BFC2140 · Corporate Finance
Share Valuation & the Dividend-Discount Model
The dividend-discount model (DDM) values a share as the present value of all the dividends it will ever pay, discounted at the required return on equity. This chapter covers the zero-growth, constant-growth (Gordon) and multi-stage growth versions, the implied-return rearrangement, preference shares as a perpetuity, and the model's limitations. It is examined as Section B numerical pricing (constant and multi-stage) and Section C reasoning about which growth assumption fits and why the model fails for non-dividend-paying or super-growth firms.
What this chapter covers
- 01Intrinsic value as the present value of all expected future dividends
- 02Zero-growth model: P₀ = D/rₑ (a level-dividend perpetuity)
- 03Constant-growth (Gordon) model: P₀ = D₁/(rₑ − g) = D₀(1 + g)/(rₑ − g), valid when rₑ > g
- 04Multi-stage / variable growth: PV of explicit dividends plus PV of a terminal price
- 05The implied (expected) return: rₑ = D₁/P₀ + g — dividend yield plus capital-gains yield
- 06Preference shares valued as a perpetuity: P = D_p/r_p
- 07The dividend-vs-growth trade-off and the limitations of the DDM
Two-stage dividend-discount model
- 1 markProject the explicit high-growth dividends: D₁ = 2.00 × 1.09 = $2.18, D₂ = 2.18 × 1.09 = $2.376, D₃ = 2.376 × 1.09 = $2.590.
- 1 markFind the first stable-growth dividend: D₄ = D₃ × 1.04 = 2.590 × 1.04 = $2.694.
- 1 markCompute the terminal price at the end of year 3 with the Gordon model: P₃ = D₄/(rₑ − g) = 2.694/(0.11 − 0.04) = 2.694/0.07 = $38.49.
- 1 markDiscount the year-1 and year-2 dividends to today: 2.18/1.11 = 1.964 and 2.376/1.11² = 1.929.
- 1 markDiscount the combined year-3 cash flow (D₃ plus the terminal price): (2.590 + 38.49)/1.11³ = 41.08/1.367 = 30.029.
- 1 markSum the present values: P₀ = 1.964 + 1.929 + 30.029 = $33.92.
Key terms
- Dividend-discount model (DDM)
- A share-valuation model that sets intrinsic value equal to the present value of all expected future dividends, discounted at the required return on equity rₑ. All its variants (zero, constant and multi-stage growth) are special cases of this one idea.
- Constant-growth (Gordon) model
- P₀ = D₁/(rₑ − g), where dividends grow at a single constant rate g forever. It is valid only when rₑ > g; if g ≥ rₑ the formula breaks down and a multi-stage model is needed.
- Multi-stage (variable) growth model
- Values a share whose growth changes over time: discount each explicitly forecast dividend, then add the present value of a terminal price (itself a Gordon value of the dividends in the stable phase) calculated at the end of the high-growth period.
- Implied / expected return
- Rearranging the Gordon model gives rₑ = D₁/P₀ + g — the dividend yield plus the (constant) capital-gains/growth yield. It is the return the market price implies investors expect to earn.
- Preference shares
- Shares paying a fixed dividend with priority over ordinary dividends; valued as a perpetuity P = D_p/r_p. They behave like a hybrid between a bond and equity and reappear as the cost of preference shares in WACC.
- Terminal value
- The value, at the end of the explicit forecast horizon, of all dividends beyond it — usually a Gordon value of the first stable-growth dividend. It must be discounted back to today and typically makes up most of a share's value.
Share Valuation & the Dividend-Discount Model FAQ
When can I use the Gordon (constant-growth) model and when must I go multi-stage?
Use the single-stage Gordon model only when dividends grow at one constant rate forever and that rate is below the required return (rₑ > g). If the firm has a high-growth phase that will slow to a sustainable rate, or different growth in different periods, use the multi-stage model: discount each explicit dividend, then add the present value of a terminal Gordon value computed from the first stable-growth dividend. If g ≥ rₑ in the Gordon formula you get a negative or infinite price — a sign you have the wrong model or an unsustainable growth assumption.
Do I grow by D₀ or D₁ in the numerator?
The Gordon numerator is always next period's dividend, D₁ = D₀(1 + g). The most common error is to put the just-paid dividend D₀ on top — that understates the price. In multi-stage problems, the terminal value uses the first dividend of the stable phase (e.g. D₄ if the high-growth phase ends at year 3), grown by the long-run rate, not the high-growth rate.
How do I find the required return rₑ from the price?
Rearrange the Gordon model to rₑ = D₁/P₀ + g. This splits the expected return into a dividend yield (D₁/P₀) and a capital-gains yield (g, the constant dividend/price growth rate). It is the same expected-return idea you will meet again as the cost of equity, where rₑ from the DDM is one of the two ways (alongside the CAPM) to estimate it.
What are the limitations of the dividend-discount model?
The DDM is only as good as its inputs: it needs a firm that pays dividends, is highly sensitive to the assumed growth rate g and required return rₑ (small changes swing the price a lot, especially when rₑ − g is small), and cannot handle g ≥ rₑ. It is awkward for firms that pay no dividends or have volatile, unpredictable payouts. For those, analysts turn to free-cash-flow valuation or multiples, but the DDM remains the cleanest illustration that a share is worth the present value of what it returns to shareholders.
How is share valuation examined in BFC2140?
It appears in the Week 6 MST (valuation is in Weeks 1-5) and again on the final. Expect Section B numerical questions pricing a share with the constant-growth or two-stage model, solving for the implied return, or valuing preference shares as a perpetuity, plus Section C reasoning about which growth assumption is appropriate and what the model's limitations are. The constant-and-variable-growth DDM is explicitly listed as a high-yield recurring skill.
Exam move
Anchor everything to the one idea — a share is worth the present value of its future dividends — and the formulas become variations on a theme. Memorise the Gordon model and always check rₑ > g before using it, and practise the implied-return rearrangement rₑ = D₁/P₀ + g so you can move between price and return fluently. For multi-stage problems, draw a dividend timeline, mark where growth changes, compute the terminal value at the correct year using the first stable-growth dividend, and remember to discount it back. Treat preference shares as a simple perpetuity (D_p/r_p) and note that both the DDM equity cost and the preference cost return in the WACC chapter. Be ready to discuss limitations in words — sensitivity to g and rₑ, the rₑ > g requirement, and the trouble with non-dividend payers — because Section C rewards that reasoning, not just the number.
