Question

J&j exporters paid a $1.80 per share annual dividend last month. the company is planning on paying $2.00, $2.50, $2.75, and $3.00 a share over the next four years, respectively. after that the dividend will be constant at $3.20 per share per year. what is the market price of this stock if the market rate of return is 13 percent?

Answer 1

Answer: The market price of this stock is $22.57.

In this question, we ignore last year's dividend of $1.80 as it is irrelevant.

We compute the Present Value (PV) of the dividends of each of the following four years as follows:

`PV_(dividends) = (2)/(1.13) + (2.5)/(1.13^2) +(2.75)/(1.13^3) + (3)/(1.13^4)`

`PV_(dividends) = 7.473622342`

Next, we calculate the PV of dividends from the 5 year onwards. Here dividend is constant at $3.20 and is expected to be paid for ever. The PV of a perpetuity at the end of year 4 is:

`V_(perpetual dividend) = (Perpetuity Amount)/(Discount Rate)`

`V_(perpetual dividend) = (3.2)/(0.13)`

The value of a perpetual dividend of $3.20 at the end of year 4 is $24.61538462

Next we find the PV of the value of perpetual dividend as follows:

`PV_(perpetual dividend) = (24.61538462)/(1.13^4)`

`PV_(perpetual dividend) = 15.09707637`

`Market Price of the stock = PV_(dividends) + PV_(perpetual dividend)`

`Market Price of the stock = 7.473622342 + 15.09707637`

Market price of the stock = $22.57069872