Question

Consider a firm that has just paid a dividend of $2. An analyst expects dividends to grow at a rate of 8 percent per year for the next five years. After that dividends are expected to grow at a normal rate of 5 percent per year. Assume that the appropriate discount rate is 7 percent.

Refer to Exhibit 8.3. The price of the stock today (P₀) is

Answer 1

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 dividends and terminal value ( value of all future dividends receivable at a point of time if growth rate is constant)

D0 = Current dividend = $2

D1 = D0 x ( 1 + Growth rate)

G = 8% for next 5 years and 5% after that forever

So, D1 = Dividend next year = $2 x 1.08

= $2.16

Similarly, D2 = $2.16 x 1.08

= $2.33

D3 = Expected dividend in 3 years

= $2.33 x 1.08

= $2.52

D4 = $2.52 x 1.08

= $2.72

D5 = $2.72 x 1.08

= $2.94

D6 = $2.94 x 1.05

= $3.09

Terminal value at the end of 5^th year

= D6 / ( Re- G)

Where,

Re = Required rate of return = 7% or 0.07

So, Terminal value at end of 5^th year ( as dividends will have constant growth rate from 6^th year onwards, value of all those dividends is calculated at the end of 5^th year)

= $3.09 / (0.07 – 0.05)

= $3.09 / 0.02

= $ 154.28

The following table shows the calculations

Present value factor

= 1 / ( 1 + Re ) ^ n

Where,

n = Number of years

So, PV Factor for year 2 will be

= 1 / (1.07 ^ 2)

= 1 / 1.1449

= 0.873438

Calculations	A	B	C = A x B
Year	Cash Flows	PV Factor	Present Value
1	2.16	0.934579	2.02
2	2.33	0.873439	2.04
3	2.52	0.816298	2.06
4	2.72	0.762895	2.08
5	2.94	0.712986	2.10
5	154.28	0.712986	110.00
		Price	120.28

So, the price of the stock today is $120.28