Question

i) What would be the expected price of a stock when dividends are expected to grow at a 25% rate for three years, then grow at a constant rate of 5%, if the stock’s required return is 13% and next year’s dividend will be $4.00?

ii) The ordinary shares of FED Limited are selling for $26.75 on the open market. A dividend of $3.68 is expected to be distributed, and the growth rate of this company is estimated to be 5.5%. If Bob Dean, an average investor, is considering purchasing this share at the market price, what is his expected rate of return?

iii) What rate of return is expected from a stock that sells for $30 per share, pays $1.50 annually in dividends, and is expected to sell for $33 per share in one year?

Answer 1

Answer:

i).

The value of the stock is the present value of the dividend cash flow stream. First, compute the expected dividends and the price of the stock after year 2 when growth stabilize.

.

D1= $4

D2= 4* 1.25=5

D3= 5*1.25= 6.25

D4= 6.25*1.05=6.5625

The value of the stock in year 3 attributed to the constant growing dividend stream is calculated as

P3 = D4/ ( r-g)

Price after year 3 =6.5625/ (0.13-0.05) =82.0313

So, the present value of the stock using a discount rate of 0.13 is

The expected price of the stock (P0)=4 / (1.13) + 5/ (1.13) ^{^2} +(6.25+ 82.0313) / (1.13)^{^3}

P0=$68.64

.

ii).

The equation for the expected return using Gordon constant growth modelis:

K_s = D₁ / P₀ +g

Where,

K_s = expected return

D₁=Expected Dividend per share at time 1

P₀=market price per share at time 0

g = expected dividend growth rate

Here,

D1 =3.68%

P0= $26.75

g = 5.5%

Ks =?

Ks =( $3.68 / $26.75) + 5.5%

Ks = .1376 + .055

Ks = .1926 or 19.26%

.

iii).

Rate of return is expected from a stock = D1/Share Price + Growth rate

Rate of return is expected from a stock = 1.5/30 + (33-30)/30

Rate of return is expected from a stock = 15%