Question

The common stock of a firm paid a dividend of $1.75 in the year just ended. Suppose their dividend is expected to grow at a rate of 10% in the coming year, 8% in year two, and at a rate of 4% annually thereafter. If the required rate of return is 10%, what is the current value of their stock? I know the answer ($33.25) I want to know how to get the answer without a calculator (excel is fine).

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 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 3rd year and onwards, the terminal value will be calculated at the end of 2nd year

Dividend for year 1 ( D1 )

= Current dividend x ( 1 + Growth rate)

= $1.75 x 1.10

= $1.93

Similarly, D2 = $1.93 x 1.08

= $2.08

Similarly, D3 = $2.08 x 1.04

= $2.16

Expected value of all future dividends receivable ( terminal value) at the end of 2nd year

= D3 / ( Re – G)

Where,

Re = Required rate of return = 10% or 0.10

G = Growth rate = 4% or 0.04

= $2.16 / ( 0.10 – 0.04)

= $2.16 / 0.06

= $36.04

Present value factor

= 1 / ( 1 + Re ) ^ n

Where,

n = Number of years = 1 to 2

So, PV Factor for year 2 will be

= 1 / (1.10 ^ 2)

= 1 / 1.21

= 0.826446

The following table shows the calculations :

Calculations
Year	Cash Flow	PV Factor	Present Value
1	1.93	0.909091	1.75
2	2.08	0.826446	1.72
2	36.04	0.826446	29.78
		Price	33.25

So, the price of the stock is $33.25