The Red Bud Co. pays a constant dividend of \( \$ 1.70 \) a share. The company announced today that it will continue to do this for another 2 years after which time they will discontinue paying dividends permanently. What is one share of this stock worth today if the required rate of return is 7.3 percent? a. \( \$ 1.82 \) b. \( \$ 4.76 \) c. \( \$ 3.40 \) o d. \( \$ 3.06 \) e. \( \$ 1.89 \)
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To determine the present value of one share of stock based on the given constant dividend, we can use the formula for the present value of future cash flows. Since Red Bud Co. will pay a dividend of \$1.70 for the next two years and then stop, we can calculate the present value of these dividends. The present value (PV) of the dividends can be calculated as follows: \[ PV = \frac{D_1}{(1 + r)^1} + \frac{D_2}{(1 + r)^2} \] Where: - \(D_1\) and \(D_2\) are the dividends received in year 1 and year 2, respectively (\$1.70 each), - \(r\) is the required rate of return (7.3% or 0.073). Calculating this gives: \[ PV = \frac{1.70}{(1 + 0.073)^1} + \frac{1.70}{(1 + 0.073)^2} \] \[ PV = \frac{1.70}{1.073} + \frac{1.70}{1.073^2} \] \[ PV = 1.58 + 1.47 \] \[ PV \approx 3.05 \] So, the present value of one share of this stock today is approximately \$3.06. The correct answer is d. \( \$ 3.06 \).
