (Hint: the number of shares that the company can repurchase for \$1,000 at the end of year 1, obviously, depends on the company’s overall value at that point in time). (a) 110.1 (b) 100.0 (c) 90.91 (d) 89.19 (e) 88.88

Lets calculate price of stock toady

Dividend per share = Total dividend /No of shares

=1000\$/100

=\$10

Price of stock = Dividend/Required rate of return

=\$10/10%

=\$100

Note : Total cash flow to shareholder will remain \$1000, irrespective of the way it is distributed.

Price of stock at end of year 1 = 100(1+r)

=100(1+0.1)

=100(1.1)

=\$110

Thus number of shares to be repurchased at end of year 1 = Size of repurchase/Price per share

=(1000)/110

=9.091 Shares

Thus number of shares outstanding at end of year 1 = 100-9.09 = 90.909

i.e 90.91 Shares

Thus ans) (c) 90.91