You are reading the 2026 curriculum (exams up to November 2026). Sitting in February 2027 or later? Go to the 2027 Equities guide.

Learning Module 8 of Equity Investments 11–14% of the exam

Equity Valuation: Concepts and Basic Tools

6 lessons. About 42 minutes in cram mode, 190 minutes in full.

Start with lesson 1 Learn with Sensei Read the module summary

Lessons

1
Intrinsic value vs price, and the three families of valuation models
evaluate 6 min cram, 28 min full
2
Dividends, stock splits and share repurchases
describe 6 min cram, 26 min full
3
Dividend discount and free-cash-flow-to-equity models
explain 6 min cram, 28 min full
4
Gordon growth model and preferred stock valuation
calculate 8 min cram, 36 min full
5
Two-stage (multistage) dividend discount model
calculate 8 min cram, 32 min full
6
Price multiples, enterprise value and asset-based valuation
explain 8 min cram, 40 min full

What the exam expects you to do

Evaluate whether a security, given its current market price and a.Intrinsic value vs price, and the three families of valuation models
Value estimate, is overvalued, fairly valued, or undervalued by the market.Intrinsic value vs price, and the three families of valuation models
Describe major categories of equity valuation models.Intrinsic value vs price, and the three families of valuation models
Describe regular cash dividends, extra dividends, stock dividends, stock splits, reverse stock splits, and share repurchases.Dividends, stock splits and share repurchases
Describe dividend payment chronology.Dividends, stock splits and share repurchases
Explain the rationale for using present value models to value equity and describe the dividend discount and free-cash-flow-to-equity models.Dividend discount and free-cash-flow-to-equity models
Explain advantages and disadvantages of each category of valuation model.Intrinsic value vs price, and the three families of valuation models
Calculate the intrinsic value of a non-callable, non-convertible preferred stock.Gordon growth model and preferred stock valuation
Calculate and interpret the intrinsic value of an equity security based on the Gordon (constant) growth dividend discount model or a two-stage dividend discount model, as appropriate.Gordon growth model and preferred stock valuation
Identify characteristics of companies for which the constant growth or a multistage dividend discount model is appropriate.Gordon growth model and preferred stock valuation
Explain the rationale for using price multiples to value equity, how the price to earnings multiple relates to fundamentals, and the use of multiples based on comparables.Price multiples, enterprise value and asset-based valuation

Module summary

The whole module on one sheet, organised by lesson: what to memorize, how the ideas fit together, the formulas and the key terms. No paragraphs, just what you need to revise.

Hide what I know

How deeply to learn each part

Know the idea: Understand it in general. It frames other topics, but you will not calculate with it.
Use it: Understand it well enough to solve a question with it. Recognize when it applies.
Memorize: Learn it by heart. The exam will not give it to you.

Intrinsic value vs price, and the three families of valuation models

Known

MemorizeThe verdict rule

Estimate vs price	Verdict	Action
V > P	undervalued	buy candidate
V = P (or P inside the error band)	fairly valued	no action
V < P	overvalued	avoid or sell

Memory hook Value is what you get, price is what you pay. If you get more than you pay, it is cheap.

Know it cold Act only when the gap beats your model uncertainty AND price is expected to converge to value in your horizon.

MemorizeWhich family fits which company

Family	Best fit	Main weakness
Present value	mature dividend payer; stable, forecastable cash flows	very sensitive to r and g; needs long forecasts
Multiplier	company with listed, similar peers	relative only; accounting differences; negative earnings
Asset-based	bank, investment holding firm, liquidation, private firm with few intangibles	intangibles and specialized assets are hard to value

Memory hook Cash flows, peers, or assets: ask which of the three you can measure most reliably for this company.

Know it cold A multiple tells you cheap or dear compared with peers, never cheap or dear in absolute terms.

