Question

The risk-free rate is 2.19% and the market risk premium is 8.74%. A stock with a β of 0.96 just paid a dividend of $2.42. The dividend is expected to grow at 22.65% for three years and then grow at 3.62% forever. What is the value of the stock?

The risk-free rate is 2.77% and the market risk premium is 7.64%. A stock with a β of 1.28 just paid a dividend of $2.96. The dividend is expected to grow at 20.83% for five years and then grow at 4.65% forever. What is the value of the stock?

Answer 1

Dear student, only one question is allowed at a time. I am answering the first question

We have to calculate the required rate of return ( Re ) as per Capital Asset Pricing Model

Re = Rf + (Rm – Rf) x Beta

Where,

Re = Required rate of return

Rf = Risk free rate of return = 2.19%

Rm – Rf = Market risk premium = 8.74%

Beta = Beta of the stock = 0.96

So, Re = 2.19 + 8.74 x 0.96

= 2.19 + 8.39

= 10.58%

Price of a stock is the present value of all future cash flows receivable from the stock discounted at required rate of return

Future cash flows are annual dividends and terminal value of dividends

Where,

Terminal value of dividends is the value of all future dividends receivable when the growth rate is constant. This is calculated at the end of the year after which there will be a constant growth rate of dividends. For example, if the dividends start growing at constant rate from 4^th year and onwards, the terminal value will be calculated at the end of 3^rd year

Dividend for year 1 ( D1 )

= Current dividend x ( 1 + Growth rate)

= $2.42 x 1.2265

= $2.97

Similarly, D2 = $2.97 x 1.2265

= $3.64

Similarly, D3 = $3.64 x 1.2265

= $4.46

D4 = $4.46 x 1.0362

= $4.63

Expected value of all future dividends receivable ( terminal value) at the end of 3^rd year

= D4 / ( Re – G)

= $4.63 / ( 0.1058 – 0.0362)

= $4.63 / 0.0696

= $66.52

Present value factor

= 1 / ( 1 + Re ) ^ n

Where,

Re = Rate of interest = 10.58% or 0.1058

n = Number of years = 1 to 3

So, PV Factor for year 2 will be

= 1 / ( 1.1058 ^ 2)

= 1 / 1.22279364

= 0.817799

The following table shows the calculations :

Calculations	A	B	C = A x B
Year	Cash Flow	PV Factor	Present Value
1	2.97	0.904323	2.69
2	3.64	0.817799	2.98
3	4.46	0.739555	3.30
3	66.52	0.739555	49.20
		Price	58.16

So, the price of the stock is $58.16