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 4 of Equity Investments 11–14% of the exam

Overview of Equity Securities

5 lessons. About 26 minutes in cram mode, 120 minutes in full.

Start with lesson 1 Learn with Sensei Read the module summary

Lessons

1
Common shares and preference shares
describe 6 min cram, 28 min full
2
Public vs private equity: venture capital, buyouts and PIPEs
compare 4 min cram, 20 min full
3
Investing in foreign shares: direct, depository receipts and global shares
describe 6 min cram, 24 min full
4
Risk and return of equity securities, and why companies issue them
compare 4 min cram, 20 min full
5
Book value vs market value, ROE and the cost of equity
compare 6 min cram, 28 min full

What the exam expects you to do

Describe characteristics of types of equity securities.Common shares and preference shares
Describe differences in voting rights and other ownership characteristics among different equity classes.Common shares and preference shares
Compare and contrast public and private equity securities.Public vs private equity: venture capital, buyouts and PIPEs
Describe methods for investing in non-domestic equity securities.Investing in foreign shares: direct, depository receipts and global shares
Compare the risk and return characteristics of different types of equity securities.Risk and return of equity securities, and why companies issue them
Explain the role of equity securities in the financing of a company’s assets.Risk and return of equity securities, and why companies issue them
Contrast the market value and book value of equity securities.Book value vs market value, ROE and the cost of equity
Compare a company’s cost of equity, its (accounting) return on equity, and investors’ required rates of return.Book value vs market value, ROE and the cost of equity

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.

Common shares and preference shares

Known

MemorizeCommon vs preference shares

	Common	Preference
Dividend	at the board's discretion, can grow	fixed, paid before common
Liquidation	last: gets the residual	ahead of common, up to par
Votes	yes	usually none
Risk and return	highest	lower

Memory hook Common is the owner (votes, leftovers). Preference is a bond with a fixed payment that cannot force default.

Know it cold Missing a preference dividend is not a default.

MemorizeVoting rules

Rule	Votes a holder casts	Who it helps
Statutory	$S$ for each seat	the majority
Cumulative	$S \times K$ , split as chosen	minority holders

Memory hook Cumulative = Concentrate. Shares times seats, then pile them on one candidate.

Know it cold Cumulative voting (common, board elections) is not cumulative preference (dividends in arrears).

MemorizePreference features and the holder's risk

Feature	Effect	Holder risk
Cumulative	missed dividends accrue	lower
Non-cumulative	missed dividends lost	higher
Participating	extra dividend if profits are high	more upside
Convertible	can switch into common	common upside, preference floor
Callable	issuer may redeem	higher
Putable	holder may sell back	lower

Memory hook Whoever holds the option gains. The holder's options cut risk; the issuer's options add it.

Know it cold Dividends due = (years missed + 1) × rate × par.

Key terms

common shares Use it
residual claim Use it
statutory voting Memorize
cumulative voting Memorize
vote by proxy Know the idea
share classes Use it
callable common shares Use it
putable common shares Use it
preference shares Use it
cumulative preference shares Memorize
non-cumulative preference shares Memorize
dividends in arrears Use it
participating preference shares Memorize
non-participating preference shares Use it
convertible preference shares Memorize

The two main kinds of equity security

Equity securitiesownership claims on a company

Common shares Memorize residual claim, votes, highest risk and upside
- Voting rule statutory or cumulative
- Share classes different votes or dividend claims
- Callable or putable issuer buys back, or holder sells back
Preference shares Memorize fixed dividend first, priority in liquidation, usually no vote
- Dividend history cumulative or non-cumulative
- Profit sharing participating or non-participating
- Other options convertible, callable, putable

Features that change a preference share

Preference share featuresmix and match: for example cumulative and participating

Dividend history Memorize what happens to a missed dividend
- Cumulative Memorize accrues, paid before any common dividend
- Non-cumulative Memorize lost for good
Profit sharing Memorize what happens when profits are high
- Participating Memorize fixed dividend plus extra when profits pass a set level
- Non-participating fixed dividend and par only
Options who can change the deal
- Convertible Memorize holder can switch into common
- Callable issuer can redeem
- Putable holder can sell back

Formulas

Votes under cumulative voting Memorize

V = S \times K

Quick example

A holder with 500 shares and 3 board seats up for election has 500 × 3 = 1,500 votes, which can all go to one candidate. Under statutory voting the most for any one candidate is 500.