Key terms

intrinsic value Use it
market price Know the idea
undervalued Memorize
overvalued Memorize
fairly valued Memorize
present value models Use it
discounted cash flow models Know the idea
multiplier models Use it
market multiple models Know the idea
asset-based valuation models Use it

Value against price: the three verdicts

Intrinsic value estimate V against market price Pa verdict only counts if the gap is bigger than your uncertainty

Undervalued Memorize V above P; a candidate to buy
Fairly valued Memorize V equals P, or P sits inside your error band
Overvalued Memorize V below P; avoid, sell or short

Three families of equity valuation models

Equity valuation modelsanalysts often use more than one and compare

Present value (discounted cash flow) Use it PV of cash flows to shareholders
- Dividend discount model cash flow is dividends
- Free-cash-flow-to-equity model cash flow is dividend-paying capacity
Multiplier (market multiple) Use it a multiple of a fundamental
- Price multiples P/E, P/B, P/S, P/CF
- Enterprise value multiples EV/EBITDA, EV/sales
Asset-based Use it fair value of assets minus liabilities

Formulas

Value gap (upside) Use it

\text{gap} = \dfrac{V}{P} - 1

Quick example

An analyst values a share at 30.00 and it trades at 33.60. 30.00 ÷ 33.60 − 1 = −10.71%, so the share looks overvalued.

On your calculator

30÷33.6−1= −0.1071

30ENTER33.6÷1− −0.1071

ENTER enter (on the HP, puts the number on the stack)

Dividends, stock splits and share repurchases

Known

MemorizePayouts: effect on shareholder wealth

Event	Shares	Price	Total value
Cash dividend	same	falls by about D	cash received offsets
Stock dividend, split	up	down in proportion	unchanged
Reverse split	down	up in proportion	unchanged
Share repurchase	down	about the same	same as a dividend of equal size

Memory hook Cutting the pie into more slices does not make more pie.

Know it cold Stock dividends and splits are not relevant for valuation. New price = old price ÷ (new shares per old share).

MemorizeDividend dates in order

Order	Date	What matters
1	Declaration	amount and dates announced
2	Ex-dividend	buy before this date to receive the dividend
3	Holder of record	register is checked
4	Payment	cash arrives

Memory hook Declare, Ex, Record, Pay. Ex comes before Record because settlement takes a day or two.

Know it cold Buy BEFORE the ex-date to get the dividend. On the ex-date the price falls by about the dividend.

MemorizeWhy companies repurchase shares

Reason	Meaning
Signal	management thinks the shares are undervalued
Flexibility	amount and timing are discretionary, unlike a regular dividend
Tax efficiency	where dividends are taxed more than capital gains
Absorb dilution	shares issued when employees exercise stock options

Memory hook S-F-T-A: Signal, Flexibility, Tax, Absorb.

Know it cold Repurchased shares get no dividends, no votes and are left out of EPS.

Key terms

regular cash dividend Memorize
extra dividend Memorize
special dividend Know the idea
liquidating dividend Use it
stock dividend Memorize
bonus issue of shares Know the idea
stock split Memorize
reverse stock split Memorize
share repurchase Memorize
buyback Know the idea
declaration date Memorize
ex-dividend date Memorize
holder-of-record date Memorize
payment date Memorize

Ways a company pays shareholders or reshapes its shares

Payouts and share-count changesonly the first group moves cash to shareholders

Cash returned Memorize cash leaves the company
- Regular cash dividend set intervals; quarterly in US and Canada, semiannual in Europe and Japan, annual in some others
- Extra (special) dividend irregular or on top of the regular one; cyclical and restructuring firms
- Liquidating dividend return of capital, not of earnings
- Share repurchase (buyback) equivalent to a cash dividend of the same amount, all else equal
Share count changed, no cash Memorize value of the pie is unchanged
- Stock dividend (bonus issue) new shares, typically 2% to 10%
- Stock split more shares, lower price
- Reverse stock split fewer shares, higher price

The dividend timetable, in order

Dividend payment chronologyset in motion when the board votes to pay

1. Declaration date Memorize board announces amount and dates
2. Ex-dividend date Memorize first day shares trade without the dividend; price drops by about D
3. Holder-of-record date Memorize owners on the register are paid; one or two business days after the ex-date
4. Payment date Memorize cash is sent

Formulas

Price after a split or stock dividend Use it

P_1 = \dfrac{P_0}{k}, \quad k = \dfrac{\text{new shares}}{\text{old shares}}

Quick example

A 4-for-3 split (k = 1.3333) of a share at 80.00 gives 80.00 ÷ 1.3333 = 60.00. A 20% stock dividend is k = 1.20, and a 1-for-5 reverse split is k = 0.20.

