Gordón Growth Model

CFA Level I
#1

What is the reasoning for subtracting g for the perpetual DDM???

thanks in advance

#2

The short answer is that we subtract g because it gives the correct value.

The long answer involves algebra:

P0 = D1/(1 + r) + D1(1 + g)/(1 + r)2 + D1(1 + g)2/(1 + r)3 + ∙ ∙ ∙

Multiplying both sides by (1 + g)/(1 + r) gives:

P0(1 + g)/(1 + r) = D1(1 + g)/(1 + r)2 + D1(1 + g)2/(1 + r)3 + ∙ ∙ ∙

Subtracting the second equation from the first, we have:

P0 − P0(1 + g)/(1 + r) = D1/(1 + r)

P0[1 − (1 + g)/(1 + r)] = D1/(1 + r)

P0[(1 + r)/(1 + r) − (1 + g)/(1 + r)] = D1/(1 + r)

P0[(1 + r) − (1 + g)]/(1 + r) = D1/(1 + r)

P0(1 + r − 1 − g)/(1 + r) = D1/(1 + r)

P0(r − g)/(1 + r) = D1/(1 + r)

P0(r − g) = D1

P0 = D1/(r − g)

#3

Thank you S2000! Besides the maths, what is the financial reason behind it? Is it like having a net cost ? Cost- growth

#4

Seriously?

The financial reason is that if dividends grow faster, the stock’s worth more.

#5

There’s really noting to the formula but the math - it’s the limit of a infinite series that expresses the present value of the stock’s future cash flows. Remember - one of the key concepts in valuation is that the value of anything is the present value of the expected future cash flows from owning it. The formula gives you the following concepts

  1. higher expected next period’s dividend means higher price (remember - the price is the present value, so higher future cash flows means higher present value

  2. Higher growth means higher price - higher growth means higher future cash flows, and higher future cash flows means higher present value

  3. Higher required rate of return means LOWER price - remember, present values are INVERSELY related to the discount rate.

However, to be clear, this isn’t the “meaning” of the formula - it simply comes from the math (As S2000 has shown)