On your calculator

500×3= 1500

500ENTER3× 1500

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

Dividend due on cumulative preference shares Use it

D = (n + 1) \times r \times \text{par}

Quick example

6% cumulative preference shares, par USD 25, one year missed. (1 + 1) × 0.06 × 25 = USD 3.00 per share before any common dividend.

On your calculator

1+1=×0.06×25= 3

1ENTER1+0.06×25× 3

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

Shares needed to guarantee one board seat Know the idea

S > \dfrac{N}{K + 1}

Quick example

1,000 shares outstanding and 4 seats. Hold more than 1,000 ÷ (4 + 1) = 200 shares, so 201 guarantee a seat.

On your calculator

1000÷(4+1)= 200

1000ENTER4ENTER1+÷ 200

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

Public vs private equity: venture capital, buyouts and PIPEs

Known

MemorizePublic vs private equity

	Public	Private
Buyers	anyone	a limited group of institutions and qualified investors
Liquidity	high, exchange-traded	low, no active secondary market
Price	quoted daily	negotiated, valued rarely
Disclosure	extensive	limited
Owners' influence	low for most holders	often high
Horizon	short-term pressure	long-term focus possible
Running costs	listing and reporting costs	lower reporting costs

Memory hook Private equity trades liquidity and transparency for control and patience.

Know it cold Private investors demand a higher return to pay for illiquidity.

MemorizeThree types of private equity

Type	Target	Funding	Exit
Venture capital	young, unlisted company	equity	IPO or sale, often in 3 to 10 years
LBO / MBO	listed company taken private	mostly debt	relisting or sale
PIPE	already listed company	new shares sold privately, at a discount	holder sells later

Memory hook PIPE has "public" in its name: the issuer is listed, the sale is private.

Know it cold MBO is an LBO where the buyers are the managers.

Key terms

public equity Know the idea
private equity securities Use it
private placement Know the idea
venture capital Memorize
leveraged buyout (LBO) Memorize
management buyout Memorize
private investment in public equity (PIPE) Memorize

The three main kinds of private equity

Private equity investingshares that do not trade on an exchange

Venture capital Memorize young company, equity for growth, exit by IPO or sale
Leveraged buyout (LBO) Memorize listed company bought with heavy debt and taken private
- Management buyout Memorize the buyers are mainly existing managers
PIPE Memorize listed company sells shares privately, usually at a discount

Investing in foreign shares: direct, depository receipts and global shares

Known

MemorizeSponsored vs unsponsored

	Sponsored	Unsponsored
Who sets it up	foreign company with a bank	the bank alone
Votes	holders	the depository bank
Disclosure	more (registered)	less

Memory hook Sponsored = the company is on board, so you vote. Unsponsored = the bank keeps the vote.

Know it cold Only a sponsored DR carries the voting rights to the holder.

MemorizeADR levels

Type	Trades	Raises capital?
Level I	over the counter	no
Level II	US exchange	no
Level III	US exchange	yes, public offering
Rule 144A	private, unlisted	yes, private placement

Memory hook The money arrives at Level III, or privately under Rule 144A.

Know it cold A DR price = shares per receipt × local price ÷ exchange rate (local per USD).

MemorizeGDR, GRS, BLDR

Name	What it is
GDR	a receipt issued outside the home market and the US, mostly in USD
GRS	the share itself, registered and traded in several markets and currencies
BLDR	an ETF holding a basket of depository receipts

Memory hook GDR = receipt. GRS = the real share, everywhere. BLDR = a basket.