On your calculator

80÷4×3= 60

80ENTER4÷3× 60

ENTER enter (on the HP, puts the number on the stack)

Ex-dividend price Use it

P_{ex} \approx P_{cum} - D

Quick example

A share closes at 48.00 the day before its ex-dividend date and the dividend is 0.90. The price should open near 48.00 − 0.90 = 47.10.

On your calculator

48−0.9= 47.1

48ENTER0.9− 47.1

ENTER enter (on the HP, puts the number on the stack)

Dividend discount and free-cash-flow-to-equity models

Known

MemorizePresent value model formulas

Model	Formula	Discount rate
DDM, forever	$V_0 = \sum D_t / (1+r)^t$	required return on equity
DDM, holding period n	$\sum_{t=1}^{n} D_t/(1+r)^t + P_n/(1+r)^n$	required return on equity
FCFE	$V_0 = \sum FCFE_t / (1+r)^t$	required return on equity (never WACC)

Memory hook Same engine, different fuel: dividends or FCFE, discounted at the shareholders' return.

Know it cold FCFE = CFO − FCInv + net borrowing. The sale price at the end of the holding period is part of the value.

MemorizeDDM against FCFE

	DDM	FCFE
Cash flow	dividends paid	cash available after reinvestment and debt flows
Suits	stable payers; minority holders	non-payers; dividends that do not reflect capacity
Weakness	hard for non-payers	can be negative and volatile

Memory hook Minority holders get paid in dividends, so dividends are their cash flow. A controlling owner can decide to pay out FCFE.

Know it cold Intrinsic value does not depend on the investor's holding period.

Key terms

dividend discount model (DDM) Memorize
free-cash-flow-to-equity models Use it
free cash flow to equity (FCFE) Memorize
required rate of return on equity Use it
holding period Use it
terminal stock value Use it

Present value models of equity

Present value (discounted cash flow) modelsdiscount cash flows to shareholders at the required return on equity

Dividend discount model (DDM) Memorize cash flow is the dividend actually paid
- Best for stable payers; minority holders who only receive dividends
- Weak for non-payers; payouts that do not track capacity
Free-cash-flow-to-equity model (FCFE) Memorize cash flow is dividend-paying capacity
- Best for non-payers; control perspective
- Weak for FCFE can be negative and volatile; needs full forecasts

Building FCFE

FCFEcash available to common shareholders

Cash flow from operations (CFO) Memorize net income + non-cash charges − investment in working capital
minus Fixed capital investment (FCInv) Memorize reported capital expenditure is the usual proxy
plus Net borrowing Memorize new borrowing minus repayments, not gross borrowing

Formulas

Dividend discount model (infinite horizon) Memorize

V_0 = \sum_{t=1}^{\infty} \dfrac{D_t}{(1 + r)^t}

Quick example

The value is the present value of every future dividend at the required return r. It holds whatever the investor's own holding period is.

Value over a finite holding period Memorize

V_0 = \sum_{t=1}^{n} \dfrac{D_t}{(1 + r)^t} + \dfrac{P_n}{(1 + r)^n}

Quick example

Dividends of 1.50 and 1.60, then a sale at 40.00 at the end of year 2, with r = 8%. 1.50 ÷ 1.08 + (1.60 + 40.00) ÷ 1.08² = 37.05.

On your calculator

CF2NDCLR WORK
0ENTER↓1.5ENTER↓↓41.6ENTER
NPV8ENTER↓CPT 37.0542

CF cash flow worksheet · 2ND second function (the shifted label above a key) · CLR WORK clear the worksheet · ENTER enter (on the HP, puts the number on the stack) · NPV net present value · CPT compute

fCLEAR REG
0gCF01.5gCFj41.6gCFj8i
fNPV 37.0542

f gold shift key · CLEAR REG clear all registers · g blue shift key · CF0 cash flow at time zero · CFj cash flow j · i interest rate per period · NPV net present value

One-year value Use it

V_0 = \dfrac{D_1 + P_1}{1 + r}

Quick example

A dividend of 0.80 and a sale at 26.00 in one year, with r = 10%. (0.80 + 26.00) ÷ 1.10 = 24.36.

On your calculator

0.8+26=÷1.1= 24.3636

0.8ENTER26+1.1÷ 24.3636

ENTER enter (on the HP, puts the number on the stack)

Free cash flow to equity Memorize

FCFE = CFO - FCInv + \text{net borrowing}

Quick example

CFO of 240, fixed capital investment of 130, new borrowing of 60 and repayments of 25. 240 − 130 + (60 − 25) = 145.

