Equity Instrument Features: formula sheet

Key formulas

Order of claims on assets

Debt holders > Preference shareholders > Common shareholders

Common equity is the residual claim. Each class is paid in full before the next one receives anything.

Order of claims on income

Interest on debt > Preferred dividends > Common dividends

Interest is a contractual obligation. Preferred and common dividends are paid only if declared.

Annual preferred dividend

Dividend = Dividend rate × Par value

For example, a 5% preferred with par value $100 pays $5 per share per year.

Cumulative arrears

Dividend owed = Annual dividend × Number of years missed (plus the current year)

Applies only to cumulative preferred. Arrears must be paid before any common dividend.

Conversion value of convertible preferred

Conversion value = Conversion ratio × Current common share price

Compare with the market price of the preferred to judge whether conversion is attractive.

Liquidity

Public: high (exchange trading). Private: low (negotiated sale, fund lock-up)

Illiquidity is the main cost of private equity, and investors expect to be paid for it.

Valuation basis

Public: market price. Private: model, comparables or last funding round

Private valuations are estimates and may be stale or smoothed.

Disclosure

Public: extensive, mandated by regulators. Private: limited, set by contract

Private investors rely on due diligence and contractual information rights.

Venture capital vs buyout

VC: early-stage, equity funded, high failure rate. Buyout: mature firm, often leveraged, steady cash flow

Leverage is a defining feature of an LBO, not of venture capital.

Exit routes

IPO, trade sale (strategic buyer), secondary sale to another fund, recapitalization, liquidation

Exit is how private equity investors realize returns.

DR value per receipt

Value of one DR = Price of underlying share (in local currency) × DR ratio × exchange rate (DR currency per local currency)

The DR ratio is the number of underlying shares per receipt. Use a fraction if one receipt represents part of a share.

Sponsored vs unsponsored

Sponsored: issuer is party to the deposit agreement. Unsponsored: depository bank issues without the issuer's participation.

Sponsored programs generally give holders better rights, including voting through the depository.

ADR vs GDR

ADR: traded in the US, priced in USD. GDR: issued outside the US and outside the issuer's home country, often in multiple markets.

Both are receipts, not the shares themselves.

Price return

Price return = (P1 − P0) ÷ P0

P0 is the purchase price, P1 is the ending price. Excludes dividends.

Dividend yield

Dividend yield = D ÷ P0

Uses the starting price, not the ending price, when measuring return.

Total return (single period)

Total return = (P1 − P0 + D) ÷ P0 = price return + dividend yield

Assumes the dividend is received during or at the end of the period and not reinvested.

Domestic-currency return

R(domestic) = (1 + R(local)) × (1 + R(currency)) − 1

R(currency) is the percentage change in the foreign currency's value in your home currency.

Approximate domestic return

R(domestic) ≈ R(local) + R(currency)

Ignores the cross term. Use only if the options are far apart. The exact formula is safer.

Currency change from a direct quote

Change in foreign currency value = S1 ÷ S0 − 1

Only when S is quoted as home currency per 1 unit of foreign currency. If quoted the other way, use S0 ÷ S1 − 1.

Book value of equity

Book value of equity = Total assets − Total liabilities

Accounting figure. Preferred shares are usually removed to get common equity.

Market value of equity

Market capitalization = Share price × Shares outstanding

Use shares outstanding, not shares authorized.

Book value per share

BVPS = (Common equity) ÷ (Shares outstanding)

Compare with the market price per share to see the market-to-book gap.

Return on equity

ROE = Net income ÷ Average book value of equity

If the question gives only one equity figure, use it. With preferred shares, use net income minus preferred dividends over common equity.

Cost of equity

Cost of equity = Minimum required return on equity

A market-based required return, not an accounting number. It is higher than the cost of debt because equity bears more risk.

Value-creation test

ROE > Cost of equity → value created; ROE < Cost of equity → value destroyed

A rule of thumb, since ROE is based on book values.

Quick revision

• Common shareholders hold the residual claim: they are paid after creditors and preferred shareholders.
• Common shares usually carry voting rights; preferred shares usually do not.
• Preferred shares usually pay a fixed dividend and rank ahead of common shares for dividends and liquidation.
• Cumulative preferred shares accumulate unpaid dividends that must be paid before common dividends.
• Participating preferred shares can receive extra dividends beyond the stated rate under set conditions.
• Convertible preferred shares can be exchanged for common shares at a set ratio, which benefits the holder.
• Callable shares benefit the issuer; putable shares benefit the holder.
• Private equity is less liquid and has less disclosure than public equity, and valuation is harder.
• Depository receipts trade in the local market of the investor while the underlying shares are held by a custodian bank.
• Total return = (P1 − P0 + D1) ÷ P0, made up of price change and dividend yield.
• For foreign holdings, the investor's return also includes the currency movement.
• Equity gives a company permanent capital with no required repayment, and book value of equity = assets − liabilities.

Common mistakes

• Thinking a missed preferred dividend is a default. Fix: Dividends are paid only if declared. Missing one is not a default. For cumulative preferred, it creates arrears instead.
• Confusing cumulative with participating. Fix: Cumulative is about catching up on missed dividends. Participating is about sharing in earnings above the stated dividend.
• Saying private equity has observable market prices Fix: Private holdings are valued by models or recent transactions. Prices are estimates, not trades.
• Mixing up venture capital and buyout Fix: Venture capital is early-stage with little debt. Buyouts target mature firms and often use leverage.
• Saying a DR holder owns the shares directly. Fix: Remember that the custodian holds the shares and the holder owns a receipt that represents them.
• Thinking DRs remove currency risk. Fix: The DR price still reflects the underlying share price and exchange rate, so currency exposure remains.
• Dividing the dividend by the ending price to get dividend yield for return purposes. Fix: For a holding period return, always divide by the starting price P0.
• Leaving dividends out of the return. Fix: Re-read the stem for any dividend, then include it in the numerator.
• Treating ROE as the cost of equity. Fix: ROE is what the firm earned on book equity. Cost of equity is what investors require. Compare them, do not swap them.
• Using total equity including preferred shares for common ROE. Fix: Subtract preferred dividends from net income and preferred equity from the denominator for common shareholders.

Exam tips

• Memorise the claim order once: debt, preferred, common. Many wrong options simply swap two of them.
• Questions on features usually test who benefits. Tag each feature as holder-friendly or issuer-friendly before reading the options.
• Watch for absolute words such as 'always' or 'guaranteed' about preferred dividends. They are usually wrong.
• With no penalty for wrong answers, never leave a question blank. Eliminate options that break the priority order, then pick from what remains.
• In arrears questions, count every missed year plus the current year, and multiply by the full annual dividend.
• Expect comparison questions: eliminate any option that gives private equity higher liquidity or full disclosure.
• Link venture capital to early stage and buyout to mature, leveraged targets.
• Read for the word 'management' (MBO) or 'leveraged' (LBO) to name the buyout type.