Question

Suppose that people are sure that a firm will earn annual profit of \(\$ 10\) per share forever. If the interest rate is 10 percent, how much will people pay for a share of this firm's stock? Suppose that people become uncertain about future profit. What would happen to the price they would be willing to pay? (Your answer will be descriptive only.)

Short answer

When people are sure about the future profit of the firm, they would be willing to pay \$100 for a share. However, if they become uncertain about the future profit, because of the perceived increased risk, they would demand a higher return for their investment. This increase in the required return (interest rate) would resultatively decrease the price they would be willing to pay for a share.

Step-by-step solution

Calculating the price of the share using the perpetuity formula

The formula for perpetuity is given as \(P = \frac{C}{r}\) where \(P\) is the price of the share, \(C\) is the cash flow per period which is the annual profit per share and \(r\) is the interest rate. Here, \(C = \$10\) and \(r = 0.10\). Substituting these values into the formula, the price of the share (\(P\)) would be calculated as \(\frac{\$10}{0.10}\).

Understanding the impact of uncertainty on the price of the share

When people become uncertain about future profit, they perceive a higher risk. This would typically lead to a higher required rate of return (interest rate), which would decrease the price of the share. This is because the price of the share is inversely proportional to the interest rate. The greater the interest rate (reflecting greater risk), the less people are willing to pay for the share.