On your calculator

240−130+(60−25)= 145

240ENTER130−60ENTER25−+ 145

ENTER enter (on the HP, puts the number on the stack)

FCFE valuation Use it

V_0 = \sum_{t=1}^{\infty} \dfrac{FCFE_t}{(1 + r)^t}

Quick example

Same as the DDM, with FCFE per share in place of the dividend, and still discounted at the required return on equity.

Required return from CAPM Use it

r = R_f + \beta \times \text{market risk premium}

Quick example

Risk-free rate 3%, beta 1.2, market risk premium 5.5%. 3 + 1.2 × 5.5 = 9.6%.

On your calculator

1.2×5.5+3= 9.6

1.2ENTER5.5×3+ 9.6

ENTER enter (on the HP, puts the number on the stack)

Gordon growth model and preferred stock valuation

Known

MemorizeValue formulas and which dividend to use

Security	Formula	Numerator
Perpetual preferred	$V_0 = D / r$	D = dividend rate × par
Gordon growth	$V_0 = D_1 / (r - g)$	D₁ = D₀ × (1 + g), next year's dividend
Implied required return	$r = D_1/P_0 + g$	dividend yield + growth
Sustainable growth	$g = b \times ROE$	b = 1 − payout

Memory hook The model values the stream from NEXT year, so the numerator is one step ahead: D₁, not D₀.

Know it cold Require r > g. Discount preferred dividends at the required return, never at the dividend rate.

MemorizeGordon assumptions

Assumption	If it fails
Dividends are the right cash flow	use FCFE
Growth constant forever	use a multistage DDM
Required return constant	model is no longer valid
g < r	value is infinite or negative

Memory hook Value explodes as g approaches r: 42.92, 52.00, 65.63, 88.33 for g = 3, 4, 5, 6% (D₀ = 2.50, r = 9%).

Know it cold Fits mature, stable payers (utilities, staples). A high-growth or no-dividend company does not fit.

Key terms

preferred stock Use it
perpetuity Know the idea
Gordon growth model Memorize
constant growth DDM Know the idea
sustainable growth rate Memorize
retention rate Memorize

When the constant growth model fits

Is the Gordon growth model appropriate?it needs stable dividends growing below r, forever

Good fit Use it mature, profitable, pays a dividend
- Stable payout and growth near or below long-run nominal economic growth
- Not sensitive to the business cycle regulated water utility, household goods maker
Poor fit Use it use FCFE, a multistage DDM or multiples
- No dividend, or erratic dividends nothing stable to extrapolate
- Growth above r, or growth set to change formula fails, or growth fades

How features change preferred stock value

Non-callable, non-convertible preferred stockthe base case: V = D ÷ r (perpetual) or bond-style (dated)

Callable by the issuer Use it issuer holds the option, so value to the investor is lower
Retractable (putable) by the holder Use it holder holds the option, so value is higher
Convertible into common shares Know the idea conversion right adds value for the holder

Formulas

Perpetual preferred stock Memorize

V_0 = \dfrac{D}{r}, \quad D = \text{dividend rate} \times \text{par}

Quick example

A 5.2% preferred share on par of 60.00 pays 3.12. At a required return of 6.5%, 3.12 ÷ 0.065 = 48.00.

On your calculator

0.052×60÷0.065= 48

0.052ENTER60×0.065÷ 48

ENTER enter (on the HP, puts the number on the stack)

Preferred stock with a maturity date Use it

V_0 = \sum_{t=1}^{n} \dfrac{D}{(1 + r)^t} + \dfrac{F}{(1 + r)^n}

Quick example

Par (F) of 50.00, annual dividend of 2.75, eight years to maturity, r = 6.5%. Value = 46.96, valued like a bond.

On your calculator

2NDCLR TVM
8N6.5I/Y2.75PMT50FV
CPTPV −46.96

2ND second function (the shifted label above a key) · CLR TVM clear the time value of money keys · N number of periods · I/Y interest rate per year (per period when P/Y is 1) · PMT payment · FV future value · CPT compute · PV present value

fCLEAR FIN
8n6.5i2.75PMT50FV
PV −46.96

f gold shift key · CLEAR FIN clear the financial registers · n number of periods · i interest rate per period · PMT payment · FV future value · PV present value

Gordon growth model Memorize

V_0 = \dfrac{D_1}{r - g} = \dfrac{D_0\,(1 + g)}{r - g}

Quick example

Last dividend 1.50, g = 5%, r = 11%. D₁ = 1.575 and 1.575 ÷ 0.06 = 26.25.

