The value of the firms stock is the present value of its expected future dividends. If DtDt stands for dividend at period tt and rsrs is the required rate of return, which is a riskless rate plus a risk premium, then the expected value of firms stock is determined as follows:

Value of stock, P0Value of stock, P0^	= =	PV of expected future dividendsPV of expected future dividends
	= =	D1(1+rs)1+D2(1+rs)2+ ... +D(1+rs)D11+rs1+D21+rs2+ ... +D1+rs
	= =	t = 1Dt(1+rs)tt = 1Dt1+rst

For many companies it is reasonable to predict that dividends will grow at a constant rate, gg. Thus, the previous equation may be rewritten as follows:

P0P0^	= =	D0(1+g)1(1+rs)1+D0(1+g)2(1+rs)2+ ... +D0(1+g)(1+rs)D01+g11+rs1+D01+g21+rs2+ ... +D01+g1+rs
	= =	D0(1+g)rsgD01+grsg
	= =	D1rsgD1rsg

If the stock is in equilibrium, rsrs must equal the expected dividend yield plus an expected capital gains yield. Thus, you can solve for an expected rate of return, rsrs^:

Expected rate of return, rsExpected rate of return, rs^	= =	Expected dividend yield+Expected growth rate, or capital gain yieldExpected dividend yield+Expected growth rate, or capital gain yield
	= =	D1P0+gD1P0+g

Suppose that the last dividend, which the firm just paid on its stock, is D0=$1.00D0=$1.00 and the stocks last closing price is $21.80$21.80. It is expected that earnings and dividends will grow at a constant rate of g=9.00%g=9.00% per year and that the stocks price will grow at this same rate. Let us assume that the stock is fairly priced, that is, it is in equilibrium, and the most appropriate required rate of return is rs=14.00%rs=14.00%.

The dividend received in period 1 is D1=$1.00(1+0.0900)=$1.09D1=$1.001+0.0900=$1.09 and the estimated intrinsic value in the same period is based on the constant growth model: P1=D2rsgP1^=D2rsg.

Using the same logic, compute the dividends, prices, and the present value of each of the dividends at the end of each period.

Period	Dividend	Price	PV of dividend at 14.00%
	(Dollars)	(Dollars)	(Dollars)
0	$1.00	$21.80
1	1.09
2
3
4
5

The dividend yield for period 1 is and it will each period.

The capital gain yield expected during period 1 is and it will each period.

If it is forecasted that the total return equals 14.00% for the next 5 years, what is the forecasted total return out to infinity?

5.00%

9.00%

14.00%

23.00%

Note that this stock is called a Hold as its forecasted intrinsic value is equal to its current price P0=D1rsg=$1.090.14000.0900=$21.80P0^=D1rsg=$1.090.14000.0900=$21.80 and the expected total return is equal to the required rate of return rsrs. If the market was more pessimistic and the growth rate would be 8.00% rather than 9.00%, the stocks forecasted intrinsic value would be P0=$1.090.14000.0800=$18.17P0^=$1.090.14000.0800=$18.17, which is less than $21.80. In this case, you would call the stock a Sell.

Suppose that the growth rate is expected to be 10.00%. In this case, the stocks forecasted intrinsic value would be its current price, and the stock would be a .