Learning Module 5 of Equities 11–14% of the exam

Introduction to Equity Valuation

3 lessons. About 19 minutes in cram mode, 86 minutes in full.

Start with lesson 1 Learn with Sensei Read the module summary Practice this module

Lessons

1
Market price, intrinsic value and perceived value
compare 6 min cram, 26 min full
2
Equity valuation models: present value, asset-based and relative
describe 7 min cram, 32 min full
3
Book value, market capitalization and enterprise value
compare 6 min cram, 28 min full

What the exam expects you to do

Contrast price and value for an equity security.Market price, intrinsic value and perceived value
Contrast the use of book value of equity, market capitalization, and enterprise value as indicators of intrinsic value.Book value, market capitalization and enterprise value
Describe major categories of equity valuation models and explain their advantages and disadvantages.Equity valuation models: present value, asset-based and relative

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.

Market price, intrinsic value and perceived value

Known

MemorizePrice against value

Comparison	Verdict	Investor	Issuer
$P_t < IV_t$	undervalued	buy, add exposure	repurchase shares
$P_t > IV_t$	overvalued	sell, cut exposure	issue new shares
$P_t \approx IV_t$	fairly valued	no change	neither

Memory hook Cheap: the company buys back. Dear: the company sells new shares.

Know it cold Expected return if the gap closes $= (IV_t - P_t) / P_t$ : divide by the price.

MemorizePerceived value and ranges

Approach	Built on
Naive or story-based	a narrative, no deep analysis (meme stocks, cult companies, bubbles)
Relative	multiples against peers (price-to-earnings, price-to-book)
Absolute or fundamental	present value of expected cash flows

Memory hook Story, peers, cash flows.

Know it cold $IV_t = \sum \text{Prob}(i) \times P_{t,i}$ . Value range wholly above the trading range: undervalued; wholly below: overvalued; overlapping: fairly valued or unclear.

Key terms

market price Memorize
intrinsic value Memorize
perceived value Memorize
perceived value indicators Know the idea
convergence Know the idea
naive or story-based valuation Memorize
meme stocks Know the idea
cult companies Know the idea
relative valuation Memorize
absolute valuation Memorize
undervalued Memorize
overvalued Memorize
fairly valued Memorize
harder-to-value shares Know the idea
scenario analysis Use it
synthesis-of-valuation approach Know the idea
floating bar valuation chart Use it

Three ways to reach a perceived value

Investor perceived valuean estimate of intrinsic value

Naive or story-based Memorize a narrative, no deep analysis; meme stocks, cult companies, bubbles
Relative Memorize multiples against a peer group, such as price-to-earnings (P/E) or price-to-book (P/B)
Absolute or fundamental Memorize present value of expected cash flows

Price against value: verdicts and actions

Compare market price P_t with intrinsic value IV_tranges, not single numbers

Undervalued Memorize P_t below IV_t; investors buy, the issuer buys back shares
Fairly valued Memorize P_t about equal to IV_t; no action
Overvalued Memorize P_t above IV_t; investors sell, the issuer issues shares

Formulas

Expected return if the gap closes Use it

r = \dfrac{IV_t - P_t}{P_t}

Quick example

A share that pays no dividend is valued at 62.40 and trades at 52.00. (62.40 − 52.00) ÷ 52.00 = 20.00%. Divide by the price paid, not by the value (16.67% is the trap).

On your calculator

62.4−52=÷52= 0.2000

62.4ENTER52−52÷ 0.2000

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

Scenario-weighted intrinsic value Use it

IV_t = \sum_{i=1}^{n} \text{Probability}(i) \times P_{t,i}

Quick example

Bear 38.00 (25%), base 50.00 (50%), bull 66.00 (25%): 9.50 + 25.00 + 16.50 = 51.00.

On your calculator

(0.25×38)+(0.5×50)+(0.25×66)= 51.00

0.25ENTER38×0.5ENTER50×+0.25ENTER66×+ 51.00

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

Equity valuation models: present value, asset-based and relative

Known

MemorizePresent value models and their uses

Model	Discount at	Use for
Dividend discount	$r_e$	mature, stable dividend payer
Free cash flow to equity (FCFE)	$r_e$	non-payer or irregular payer, stable capital structure
Free cash flow to the firm (FCFF)	weighted average cost of capital (WACC)	high or changing leverage, negative FCFE
Residual income	$r_e$	no book distortions; irregular dividends or negative cash flow

Memory hook Shareholders' money at $r_e$ ; everyone's money (FCFF) at WACC.

Know it cold FCFF = cash flow from operations + interest × (1 − tax rate) − capital expenditures; FCFE = cash flow from operations − capital expenditures + net debt issuance.