Know it cold You never need to exchange currency to trade a GRS.

Key terms

direct investing Use it
foreign exchange gains (or losses) Use it
depository receipt Memorize
depository bank Use it
sponsored depository receipt Memorize
unsponsored depository receipt Memorize
American depository receipt Memorize
American depository share Use it
global depository receipt (GDR) Memorize
global registered share (GRS) Memorize
basket of listed depository receipts (BLDR) Use it

Ways to own a company listed in another country

Owning foreign sharesfrom your home market, or from theirs

Direct investing Use it buy on the foreign exchange, in its currency
Depository receipt (DR) Memorize a bank holds the shares; the receipt trades like a local share
- American depository receipt (ADR) Memorize traded in the US, in USD
- Global depository receipt (GDR) Memorize issued outside the home market and outside the US
Global registered share (GRS) Memorize the share itself, traded in several markets and currencies
Basket of listed DRs (BLDR) Use it a fund holding many depository receipts

ADR levels: where they trade and whether they raise capital

ADR typesthe more SEC registration, the more you can do

Level I Memorize over the counter; no new capital
Level II Memorize listed on a US exchange; no new capital
Level III Memorize listed; can raise capital in a public offering
Rule 144A Memorize unlisted; raises capital by private placement to institutions

Formulas

Depository receipt price Use it

P_{DR} = \dfrac{Q \times P_{local}}{X}

Quick example

A receipt represents 2 shares trading at JPY 3,150, with JPY 150 per USD. 2 × 3,150 ÷ 150 = USD 42.00.

On your calculator

2×3150÷150= 42

2ENTER3150×150÷ 42

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

Risk and return of equity securities, and why companies issue them

Known

MemorizeRisk ladder

Type	Lowest risk to highest risk
Preference	putable, cumulative, non-cumulative, callable
Common	putable, ordinary, callable
Overall	preference is less risky than common

Memory hook Holder's options (put, convert, accrue) cut risk. Issuer's options (call) add it.

Know it cold Preference is less risky than common because its dividend is fixed, paid first, and its liquidation amount is par.

MemorizeReturn formulas

Return	Formula
Equity total return	$(P_1 - P_0 + D_1) \div P_0$
Foreign share, own currency	$(1 + R_{local})(1 + R_{FX}) - 1$

Memory hook Currency multiplies the whole local return. It never adds to it.

Know it cold Reinvested dividends compound, so over long periods they make up a large part of equity returns.

MemorizeWhy companies issue equity

Memory hook Assets, growth, acquisitions, staff pay, and a loss cushion.

Know it cold Dividends are not interest: they are not a required payment, and in general they are not tax deductible.

Key terms

total return Memorize
dividend income Know the idea
reinvested dividends Use it
foreign exchange gains (or losses) Use it
equity risk Use it
preference share risk Use it
putable shares Use it
callable shares Use it

Where an equity's return comes from

Total returnwhat the investor earns in the period

Price change Memorize sale price minus purchase price
Dividend income Memorize cash or stock dividends received
Currency gain or loss Use it foreign shares only

Equity risk from lowest to highest

Risk of equity securitiescertain cash flows lower it; issuer options raise it

Preference shares Memorize less risky than common: fixed dividend, paid first, priority in liquidation
- Putable Memorize lowest: holder can sell back
- Cumulative Memorize missed dividends wait for you
- Non-cumulative Memorize missed dividends are lost
- Callable Memorize highest: issuer can end a good deal
Common shares Memorize residual claim, last in line, unlimited upside
- Putable common Memorize lowest: price floor
- Ordinary common middle
- Callable common Memorize highest: issuer can buy back

What equity does for a company

Why companies issue equitycapital with no required payments

Finance assets and growth Memorize long-term assets, research, new regions, acquisitions
Create a currency Use it shares for acquisitions and pay for employees
Cushion creditors Memorize absorbs losses first, so debt is cheaper and available

Formulas

Equity total return Memorize

R = \dfrac{P_1 - P_0 + D_1}{P_0}

Quick example

Buy at 45.00, receive 1.35 of dividends, sell at 47.70. (47.70 − 45.00 + 1.35) ÷ 45.00 = 9.00%.

