Question

The expected dividends for a stock are: Year 1=$2, Year 2=$3, after Year 2, we expect dividends to grow by 6% forever. If we require an annual return of 8% from this stock, what would be the value of the stock to us? If it sells for $30 in the market, should we buy it?

Answer 1

Computation of Current market price of a share:

We know that

Current Market Price = Present value of te Future Dividend payments

Given D 1 = $ 2

D2 = $ 3

We know that Dividend in Year 3 = D2 ( 1+g)

D2 = Dividend in Year 2

g = Growth rate

D3 = $ 3 ( 1+0.06)

= $3*1.06

= $ 3.18

Hence the Dividend in Year 3 is $ 3.18

Computation of Present value of Dividend accruing from Year 3 to infinity period

PV of Dividend = D3 / ( Ke -g)

Here D3 = Dividend in Year 3

Ke = Cost of Capital

g = Growth rate

PV of Dividends = $ 3.18/( 0.08-0.06)

= $ 3.18/0.02

= $ 159

Hence PV of Dividend accruing from Year 3 to infinity at the end of Year 2 is $ 159

Compuation of Current market price of a share

Year	Dividend	Disc @ 8% [ 1/( 1+i)^n]	Discounting factor at 8%	Discounted Cash flows ( Cash flow * Discounting factor at 8%)
1	$2	1/( 1.08)^1	0.9259	$1.8519
2	$3	1/( 1.08)^2	0.8573	$2.5720
2	$159	1/( 1.08)^2	0.8573	$136.3169
			Total	$140.7407

The Value of the share is $ 140.7407.

If it sells in the market for $ 30,then the share is undervalued. So we can buy it.