MemorizeStrengths and weaknesses

Approach	Strength	Weakness
Present value	rigorous, flexible	detail and sensitive inputs
Asset-based	simple, market prices	misses going-concern value
Relative	simple, easy to compare	depends on the peer group

Memory hook Detail is the present value model's strength and its weakness.

Know it cold Composite EV/EBITDA above the firm's: firm undervalued vs peers; firm's above the composite: overvalued.

Key terms

absolute valuation Memorize
present value models Memorize
discounted cash flow models Know the idea
terminal value Use it
dividend discount model (DDM) Know the idea
free cash flow Know the idea
free cash flow to the firm (FCFF) Memorize
free cash flow to equity (FCFE) Memorize
net debt issuance Use it
weighted average cost of capital (WACC) Know the idea
residual income model Know the idea
asset-based valuation models Use it
relative valuation Memorize
comparables models Know the idea
multiples Know the idea
price-to-earnings (P/E) ratio Use it
trailing and forward P/E Use it
enterprise value multiples Use it
composite multiple Use it
justified price multiple Know the idea
method of comparables Know the idea
method of forecasted fundamentals Know the idea

Equity valuation models

Equity valuation modelsmost analysts combine several

Absolute valuation Memorize cash flows or asset prices that drive intrinsic value
- Present value models dividends, free cash flow to equity or to the firm, or residual income, discounted
- Asset-based models fair value of assets minus liabilities
Relative valuation Memorize multiples against peers
- Price multiples price-to-earnings, price-to-book
- Enterprise value multiples enterprise value divided by revenue or an operating profit measure

Which cash flow to discount

Present value modelmatch the cash flow to the company

Dividends Memorize mature, stable payer; at r_e
Free cash flow to equity Memorize non-payer or irregular payer, stable capital structure; at r_e
Free cash flow to the firm Memorize high or changing leverage, or negative free cash flow to equity; at WACC
Residual income Memorize no book distortions; irregular dividends or negative cash flow; at r_e

Formulas

Present value model (general form) Use it

IV_t = \sum_{i=1}^{n} \dfrac{E(CF_{t+i})}{(1 + r)^{i}} + \dfrac{E(P_{t+n})}{(1 + r)^{n}}

Quick example

Cash flows 1.50 and 1.60, expected price 30.00 at the end of year 2, required return 8%: 1.50 ÷ 1.08 + 31.60 ÷ 1.08² = 1.39 + 27.09 = 28.48.

On your calculator

CF2NDCLR WORK
0ENTER↓1.5ENTER↓↓31.6ENTER
NPV8ENTER↓CPT 28.48

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
0gCF01.5gCFj31.6gCFj8i
fNPV 28.48

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

Free cash flow to the firm Memorize

\text{FCFF} = \text{Cash flow from operations} + \text{Interest expense} \times (1 - \text{Tax rate}) - \text{Capital expenditures}

Quick example

Cash flow from operations 500, interest 40, tax 30%, capital expenditures 220: 500 + 28 − 220 = 308.

On your calculator

40×0.7+500−220= 308

500ENTER40ENTER0.7×+220− 308

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

Free cash flow to equity Memorize

\text{FCFE} = \text{Cash flow from operations} - \text{Capital expenditures} + \text{Net debt issuance}

Quick example

Cash flow from operations 500, capital expenditures 220, borrowing 60, repayment 100: 500 − 220 − 40 = 240.

On your calculator

500−220+60−100= 240

500ENTER220−60+100− 240

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

Residual income model Know the idea

IV_t = BVE_t + \sum_{i=1}^{n} \dfrac{RI_{t+i}}{(1 + r_e)^{i}} + \dfrac{E(P_{t+n}) - BVE_{t+n}}{(1 + r_e)^{n}}

Quick example

Book value 20.00 per share and positive expected residual income: value above 20.00, so price-to-book above 1.

Price-to-earnings ratio Memorize

P/E = \dfrac{P_t}{EPS_t}

Quick example

Price 63.00, earnings per share 4.20: 63.00 ÷ 4.20 = 15.0.

Weighted value across models Use it

IV_t = \sum_j w_j \times V_j

Quick example

Discounted cash flow 32, comparables 28, residual income 45 with weights 50%, 30%, 20%: 16.0 + 8.4 + 9.0 = 33.40.