On your calculator

47.7−45+1.35=÷45= 0.09

47.7ENTER45−1.35+45÷ 0.09

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

Foreign share return in your own currency Use it

R_{home} = (1 + R_{local})(1 + R_{FX}) - 1

Quick example

A share returns 12% in its own currency, which gains 5% against yours. 1.12 × 1.05 − 1 = 17.60%, not 17%.

On your calculator

1.12×1.05−1= 0.176

1.12ENTER1.05×1− 0.176

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

Book value vs market value, ROE and the cost of equity

Known

MemorizeBook value vs market value

	Book value	Market value
Built from	past: historical-cost accounting, retained earnings	future: expected cash flows
Calculated	assets − liabilities	price × shares
Management controls	directly	indirectly

Memory hook Book = the rear-view mirror. Market = the windshield.

Know it cold P/B above 1 means investors expect growth or value the balance sheet misses.

MemorizeROE and the value test

ROE vs cost of equity	Management is	P/B tends to be
ROE > cost of equity	creating value	above 1
ROE = cost of equity	earning just enough	near 1
ROE < cost of equity	destroying value, even if profits are positive	below 1

Memory hook Earn more on book equity than investors require, and the market will pay more than book.

Know it cold ROE = net income to common ÷ average book equity (or beginning equity if book values are stable or by convention).

Key terms

book value Use it
book value per share Use it
market value Use it
price-to-book ratio Memorize
return on equity (ROE) Memorize
cost of equity Use it
investors' required rate of return Use it

Two values for the same equity

Value of a company's equitytwo answers to "what is it worth?"

Book value Memorize assets minus liabilities, from past results
- Management influence direct, through net income and buybacks
- Per share book equity ÷ shares outstanding
Market value Memorize price × shares, from expected future cash flows
- Management influence indirect, through investors' expectations
- Link to book price-to-book ratio

Three different "returns" on equity

Returns tied to equityeasy to confuse, each answers a different question

Accounting ROE Memorize net income ÷ book equity; the past
Cost of equity Use it what the company must offer to attract and keep investors; estimated with a dividend discount model (DDM) or the capital asset pricing model (CAPM)
Investors' required return Use it each investor's minimum; varies by investor

Formulas

Book value per share Use it

BVPS = \dfrac{BVE}{N}

Quick example

Book equity of 930 million and 60 million shares. 930 ÷ 60 = 15.50 per share.

On your calculator

930÷60= 15.5

930ENTER60÷ 15.5

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

Market value of equity Use it

MVE = P \times N

Quick example

Shares at 28.40 and 25 million outstanding. 28.40 × 25 = 710 million.

On your calculator

28.4×25= 710

28.4ENTER25× 710

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

Price-to-book ratio Memorize

P/B = \dfrac{P}{BVPS}

Quick example

Price 31.00, book value per share 12.40. 31.00 ÷ 12.40 = 2.50.

On your calculator

31÷12.4= 2.5

31ENTER12.4÷ 2.5

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

Return on equity (average equity) Memorize

ROE_t = \dfrac{NI_t}{(BVE_{t-1} + BVE_t)\,/\,2}

Quick example

Net income 30, book equity 240 at the start and 260 at the end. 30 ÷ 250 = 12.00%.

On your calculator

30×2÷(240+260)= 0.12

30ENTER2×240ENTER260+÷ 0.12

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

Return on equity (beginning equity) Use it

ROE_t = \dfrac{NI_t}{BVE_{t-1}}

Quick example

Net income 30 and beginning book equity 240. 30 ÷ 240 = 12.50%.

On your calculator

30÷240= 0.125

30ENTER240÷ 0.125

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

Cheat sheet · PDF · 5 A4 pages

Overview of Equity Securities on 5 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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