The Sister's Market is preparing to pay its first dividends. It is going to pay $.60, $1.10, and $1.50 a share over the next 3 years, respectively. After that, the company has stated that the annual dividend will be $1.98 per share indefinitely. What is this stock worth to you per share if you demand a 9% rate of return?

Question

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To calculate the value of the stock, we use the dividend discount model for a stock with a growing dividend, which in this case includes specific dividends for the first three years and a perpetual dividend thereafter. The value of the stock (V) can be calculated as the present value of the dividends for the first three years plus the present value of the perpetual dividends starting from year 4. The formula for the present value of a perpetuity starting from year 4 is $ \frac{D_4}{r} $, where $D_4$ is the dividend in year 4, and $r$ is the required rate of return. However, since this value is in year 4, we need to discount it back to the present value.1. Calculate the present value of the dividends for the first three years:   - Year 1: $ \frac{0.60}{(1+0.09)^1} $   - Year 2: $ \frac{1.10}{(1+0.09)^2} $   - Year 3: $ \frac{1.50}{(1+0.09)^3} $2. Calculate the present value of the perpetual dividend starting from year 4:   - The perpetual dividend is $ \frac{1.98}{0.09} $, but this needs to be discounted back to present value: $ \frac{\frac{1.98}{0.09}}{(1+0.09)^3} $Adding these values together gives the total value of the stock. When you perform these calculations, the result is closest to option D, $19.62. This calculation accounts for the time value of money, discounting future dividends back to their present value at the required rate of return of 9%.

The Sister's Market Is Preparing to Pay Its First Dividends