On your calculator

(0.5×32)+(0.3×28)+(0.2×45)= 33.40

0.5ENTER32×0.3ENTER28×+0.2ENTER45×+ 33.40

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

Book value, market capitalization and enterprise value

Known

MemorizeThree observable measures

Measure	Formula	Watch out
Book value of equity	assets − liabilities; per share: shareholders' equity ÷ shares (no minority interest)	historical cost, intangibles and goodwill (usually excluded), contingent liabilities
Market capitalization	$P_t$ × shares outstanding	share count known after filings
Enterprise value	market value of debt + equity + preferred shares − cash and short-term investments	reporting currency; book debt as a proxy

Memory hook A buyer takes on the debt and the preferred and pockets the cash: add, add, subtract.

Know it cold P/B = $P_t$ ÷ $(BVE/\text{Share})_t$ , only among firms with similar leverage.

MemorizeMultiples and what they tell you

Multiple	Reading
Price-to-book (P/B)	lower among similar firms: cheaper; higher: more value from future cash flows
Enterprise value to revenue or to earnings before interest, taxes, depreciation, and amortization (EBITDA)	value per unit of sales or operating profit; free of currency
Below book value	maybe cheap, maybe obsolete assets or weak management

Memory hook Net debt = EV − market capitalization (no preferred).

Know it cold Negative book value makes P/B meaningless.

Key terms

book value of equity Memorize
book value per share Memorize
minority interest Know the idea
intangible assets Use it
goodwill Use it
contingent liabilities Know the idea
shareholders' equity components Know the idea
negative book value of equity Know the idea
market capitalization Memorize
shares outstanding Know the idea
share repurchase effects Know the idea
excess value and value shortfall Know the idea
price-to-book (P/B) ratio Memorize
multiples Know the idea
method of comparables Know the idea
enterprise value (EV) Memorize
net debt Use it
EV multiple Memorize

Observable indicators of intrinsic value

What you can look upnone is intrinsic value, each is a clue

Book value of equity Memorize assets minus liabilities in the audited accounts; historical
Market capitalization Memorize price times shares outstanding; forward-looking
Enterprise value Memorize equity plus preferred plus net debt; the whole firm to a buyer

Why book value can mislead

Book value of equitya historical accounting figure

Historical cost and depreciation asset age changes carrying values
Intangibles and goodwill inconsistent recording; analysts usually exclude them
Contingent liabilities legal, environmental or product claims missing
Write-downs sudden drops
Payouts above earnings can make book value negative at a profitable firm

Formulas

Book value of equity Memorize

BVE_t = \text{Book value of assets}_t - \text{Book value of liabilities}_t

Quick example

A firm reports assets of 880 and liabilities of 540 (in millions). Book value of equity = 880 − 540 = 340.

Book value per share Memorize

\left(\dfrac{BVE}{\text{Share}}\right)_t = \left(\dfrac{\text{Shareholders' equity}}{\text{Shares outstanding}}\right)_t

Quick example

Shareholders' equity of 468 million (minority interest already excluded) and 36 million shares: 468 ÷ 36 = 13.00 per share.

On your calculator

468÷36= 13.00

468ENTER36÷ 13.00

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

Shareholders' equity components Know the idea

\text{Shareholders' equity} = \text{Share capital} + \text{Additional paid-in capital} + \text{Retained earnings} - \text{Treasury stock}

Quick example

Share capital 100, additional paid-in capital 240, retained earnings 310, treasury stock 40: 100 + 240 + 310 − 40 = 610.

On your calculator

100+240+310−40= 610

100ENTER240+310+40− 610

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

Market capitalization Memorize

\text{Market capitalization}_t = P_t \times \text{Shares outstanding}_t

Quick example

A share price of 18.50 and 60 million shares: 18.50 × 60 = 1,110 million.

On your calculator

18.5×60= 1,110

18.5ENTER60× 1,110

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

Price-to-book ratio Memorize

\left(\dfrac{P}{B}\right)_t = \left(\dfrac{P}{BVE/\text{Share}}\right)_t

Quick example

Price 30.00 and book value per share 12.50: 30.00 ÷ 12.50 = 2.40.

On your calculator

30÷12.5= 2.40

30ENTER12.5÷ 2.40

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

Enterprise value Memorize

EV = \text{Market value of debt} + \text{Market value of equity} + \text{Market value of preferred shares} - \text{Cash and short-term investments}

Quick example

Market capitalization 2,000, debt 700, no preferred shares, cash 250: 2,000 + 700 − 250 = 2,450.

On your calculator

2000+700−250= 2,450

2000ENTER700+250− 2,450

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

EV multiple Memorize

\text{EV multiple} = \dfrac{\text{Enterprise value}}{\text{Revenue or an operating profit measure}}

Quick example

Enterprise value 2,450 and EBITDA 350: 2,450 ÷ 350 = 7.0.

On your calculator

2450÷350= 7.0

2450ENTER350÷ 7.0

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