Question

• Company X is paying an annual dividend of $1.35 and has decided to pay the same amount forever. How much should you pay for the stock, if you want to earn an annual rate of return of 9.5% on this investment? • You want to purchase common stock of Company X and hold it for 9 years. The company just announced they will be paying an annual cash dividend of $6.00 per share for the next 9 years. How much should you pay for the stock, if you will be able to sell the stock for $28 at the end of nine years and you want to earn an annual rate of return of 11% on this investment?

Answer 1

Case 1

Price of share = $14.21

Case 2

Price of share = $44.17

Step-by-step explanation:

Provided details,

We have the following,

Current dividend = $1.35

Growth rate = 0

Annual rate of return = 9.5%

Using dividend growth model value of share,

`(D_1)/(K_e - g) = P_0`

Where D1 = Dividend at year end

Ke = Cost of capital or expected return

P0 = price of share

g = growth rate

Thus P0 =
`(1.35)/(0.095 - 0)` = $14.21

In case 2, we have,

Dividend per share = $6.00 For a period of 9 years

Expected return = 11%

Growth rate = 0

Sale price at end of year 9 = $28

Present value annuity factor for 9 year @ 11%

= 5.537

Present value of Dividend = $6
`*` 5.537 = $33.22

Discounted value of $28 for 9 years = 0.391 {tex]\times[/tex] $28 = $10.95

As, the share will be sold after 9 years, the price will be discounted to current value.

Total present value of share = $44.17

Thus, current price = $44.17

Case 1

Price of share = $14.21

Case 2

Price of share = $44.17