IAI Actuarial Core Principles · Business Finance

Financial instruments issued or used by companies: formula sheet

Full chapter guide

Key formulas

Theoretical ex-rights price (TERP): TERP = (N × P + n × S) ÷ (N + n); N = old shares held, P = cum-rights price, n = new shares taken for those N, S = subscription price. This is the weighted average price after the issue.
Value of a right (per old share): Value of right per new share = TERP − S; Per old share, multiply by the ratio of new to old shares. Assumes the market price falls to TERP.
Funds raised: Gross proceeds = number of new shares × issue price; Net proceeds = gross proceeds − issue costs.
Rights ratio: Ratio = new shares : old shares; For example, 1 for 4 means 1 new share for every 4 held.
Earnings per share: EPS = earnings attributable to ordinary shareholders ÷ number of ordinary shares; Earnings are after interest, tax and preference dividends.
Annual preference dividend: Dividend = Rate × Nominal value × Number of shares; Always apply the rate to nominal value, not to the issue price or market price.
Cumulative arrears: Arrears = Σ unpaid dividends for earlier years; Applies only to cumulative shares. Arrears plus the current year dividend must be paid before any ordinary dividend.
Cost of irredeemable preference shares: Kp = D ÷ P0; D is the annual dividend per share and P0 is the current market price (ex-dividend). No tax adjustment is made.
Ranking on winding up: Creditors and debt > Preference shares > Ordinary shares; Preference holders are repaid at nominal value (plus arrears if cumulative and so stated) before ordinary holders receive anything.
Conversion value: Conversion value = Shares received per preference share × Ordinary share price; Compare with the market price of the preference share or its redemption value to judge whether conversion is attractive.
Order of claims on liquidation (general): Fixed-charge holders (from charged assets) → costs and preferential creditors → floating-charge holders (from floating-charge assets) → unsecured creditors → preference shareholders → ordinary shareholders; A general order only. The exact priority, especially of statutory and preferential claims, depends on the insolvency law in force. State this caveat.
Interest cover: Interest cover = Profit before interest and tax ÷ Interest payable; Covenants often set a minimum. Higher cover means lower default risk.
Gearing (debt-based): Gearing = Debt ÷ (Debt + Equity); Definitions vary. State which one you use. Some use Debt ÷ Equity.
Coupon payment: Annual coupon = Coupon rate × Nominal value; Coupon is set on nominal value, not on market price.
Current yield: Current yield = Annual coupon ÷ Market price; Ignores redemption gain or loss. It is not the redemption yield.
Conversion ratio: Conversion ratio = Nominal value of bond ÷ Conversion price; Number of ordinary shares received per bond on conversion.
Conversion value: Conversion value = Conversion ratio × Current share price; Use the expected share price at the conversion date for forward-looking questions.
Straight-debt (floor) value: Floor value = Σ coupon ÷ (1 + r)^t + Redemption ÷ (1 + r)^n; r is the yield on similar non-convertible debt. Market price is normally at least this, apart from credit effects.
Conversion premium: Premium = Market price of bond − Conversion value; Can also be shown as a percentage of conversion value. A positive premium is usual.
Warrant intrinsic value: Intrinsic value = max(Share price − Exercise price, 0); Per share. The market price of a warrant also includes time value, so it is higher than intrinsic value before expiry.
Holder's decision at conversion date: Convert if Conversion value > Redemption value; Otherwise take the cash redemption. Compare on the same date.
Annual cost of forgoing a cash discount: Cost = (d ÷ (1 − d)) × (365 ÷ (credit period − discount period)), where d is the discount as a decimal; Simple annualised form. For a compound effective rate use (1 / (1 − d))^(365 ÷ days) − 1.
Discount yield on commercial paper (simple): Yield = ((Face value − Issue price) ÷ Issue price) × (365 ÷ days to maturity); Divide by issue price, not face value. Check the day-count basis stated in the question.
Overdraft interest: Interest = Σ (daily balance overdrawn × rate ÷ 365); You pay only on the amount drawn, for the days it is drawn.
Lease versus buy: Compare PV of after-tax lease payments with PV of after-tax cost of buying, using the after-tax cost of debt; Choose the option with the lower present value of cost. Use the after-tax borrowing rate because leasing replaces borrowing.
Forward price (no income, continuous compounding): F = S₀ × e^(rT); S₀ is the spot price, r the risk-free rate and T the time in years. Assumes no storage costs, no income and no arbitrage. With annual compounding use F = S₀ × (1 + r)^T.
Forward price with known income: F = (S₀ − PV of income) × e^(rT); Use for assets paying known income, such as dividends or coupons, during the contract.
Interest rate parity (forward exchange rate): F = S × (1 + i_quote) ÷ (1 + i_base); Rates are for the same period. S and F are units of quote currency per one unit of base currency. For INR per USD, i_quote is the rupee rate and i_base is the dollar rate.
Payoff of a long call: max(S_T − K, 0) − premium; Profit to the buyer at expiry. S_T is the price at expiry and K is the strike.
Payoff of a long put: max(K − S_T, 0) − premium; Profit to the buyer at expiry. Used to protect against a fall in price.
Net payment on a plain vanilla swap (fixed payer): Net = (floating rate − fixed rate) × notional × period fraction; Positive means the fixed payer receives. Negative means the fixed payer pays. Only the net amount is normally exchanged.
Effective cost of swapped borrowing: Loan floating rate + swap fixed rate − swap floating rate received; For a floating-rate borrower who pays fixed on a swap. If the swap floating leg matches the loan, the cost is the fixed rate (plus any loan margin).

