Question

Use growing annuity formula.

You buy a share of Amazon stock and will receive $4 in dividends the following year. The dividends will grow at 5% for the next five years. You will sell the Amazon stock for $330 at the end of the five years when you get the dividends. What will be the cost of each stock if you require a 7 percent return on your initial investment?

Answer 1

We have following formula to calculate present value of growing annuity for the dividends for 5 years

PV_GA = CF/ (r - g) * [1- {(1+g)/ (1+r)} ^n]

Where,

Present value of growing annuity, PV_GA =?

First payment CF = $4

Required rate of return or Interest rate per period r = 7% per annum

Growth rate of annuity g = 5% per annum

Number of periods n = 5 years

Now putting all the values in above formula

PV_GA = $4/ (7% -5%) * [1 – {(1+5%)/ (1+7%)} ^5]

= $200 * 0.0900

= $18.01

Now we have to calculate the present value of stock selling price ($300 per share) at the end of year 5

Present value of stock selling price = Selling price at the end of year 5 / (1+ r) ^n

= $300/ (1+7%) ^5

= $213.90

Therefore the cost of each stock = Present value of growing annuity for dividends + Present value of stock selling price

= $18.01 + $213.90

= $231.91 per share

Therefore the cost of each stock will be $231.91.