On your calculator

1.5×1.05÷(0.11−0.05)= 26.25

1.5ENTER1.05× D₁
0.11ENTER0.05− r − g
÷ 26.25

ENTER enter (on the HP, puts the number on the stack)

Implied required return Memorize

r = \dfrac{D_1}{P_0} + g

Quick example

Price 36.00, last dividend 1.50, g = 3.5%. D₁ = 1.5525; 1.5525 ÷ 36.00 + 0.035 = 7.81%.

On your calculator

1.5×1.035÷36+0.035= 0.078125

1.5ENTER1.035×36÷0.035+ 0.078125

ENTER enter (on the HP, puts the number on the stack)

Implied growth rate Use it

g = \dfrac{P_0\,r - D_0}{P_0 + D_0}

Quick example

Price 52.00, last dividend 2.50, r = 9%. (52.00 × 0.09 − 2.50) ÷ (52.00 + 2.50) = 4.00%.

On your calculator

52×0.09−2.5=÷(52+2.5)= 0.04

52ENTER0.09×2.5−
52ENTER2.5+
÷ 0.04

ENTER enter (on the HP, puts the number on the stack)

Sustainable growth rate Memorize

g = b \times ROE, \quad b = 1 - \text{payout ratio}

Quick example

Payout 40%, ROE 12%. Retention b = 0.60 and g = 0.60 × 12% = 7.2%.

On your calculator

1−0.4=×0.12= 0.072

1ENTER0.4−0.12× 0.072

ENTER enter (on the HP, puts the number on the stack)

Two-stage (multistage) dividend discount model

Known

MemorizeTwo-stage DDM in four steps

Step	What to do
1	Grow D₀ at g_S to get D₁ … Dₙ
2	Find Dₙ₊₁ = Dₙ × (1 + g_L)
3	Vₙ = Dₙ₊₁ ÷ (r − g_L), valued at year n
4	V₀ = PV of D₁ … Dₙ + Vₙ ÷ (1 + r)ⁿ

Memory hook The Gordon value sits one year before its first dividend, so the dividend you need is the one AFTER the high-growth phase.

Know it cold Discount Vₙ for n years (not n + 1). Use g_L in the terminal formula, never g_S. Terminal value is usually most of the answer.

MemorizeWhich model suits which company

Company	Model
Mature, stable payout, growth below r	Gordon growth
High growth now, will fade to a sustainable rate	two-stage
Young: growth, then transition, then maturity	three-stage
No dividend or erratic dividends	FCFE or multiples

Memory hook One stage per distinct growth regime you can defend.

Know it cold The long-term growth rate must stay below r and near the economy's growth.

Key terms

multistage dividend discount model Use it
two-stage DDM Memorize
three-stage DDM Know the idea
high-growth phase Use it
mature phase Use it
terminal value Memorize

Which dividend model for which company

Choose the model by the growth pathmatch the stages to how growth will actually fade

Constant growth (Gordon) Use it already at a sustainable rate; mature
Two-stage DDM Use it a finite spell of unusually high (or low) growth, then a sustainable rate
- Typical case new product or advantage that fades as competitors arrive
- Also fits an older firm with a temporary burst or dip in growth
Three-stage DDM Know the idea growth, then a transition of declining growth, then maturity
- Typical case a young company just entering its growth phase
Not a dividend model Use it no dividend or dividends unrelated to capacity: FCFE or multiples

Formulas

Two-stage dividend discount model Memorize

V_0 = \sum_{t=1}^{n} \dfrac{D_0(1 + g_S)^t}{(1 + r)^t} + \dfrac{V_n}{(1 + r)^n}

Quick example

D₀ = 2.00, growth 10% for two years then 4%, r = 9%. D₁ = 2.20, D₂ = 2.42, V₂ = 2.5168 ÷ 0.05 = 50.336. V₀ = 2.20 ÷ 1.09 + (2.42 + 50.336) ÷ 1.09² = 46.42.

