Constant Growth Model

A firm has a constant growth rate of 7% and just paid a divident of $6.25. If the required rate of return is 12%, what will the stock sell for two years from now based on the DDM?

Formula = D^3/ (k-g) OR Do (1+g)^3 / (k-g)

Simple question but why do you use 3 as an exponent? I would think if you were goinig two years out, D1 would be next years dividend and D2 would the second years dividend.

P(i) = D(i) * ( 1 + g ) / ( k - g ) = D(i+1) / ( k - g )

What price does the stock trade for in two years? i.e. What is P(2)?

P(2) = D(2+1) / ( k - g ) = D(3) / ( k - g )

What is D(3)? i.e. what is the expected dividend in year 3?

D(i) * ( 1 + g )^n = D(i+n)

D(0) * ( 1 + g )^3 = D(0+3) = D(3)

^^^So that’s why there’s a 3 as an exponent.

(But if your question was about this formula => D^3/ (k-g), that makes no sense. Perhaps it is supposed to just be D3/ (k-g) )

Isn’t the formula:

P = D0(1+g)^n / (k - g)

So D0 = 6.25

G = 0.07

k = 0.12

n = 2

I don’t understand why it would be 3, maybe it is something in the wording?

You useexpected dividend 3yrs from now to calculate the value of the firm 2yrs from now.

It’s probably more helpful to view the formula as P(t) = D(t+1)/(r-g).

In other words, the price at any point is based on the NEXT expected dividend. So, if (for example) the question said "the next expected dividend is $3), you would simply use $3 in the numerator (and not 3 x (1+g)).

The only reason you use D(0)(1+g) is to get the next dividend).

So, since you need the price TWO years from now, you need the dividend THREE years from now.

If they’d given you the next expected dividend, that would have been D(1). So in that case, you’d only need to compound it forward two years.

Appreciaite it all–that was helpful.

The value you have is of third year because you need to find out the price of stock 2 years back.

So, think about the formula of GGM here to find out P0 we need to divide by (1+R)^3