# CFA Level I: Dividend Discount Model & Gordon Growth Model

The simplest present value model for estimating the worth of company is the dividend discount model. It assumes that the company issues regular dividends and there is a constant required rate of return. The idea is that the value of the company is the present value of the sum of its dividend cash flows.

• Dividend Discount Model (over (t) periods): V­­ = Σ(Dt)/(1+r)t
• Dividend Discount Model (sold after (n) periods): V­­ = Σ[(Dt)/(1+r)]t + Pn/(1+r)n
• Where Pn = (Dn+1 + Pn+1)/(1+r)n+1

The second equation includes a valuation if the stock is held for (n) periods and then sold. The terminal value, P­n must be added to the DDM, which is the PV of price in the sale period plus any additional dividends.

### Gordon Growth Model

With the basic DDM equation, we assume an infinite/constant series of cash dividends. To add complexity to the model, we can include an estimate of the growth rate, (g), for the dividends, so that they increase over time. In practice, this works best for mature companies in non-cyclic industries, like utility companies. This model is called the Gordon Growth Model.

• Gordon Growth Model: V­­ = [D0(1+g)]/(r-g) = D1/(r-g)
• Where (g) = b x ROE
• B = earnings retention (1 – Dividend Payout Ratio)

This is still bases the value of company as a perpetuity of its cash flow.

### Multistage Dividend Discount Models

To better model growing companies, we can add another layer of complexity to the DDM. The Multistage DDM assumes that the growth rate of dividends will change during the company’s growth stage but eventually become a constant perpetuity. We can include any number of growth stages for the MDDM, but we begin with a two-stage DDM equation.

• Two-Stage DDM: V­­ = Σnt[D0(1+gs)t/(1+r)t] + Vn/(1+r)n
• Vn = Dn+1/(r-gl)
• Dn+1 = D0(1+gs)n(1+gl)
• Where gs = early-stage dividend growth rate
• Where gl = perpetuity-stage dividend growth rate

In the two stage model, we find the PV of the sum of the dividends growing at the early stage growth rate, and add to that the PV of the terminal value. The terminal value is the first dividend of the perpetuity growth rate, divided by (r-gl). To find this first dividend value, we multiply the original dividend by all the growth that has occurred, plus one more period at the perpetuity stage growth rate.

If we were to add another growth stage, like a transitional growth rate, to create a three-stage DDM, we would have an additional summation for the PV of the dividends during that stage, starting at the with the last dividend value during the early stage, and our terminal value dividend would reflect the total dividend growth as well.