Questions: JJ Industries will pay a regular dividend of 0.85 per share for each of the next four years. At the end of the four years, the company will also pay out a 79 per share liquidating dividend, and the company will cease operations. If the discount rate is 9 percent, what is the current value of the company's stock? Note: Do not round intermediate calculations. Round your answer to 2 decimal places.

Solution Steps

To find the current value of the company's stock, we need to calculate the present value of all future dividends. This includes the regular dividends for the next four years and the liquidating dividend at the end of the fourth year. We will discount each of these cash flows back to the present value using the given discount rate of 9%.

The present value of the regular dividends over the next four years is calculated using the formula for the present value of an annuity: \[ PV_{\text{regular}} = \sum_{t=1}^{4} \frac{D}{(1 + r)^t} \] where \(D = 0.85\) and \(r = 0.09\).

\[ PV_{\text{regular}} = \frac{0.85}{(1 + 0.09)^1} + \frac{0.85}{(1 + 0.09)^2} + \frac{0.85}{(1 + 0.09)^3} + \frac{0.85}{(1 + 0.09)^4} \]

\[ PV_{\text{regular}} \approx 0.7798 + 0.7154 + 0.6562 + 0.6024 = 2.7538 \]

The present value of the liquidating dividend at the end of the fourth year is calculated using the formula: \[ PV_{\text{liquidating}} = \frac{L}{(1 + r)^4} \] where \(L = 79\) and \(r = 0.09\).

\[ PV_{\text{liquidating}} = \frac{79}{(1 + 0.09)^4} \approx \frac{79}{1.4116} \approx 55.9656 \]

The current value of the company's stock is the sum of the present values of the regular dividends and the liquidating dividend: \[ PV_{\text{total}} = PV_{\text{regular}} + PV_{\text{liquidating}} \]

\[ PV_{\text{total}} \approx 2.7538 + 55.9656 = 58.7194 \]

Final Answer