25400 · Financial Literacy
Shares & Equity Valuation
Week 5 (second half) values equity. After distinguishing ordinary from preference shares, you apply the Dividend Discount Model: constant dividend (P0 = D1/i), the constant-growth Gordon model (P0 = D1/(i − g)), multi-year and two-stage changing-growth cases, with growth estimated as g = ROE × (1 − payout). You invert the Gordon model for the cost of common equity (Re = D1/P0 + g) and the cost of preference equity (Rp = D1/P0), then estimate the required return with CAPM, E(r) = Rf + β(Rm − Rf). These feed directly into the WACC of Week 8.
What this chapter covers
- 01Ordinary vs preference shares: variable dividend and voting vs fixed dividend, priority, usually non-voting (valued like a perpetuity)
- 02Finite-horizon DDM: P0 = Σ D_t/(1 + i)^t + Pn/(1 + i)^n (1-, 2-, 3-year variants)
- 03Constant (zero-growth) dividend: P0 = D1 / i
- 04Gordon constant-growth model: P0 = D1 / (i − g) = D0(1 + g)/(i − g), requires i > g
- 05Two-stage / changing growth: discount explicit dividends, then add PV of the terminal (Gordon) value
- 06Sustainable growth g = ROE × (1 − dividend payout ratio)
- 07Cost of common equity Re = D1/P0 + g; cost of preference equity Rp = D1/P0
- 08CAPM: E(r) = Rf + β(Rm − Rf) = Rf + β·MRP
Gordon-growth share price and cross-checking the cost of equity
- +1Sustainable growth g = ROE × (1 − payout) = 0.10 × (1 − 0.60) = 0.10 × 0.40 = 4%. The firm retains 40% of earnings and earns 10% on them, so dividends grow 4% a year.
- +1Next dividend D1 = D0(1 + g) = 2.00 × 1.04 = $2.08.
- +1Gordon price P0 = D1/(i − g) = 2.08 / (0.10 − 0.04) = 2.08 / 0.06 = $34.67. (The model is valid because i = 10% exceeds g = 4%.)
- +1CAPM cross-check: E(r) = Rf + β(Rm − Rf) = 3.5% + 1.2 × (9% − 3.5%) = 3.5% + 1.2 × 5.5% = 3.5% + 6.6% = 10.1% ≈ the 10% required return used above, so the valuation inputs are internally consistent.
Key terms
- Ordinary (common) share
- An equity instrument with variable dividends, voting rights and a residual claim on assets and profits after all other claimants. Valued with the dividend discount model.
- Preference (preferred) share
- An equity instrument paying a fixed dividend with priority over ordinary shares for dividends and in liquidation, usually without voting rights. Because the dividend is level and perpetual, it is valued like a perpetuity: P0 = D1/Rp.
- Dividend Discount Model (DDM)
- Values a share as the present value of its expected future dividends (plus any terminal sale price). Special cases include the constant-dividend perpetuity and the constant-growth Gordon model.
- Gordon growth model
- The constant-growth DDM, P0 = D1/(i − g) = D0(1 + g)/(i − g), valid only when the required return i exceeds the growth rate g. Rearranged, it gives the cost of common equity Re = D1/P0 + g.
- Sustainable growth rate
- g = ROE × (1 − dividend payout ratio) = ROE × retention ratio: the rate at which a firm can grow dividends by reinvesting retained earnings at its return on equity.
- CAPM
- The Capital Asset Pricing Model, E(r) = Rf + β(Rm − Rf), which prices the required return on equity from the risk-free rate, the asset's beta and the market risk premium (Rm − Rf).
Shares & Equity Valuation FAQ
When can I use the Gordon growth model?
Only when dividends are expected to grow at a constant rate g forever and the required return i exceeds g. If growth is high or uneven for a few years before settling, use a two-stage model: discount the explicit dividends individually, then add the present value of a terminal (Gordon) value once growth stabilises.
Do I discount D0 or D1?
D1, next period's dividend. The Gordon price is D1/(i − g); if you are given the dividend just paid (D0), grow it first: D1 = D0(1 + g). Using D0 directly is a common error that understates the share price.
How is CAPM different from the DDM cost of equity?
Both estimate the required return on equity, but from different data. The DDM/Gordon route rearranges the pricing formula to Re = D1/P0 + g and needs a dividend and a growth estimate. CAPM builds the return from market data: the risk-free rate plus beta times the market risk premium. They are useful cross-checks on each other.
Why does equity valuation matter for later weeks?
The cost of common equity (from the DDM or CAPM) and the cost of preference equity are direct inputs to the Weighted Average Cost of Capital in Week 8, which is then the discount rate for capital budgeting. Getting these right here pays off in the WACC and NPV work.
Assessment move
Organise the DDM by case: constant dividend (P0 = D1/i), constant growth (Gordon, P0 = D1/(i − g)), and multi-stage (discount explicit dividends, then add a discounted terminal value). Always grow D0 to D1 before dividing, and check i > g. Estimate g from fundamentals with g = ROE × (1 − payout). Practise inverting the Gordon model for the cost of equity and computing CAPM as an independent check, since both feed the Week-8 WACC. Rehearse a full price-plus-cost-of-equity item under time pressure for Quiz 1, and ask Sia to build fresh constant-growth and two-stage problems and verify each discounting step.
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