Question

The next three annual dividends paid by XYZ stock are expected to be $2.79 in one year, $7.43 in two years, and $3.05 in three years. The price of the stock is expected to be $54.78 in two years. The expected annual return for the stock is 15.20 percent. What is the current price of one share of XYZ stock?

a. $49.83 (+ or - $0.05).
b. $51.82 (+ or - $0.05).
c. $46.38 (+ or - $0.05).
d. $49.30 (+ or - $0.05).
e. none of the above is within $0.05 of the correct answer.

Answer 1

a. $49.83 (+ or - $0.05).

Step-by-step explanation:

Given that :

Dividend of the first three years and the terminal value at the end of the year 2, that is the price at the end of year 2.

We know that the price of the share is the preset value of all the future dividends.

So we have to present price at the year 2 which is at present value for the end of the year 2 of the dividends beyond year 2.

To calculate the price of the stocks at present, we :

1. The present value for the price of the year 2 that is pv at the end of the year 2 of the dividend to be received beyond the year 2.

2. The present value of the dividend of the year 1 as well as year 2.

3. Then we add the steps 1 and 2 to get the present value of all the dividends.

Therefore,

The present value of the price at nth year with r rate of return is given by :

`$\frac{\text{price at nth year }}{(1+r)^n}$`

Hence, the present value of the price at the year 2 with 15.20% rate of return is =
`$(54.78)/((1+0.1520)^2)$`

`$=(54.78)/(1.327104)$`

= $ 41.28

Now present value of dividend of the first 2 years :

Dividend received at the end of the nth year with rate of return r is

=
`$\frac{\text{dividend}}{(1+r)^r}$`

Therefore the present value of the dividend of the first two years is

=
`$(2.79)/((1+0.1520)^1)+(7.43)/((1+0.1520)^2)$`

= 2.10 + 6.45

= $ 8.55

Now , $ 41.45 + $ 8.55

= $ 49.83

Thus, the current price of one share of the XYZ stock is $ 49.83