Cayman Boats plans to pay a $1.75 a share dividend at the end of each of the next 2 years. At the end of Year 3, it will pay a final liquidating dividend of $25 a share. After that, the company plans to close its doors permanently. What is the current value of this stock at a discount rate of 10 percent?

Question

Quizplus · Accepted Answer

We can use the formula for the present value of an annuity to find the present value of the two $1.75 dividends: PV = PMT x [(1 - (1 / (1 + r)^n)) / r], where PV is the present value, PMT is the payment each period, r is the discount rate, and n is the number of periods. Plugging in the values, we get: PV = $1.75 x [(1 - (1 / (1 + 0.1)^2)) / 0.1] = $3.32.

We can then use the formula for the present value of a single sum to find the present value of the $25 liquidating dividend: PV = FV / (1 + r)^n, where FV is the future value, r is the discount rate, and n is the number of periods. Plugging in the values, we get: PV = $25 / (1 + 0.1)^3 = $18.55.

Adding the present value of the dividends ($3.32) to the present value of the liquidating dividend ($18.55) gives us the total present value: $3.32 + $18.55 = $21.87. This is the current value of the stock. Therefore, the best choice is C.

Cayman Boats Plans to Pay a $1