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

Investors would pay $100 for a share of the firm's stock when they are certain of the $10 annual profit, as calculated per the perpetuity formula. However, if future profits are uncertain, investors would demand a higher return for the increased risk, meaning they'd be willing to pay less for a share.

Step-by-step solution

Understand Perpetuity Value

The value of an investment that earns a certain constant amount forever (a perpetuity) is the profit made each period divided by the interest rate. In this case, each share of the firm's stock is producing a constant $10 profit per year, so it is a perpetuity.

Calculate Per Share Value

To calculate the value of the share under the assumption that each share will earn $10 profit per year forever, and the interest rate is 10 percent (or 0.1), use the formula for the value of a perpetuity: Value = Profit / Interest Rate. Plugging in the given numbers, you would get: Value = $10 / 0.1.

Discuss Effect of Uncertainty

When the investors are uncertain about the future profits, they are taking on more risk by buying the firm’s stock. Due to this increased risk, investors would require a higher potential return to consider the investment attractive, which means they would be willing to pay less for the stock now. The exact amount of decrease in price is hard to quantify without specific numbers, but the direction of the change is towards a lower price.