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.

Question

Quizplus · Accepted Answer

At a required rate of return of 10%, the present value of $1,000 is:

PV = $1,000 / (1 + 0.10) = $909.09

This amount can be used to repurchase shares at the current market price per share. If the market price per share is $10, then the number of shares repurchased will be:

Shares = $909.09 / $10 = 90.91

Thus, the number of shares outstanding at the end of year 1 will be:

Shares outstanding = 100 - 90.91 = 9.09

However, since a fractional share cannot be repurchased, the actual number of shares outstanding at the end of year 1 will be:

Shares outstanding = 100 - 90 = 10

Company X Has 100 Shares Outstanding