On your calculator

CF2NDCLR WORK
0ENTER↓2.2ENTER↓↓52.756ENTER
NPV9ENTER↓CPT 46.4220

fCLEAR REG
0gCF02.2gCFj52.756gCFj9i
fNPV 46.4220

f gold shift key · CLEAR REG clear all registers · g blue shift key · CF0 cash flow at time zero · CFj cash flow j · i interest rate per period · NPV net present value

Terminal value (Gordon formula at year n) Memorize

V_n = \dfrac{D_{n+1}}{r - g_L}

Quick example

The last high-growth dividend is 1.80 (year 3), g_L = 3%, r = 9%. D₄ = 1.80 × 1.03 = 1.854 and V₃ = 1.854 ÷ 0.06 = 30.90.

On your calculator

1.8×1.03÷(0.09−0.03)= 30.9

1.8ENTER1.03× D₄
0.09ENTER0.03− r − g
÷ 30.9

ENTER enter (on the HP, puts the number on the stack)

First dividend of the stable phase Memorize

D_{n+1} = D_0(1 + g_S)^n(1 + g_L)

Quick example

D₀ = 1.20, three years at 15%, then 5%. D₄ = 1.20 × 1.15³ × 1.05 = 1.9163.

On your calculator

1.2×1.15×1.15×1.15×1.05= 1.9163

1.2ENTER1.15×1.15×1.15×1.05× 1.9163

ENTER enter (on the HP, puts the number on the stack)

Price multiples, enterprise value and asset-based valuation

Known

MemorizeJustified P/E and what moves it

Driver	Effect on justified P/E
Growth g up	up
Required return r up (more risk)	down
Payout p up, growth unchanged	up
Forward formula	p ÷ (r − g)
Trailing formula	p(1 + g) ÷ (r − g), i.e. forward × (1 + g)

Memory hook A multiple is a compressed discounted cash flow (DCF) valuation: growth up, risk down, multiple up.

Know it cold Raising payout usually cuts growth (g = b × ROE), so the effects interact. The model needs r > g.

MemorizePrice multiples: use and flaw

Multiple	Why use it	Flaw
P/E	earnings drive value; widely quoted	negative or one-off earnings
P/B	book value usually positive; banks	ignores intangibles
P/S	positive with losses; hard to manipulate	ignores costs and margins
P/CF	less affected by accruals	cash flow definitions vary

Memory hook Each multiple fixes the previous one’s weakness: negative earnings → sales; accruals → cash flow; losses → book.

Know it cold Multiples are RELATIVE. Cheap against peers is not cheap against intrinsic value.

MemorizeEnterprise value

Item	Treatment
Market cap	+
Debt	+
Preferred stock	+
Minority interest	+
Cash and short-term investments	− (subtract)

Memory hook EV is the takeover price: you inherit the debt but you also get the cash.

Know it cold EV/EBITDA pairs a whole-firm value with a pre-interest earnings figure, so leverage does not distort the comparison. Equity = EV − debt − preferred − minority interest + cash.

Key terms

price multiple Use it
trailing P/E Use it
forward (leading) P/E Use it
justified P/E Memorize
price-to-book Use it
price-to-sales Use it
price-to-cash-flow Use it
method of comparables Use it
law of one price Know the idea
enterprise value Memorize
EV/EBITDA Memorize
asset-based valuation Use it
book value Know the idea
carrying value Know the idea

The four common price multiples

Price multiplesprice divided by a per-share fundamental; trailing or forward, but be consistent

P/E (price to earnings) Memorize the most quoted; but negative or one-off earnings distort it
P/B (price to book value) Memorize good for banks and asset-heavy firms; ignores intangibles
P/S (price to sales) Memorize positive even with losses and hard to manipulate; ignores costs
P/CF (price to cash flow) Memorize less affected by accruals; cash flow definitions vary

From market cap to enterprise value

Enterprise value (EV)roughly the cost of buying the whole business

Market value of equity Memorize price × shares
plus Market value of debt Memorize a buyer takes on the debt
plus Preferred stock Memorize a senior claim
plus Minority interest Use it subsidiary earnings consolidated but not fully owned
minus Cash and short-term investments Memorize a buyer gets the cash; never add it

