Business Degree Certification Practice Test

What is the maximum amount you should pay for a share of stock with a dividend of $1.75 that decreases by 1.5% annually, given a required rate of return of 14%?

1. $11.29

2. $12.64

3. $13.27

4. $14.00

The correct answer is: $11.29

To determine the maximum amount you should be willing to pay for a share of stock with a declining dividend, one must use the formula for the present value of a perpetuity that is expected to decline. The formula for a perpetuity that decreases at a constant rate can be expressed as: \[ P = \frac{D}{r - g} \] Where: - \( P \) is the price of the stock, - \( D \) is the dividend in the first year, - \( r \) is the required rate of return, - \( g \) is the growth rate of the dividend (which, in this case, is negative due to the decline). Here, the annual dividend is $1.75, the required rate of return is 14% (or 0.14), and the dividend is decreasing by 1.5% annually, which means \( g = -0.015 \). Plugging the values into the formula, we have: \[ P = \frac{1.75}{0.14 - (-0.015)} \] \[ P = \frac{1.75}{0.14 + 0.015} \] \[ P = \frac{1.75}{