Quick revision

Ordinary shareholders are the residual claimants: paid last, with unlimited upside and limited liability.
Dividends on ordinary shares are discretionary; interest on debt is a legal obligation.
Preference shares usually carry a fixed dividend and rank ahead of ordinary shares but behind debt.
Cumulative preference shares carry unpaid dividends forward; participating ones share in extra profits.
Debt ranks ahead of equity on winding-up, and secured debt ranks ahead of unsecured.
A fixed charge is on specific assets; a floating charge is on a class of changing assets.
Convertible bonds give the holder the option to swap into shares, so they usually pay a lower coupon.
Warrants give the right to buy shares at a set price and can be detached and traded separately.
Conversion can dilute existing shareholders' ownership and earnings per share.
Leasing finances use of an asset without buying it; compare finance leases and operating leases by who bears ownership risks.
Companies use derivatives mainly to hedge interest rate, currency and commodity risks.
Higher gearing raises financial risk because fixed payments must be met whatever the profit.

Common mistakes

Treating ordinary shares as having a guaranteed dividend. Fix: State that ordinary dividends are discretionary and paid after fixed claims. Only the residual belongs to them.
Saying a rights issue raises money at the market price. Fix: Use the subscription price S, which is normally below market price, for the cash raised and in TERP.
Applying the dividend rate to market price or issue price. Fix: The stated rate applies to nominal value. Use market price only when calculating the current yield or cost.
Treating a missed preference dividend as a default. Fix: Dividends are discretionary. Missing one is not a legal default, though a cumulative holder keeps the right to arrears.
Saying a floating charge stops the company selling the charged assets. Fix: Fixed charge: specific asset, sale needs consent. Floating charge: changing pool, free dealing until crystallisation on default.
Treating debenture holders as owners with voting rights. Fix: Debt holders are creditors. They get interest and repayment, and normally no vote on company matters.
Using the market price of the bond instead of the nominal value to find the conversion ratio. Fix: The ratio is nominal value ÷ conversion price. The market price is only used for the premium.
Treating a warrant as if it were a loan that must be repaid. Fix: A warrant is only an option on shares. The company receives cash when it is exercised and never repays it.
Saying trade credit is free. Fix: Check for a cash discount. Calculate the annual cost of forgoing it and compare with bank interest.
Mixing up finance and operating leases. Fix: Ask who carries the risks of ownership and whether the lease covers most of the asset's life.

Exam tips

Show the block method for TERP. Examiners give marks for the working even if the arithmetic slips.
In discussion questions, structure answers by rights, risks, cost and control. Compare with debt or preference shares when the question hints at it.
For IPO versus rights issue, cover cost, speed, control, pricing and who the buyers are.
Check that the answer is sensible. TERP must sit between S and P.
Use the stated assumptions, such as no change in firm value or no transaction costs, and write them down.
In MCQs, the usual trap is ranking. Remember: debt first, preference next, ordinary last.
In written answers, name the type (cumulative, participating, convertible) and then link it to a consequence for dividends or ranking.
When asked why a company issues preference shares, give both sides: benefits such as no dilution of control and no default risk, and costs such as no tax shield and a higher required return than debt.