Company X has 100 shares outstanding. It earns $1,000 per year and expects repurchase its shares in the open market instead of paying dividends. Calculate the number of shares outstanding at the end of year-1, if the required rate of return is 10%.

Question

Quizplus · Accepted Answer

According to the Gordon Growth Model, the value of the stock is calculated as follows:

PV = (Dividend at Year 1) / (Required Rate of return - Growth rate)

Here, the dividend at year 1 is assumed to be the total earnings of the company ($1,000).

The growth rate is assumed to be zero because the company is repurchasing shares instead of paying dividends.

Therefore,

PV = $1,000 / (0.1 - 0) = $10,000

The market value of each share is then calculated as follows:

Market value per share = PV / Number of shares outstanding = $10,000 / 100 = $100

At the end of year 1, the company will use the $1,000 earnings to repurchase shares at the market value of $100 per share.

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

Number of shares outstanding = $1,000 / $100 = 10

Thus, the total number of outstanding shares will be reduced by 10, which means at the end of year-1 there will be only 90 shares outstanding.

Company X Has 100 Shares Outstanding