Module 8 · Equity

Equity Valuation: Concepts and Basic Tools

EN: DDM (Gordon, multi-stage), price multiples, asset-based valuation.
VN: DDM, định giá đa giai đoạn, hệ số giá, định giá theo tài sản.

In this module

One-period & Multi-period DDM
Gordon Growth Model
Two-stage DDM
Sustainable Growth Rate
P/E (Justified)
Other Multiples
Asset-based Valuation

1. Dividend Discount Model — General Core

\[ V_0 = \sum_{t=1}^{\infty} \frac{D_t}{(1 + r)^{t}} \]

Practice problem

Stock pays $2 next year, $2.20 in year 2, then sold at $50 end of year 2. r = 10%. Compute V0.

Show solution

V0 = 2/1.10 + (2.20 + 50)/1.10²

= 1.818 + 52.2/1.21

= 1.818 + 43.140

V0 ≈ $44.96

2. Gordon Growth Model Core

\[ V_0 = \frac{D_1}{r - g} = \frac{D_0(1 + g)}{r - g}, \quad r > g \]

Components

D₀ Most recent dividend (already paid).
D₁ Next year's expected dividend = D₀(1+g).
r Required return on equity.
g Constant growth rate of dividends (forever).

Practice problem

A stock just paid $2 dividend, expected to grow 5% forever. Required return = 10%. Fair value?

Show solution

D₁ = 2 × 1.05 = 2.10

V = 2.10 / (0.10 − 0.05)

= $42.00

3. Two-Stage DDM Core

\[ V_0 = \sum_{t=1}^{n}\frac{D_t}{(1 + r)^{t}} + \frac{V_n}{(1 + r)^{n}}, \quad V_n = \frac{D_{n+1}}{r - g_L} \]

High initial growth (g_S) for n years, then sustainable long-run growth (g_L) forever.

Practice problem

D0 = $1, gS = 15% for 3 yrs, then gL = 5%, r = 10%. Compute V0.

Show solution

D1=1.15, D2=1.3225, D3=1.5209

D4 = 1.5209(1.05) = 1.5969

Terminal V3 = 1.5969/(0.10−0.05) = 31.94

V0 = 1.15/1.10 + 1.3225/1.21 + (1.5209+31.94)/1.331

V0 ≈ $27.16

4. Sustainable Growth Rate Core

\[ g = ROE \times (1 - \text{Payout}) = ROE \times \text{Retention} \]

Practice problem

ROE = 15%, payout ratio = 40%. Compute g.

Show solution

Retention = 60%

g = 15% × 0.60

g = 9%

5. Justified Leading P/E Core

\[ \frac{P_0}{E_1} = \frac{1 - \text{Payout}}{\,r - g\,}\,\,? \quad \text{(no — see below)} \]

\[ \frac{P_0}{E_1} = \frac{\text{Payout ratio}}{r - g} \]

\[ \frac{P_0}{E_0} = \frac{\text{Payout}\,(1 + g)}{r - g} \quad \text{(trailing)} \]

Higher justified P/E with: lower r, higher g, higher payout (subject to g − r constraint).

Practice problem

Payout = 50%, r = 11%, g = 6%. Compute justified leading P/E.

Show solution

P/E = 0.50 / (0.11 − 0.06)

= 10.0×

6. Other Multiples Core

\[ P/B = \frac{\text{Price}}{\text{BV per share}} \] \[ P/S = \frac{\text{Price}}{\text{Sales per share}} \] \[ P/CF = \frac{\text{Price}}{\text{CF per share}} \] \[ EV/EBITDA = \frac{\text{Mkt cap} + \text{Debt} - \text{Cash}}{EBITDA} \]

Practice problem

Mkt cap $500M, debt $200M, cash $50M, EBITDA $80M. Compute EV/EBITDA.

Show solution

EV = 500 + 200 − 50 = 650

EV/EBITDA = 650/80

= 8.125×

7. Asset-based Valuation Concept

Value = FV(assets) − FV(liabilities). Best for resource extraction (mining), holding companies, or in liquidation. Weak for IP-heavy or service firms (intangibles undervalued).