The Market Place recently announced that it will pay its first annual dividend two years from today.The first dividend will be $0.50 a share with that amount doubling each year for the following two years.After that,the dividend is expected to increase by 4 per cent annually.What is the value of this stock today if the required return is 15 per cent?

Question

Quizplus · Accepted Answer

To find the current value of the stock, we need to calculate the present value of all expected future dividend payments and the expected future sale price.

- The first dividend payment of $0.50 per share will be made in two years. Therefore, we need to calculate the present value of this payment using the formula:

PV = FV / (1 + r)^n

where PV is the present value, FV is the future value, r is the required return, and n is the number of years.

PV of first dividend = 0.50 / (1 + 0.15)^2 = 0.32

- The second dividend payment will be $1.00 per share (double the first dividend). Therefore, we need to calculate the present value of this payment using the formula:

PV = FV / (1 + r)^n

where PV is the present value, FV is the future value, r is the required return, and n is the number of years.

PV of second dividend = 1.00 / (1 + 0.15)^3 = 0.56

- The third dividend payment will be $2.00 per share (double the second dividend). Therefore, we need to calculate the present value of this payment using the formula:

PV = FV / (1 + r)^n

where PV is the present value, FV is the future value, r is the required return, and n is the number of years.

PV of third dividend = 2.00 / (1 + 0.15)^4 = 0.86

- From year 4 onwards, the dividend is expected to grow at a rate of 4% per year. Therefore, we can use the Gordon growth model to calculate the present value of all future dividends:

PV of future dividends = (Div4 * (1 + g)) / (r - g)

where Div4 is the dividend expected to be paid at the end of year 4, g is the expected growth rate, and r is the required return.

Div4 = 2.00 * (1 + 0.04) = 2.08

PV of future dividends = (2.08 * (1 + 0.04)) / (0.15 - 0.04) = 18.07

- Finally, we need to calculate the present value of the expected sale price of the stock at the end of year 5. To do this, we can use the formula:

PV = FV / (1 + r)^n

where PV is the present value, FV is the future value, r is the required return, and n is the number of years.

PV of sale price = 0 / (1 + 0.15)^5 = 0

- Now we can add up all the present values to get the current value of the stock:

Current value = PV of first dividend + PV of second dividend + PV of third dividend + PV of future dividends + PV of sale price
Current value = 0.32 + 0.56 + 0.86 + 18.07 + 0
Current value = $12.99

Therefore, the best choice is D.

The Market Place Recently Announced That It Will Pay Its