Charta is on Google Play: practise on the go. Get the app
Charta

Use a dividend discount model with several growth stages

CFA® Level I · Equity Investments · Discounted Cash Flow (DCF) and Growth Models · EQ.1.c

The idea

A multi-stage model discounts an explicit forecast of dividends over a growth phase and then applies a terminal value, usually the constant growth formula, to the point at which growth has settled. The terminal value often dominates the answer, in many cases supplying three quarters or more of the total depending on the horizon, growth and discount rate, so the terminal growth rate deserves more scrutiny than the detailed near-term forecast that consumes most of the effort. A two-stage model with an abrupt drop in growth is a simplification; an H-model fading growth linearly is often the more plausible shape.

Formulas

Multi-stage dividend discount model

V₀ = Σ [Dₜ ÷ (1 + r)ᵗ] + terminal value ÷ (1 + r)ⁿ

Dₜ
the dividend forecast individually for each year of the first stage
r
the required return
t
the year a dividend falls in, 1 through n
n
the last year of the first stage
terminal value
the Gordon value of everything after year n, as at year n

A company growing fast now and expected to settle later. Two errors to avoid: the terminal value is struck at year n and so is discounted n years, not n + 1, and it uses the dividend of year n + 1.

A practice question

From the question bank, with the reason each wrong option is wrong.

What does a multi-stage dividend discount model add to the constant growth model?

  1. An explicit forecast period before growth settles to a sustainable rate — correct
  2. A different discount rate for each dividendWhy not: Varying the discount rate is possible but is a separate refinement. What the multi-stage model varies is the growth rate.
  3. The exclusion of terminal valueWhy not: It relies on a terminal value more than the constant growth model does — the explicit period ends and the formula takes over from there.

The explicit period accommodates a growth rate that cannot persist forever, after which the constant growth formula supplies the terminal value.

A harder one

In a typical two-stage model, which input most affects the computed value?

  1. The dividend in the first forecast yearWhy not: It scales the early cash flows, which are the smallest part of the total and the most heavily discounted.
  2. The length of the forecast periodWhy not: It matters, but mainly by changing when the terminal value is struck — which points back at the terminal assumption rather than away from it.
  3. The terminal growth rate — correct

The terminal value usually dominates the total. Small changes in it move a figure that may be three quarters of the answer, and refining year-three dividends while leaving terminal growth unexamined misallocates the analysis.

The hardest tier

Why is an abrupt drop in growth at the end of stage one a simplification worth questioning?

  1. Because it makes the model harder to computeWhy not: A step is the *easier* case to compute. The gradual fade is the extra work.
  2. Because advantage usually erodes gradually — correct
  3. Because it always overstates the valueWhy not: It can overstate or understate depending on where the step is placed. The objection is that it misdescribes the shape.

Competitive advantage rarely ends on a particular date. The shape of the decline is an assumption about the business, and a step is rarely the right shape.

In the app: 9 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.

Take the free diagnostic →

More in Discounted Cash Flow (DCF) and Growth Models