Question

1. If you buy a share of Apple Co. you will receive $4.80 in dividends next year. These dividends are expected to growth at 5% per year over the next 5 years. You expect to sell the share for $330 after 5 years once you receive the last dividends. What should be the price of each share assuming you require 7% return on your investment (Hint: Requires the use of growing annuity formula)

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 = $4.80

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 = $4.80/ (7% -5%) * [1 – {(1+5%)/ (1+7%)} ^5]

= $240 * 0.0900

= $21.61

Now we have to calculate the present value of stock selling price of Apple ($330 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

= $330/ (1+7%) ^5

= $235.29

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

= $21.61 + $235.29

= $256.90 per share

Therefore the cost of each stock of Apple will be $256.90