When asset-based valuation works

Asset-based valuationfair value of assets minus liabilities

Works well Use it few intangibles; mostly current or marketable assets
- Examples banks, investment holding firms, natural resource firms, private companies, liquidations
Works badly Use it value sits in things the balance sheet cannot show
- Valuable intangibles software, brands, customer relationships: gives only a floor
- Specialized or hard-to-price assets fair value differs from carrying value
- Hyperinflation asset values harder to estimate

Formulas

Trailing and forward P/E Use it

P/E_{trailing} = \dfrac{P_0}{E_0}, \quad P/E_{forward} = \dfrac{P_0}{E_1}

Quick example

Price 42.00, last year's EPS 2.80 and next year's forecast EPS 3.00. Trailing 42.00 ÷ 2.80 = 15.0; forward 42.00 ÷ 3.00 = 14.0.

On your calculator

42÷2.8= 15
42÷3= 14

42ENTER2.8÷ 15
42ENTER3÷ 14

ENTER enter (on the HP, puts the number on the stack)

Other price multiples Use it

P/S = \dfrac{P}{\text{sales per share}}, \quad P/CF = \dfrac{P}{\text{cash flow per share}}, \quad P/B = \dfrac{P}{BVPS}

Quick example

Price 42.00; sales per share 28.00; operating cash flow per share 5.25; book value per share 21.00. P/S = 1.5, P/CF = 8.0, P/B = 2.0.

On your calculator

42÷28= 1.5
42÷5.25= 8
42÷21= 2

42ENTER28÷ 1.5
42ENTER5.25÷ 8
42ENTER21÷ 2

ENTER enter (on the HP, puts the number on the stack)

Justified forward P/E Memorize

\dfrac{P_0}{E_1} = \dfrac{D_1/E_1}{r - g} = \dfrac{p}{r - g}

Quick example

Payout 45%, r = 10%, g = 6%. 0.45 ÷ (0.10 − 0.06) = 11.25.

On your calculator

0.45÷(0.1−0.06)= 11.25

0.45ENTER0.1ENTER0.06−÷ 11.25

ENTER enter (on the HP, puts the number on the stack)

Justified trailing P/E Memorize

\dfrac{P_0}{E_0} = \dfrac{p\,(1 + g)}{r - g}

Quick example

Payout 45%, r = 10%, g = 6%. 0.45 × 1.06 ÷ 0.04 = 11.93. It is the forward P/E times (1 + g).

On your calculator

0.45×1.06÷(0.1−0.06)= 11.925

0.45ENTER1.06×0.1ENTER0.06−÷ 11.925

ENTER enter (on the HP, puts the number on the stack)

Value by comparables Use it

V = \text{benchmark multiple} \times \text{company fundamental}

Quick example

Peer median P/E 14.0 and company EPS 3.10. 14.0 × 3.10 = 43.40.

On your calculator

14×3.1= 43.4

14ENTER3.1× 43.4

ENTER enter (on the HP, puts the number on the stack)

Enterprise value Memorize

EV = \text{market cap} + \text{debt} + \text{preferred} + \text{minority interest} - \text{cash and short-term investments}

Quick example

Market cap 1,800, debt 600, cash 150 (USD m). 1,800 + 600 − 150 = 2,250.

On your calculator

1800+600−150= 2250

1800ENTER600+150− 2250

ENTER enter (on the HP, puts the number on the stack)

EV/EBITDA Memorize

\dfrac{EV}{EBITDA}

Quick example

EV 2,250 and EBITDA 250. 2,250 ÷ 250 = 9.0×.

On your calculator

2250÷250= 9

2250ENTER250÷ 9

ENTER enter (on the HP, puts the number on the stack)

Asset-based value per share Use it

V = \dfrac{\text{fair value of assets} - \text{fair value of liabilities}}{\text{shares}}

Quick example

Assets at fair value 1,850, liabilities 1,120, 50 million shares. (1,850 − 1,120) ÷ 50 = 14.60.

On your calculator

1850−1120=÷50= 14.6

1850ENTER1120−50÷ 14.6

ENTER enter (on the HP, puts the number on the stack)

Cheat sheet · PDF · 6 A4 pages

Equity Valuation: Concepts and Basic Tools on 6 pages

What to memorize, the concept maps, every formula with a worked example and keystrokes for the TI BA II Plus and HP 12C, how each idea is asked, and the traps. Print it, or keep it on your phone.

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