IAI Actuarial Core Principles · Business Finance

Structure and methods of financing a company: formula sheet

Full chapter guide

Key formulas

Retained earnings: Retained earnings = Profit after tax − Dividends; The main internal source. Retention ratio = retained earnings ÷ profit after tax.
Gearing (debt-to-equity form): Gearing = Debt ÷ Equity; Another common form is Debt ÷ (Debt + Equity). State which one you use.
Matching principle: Asset life ≈ Finance term; Permanent assets need long-term finance. Temporary or seasonal needs suit short-term finance.
Cash generated internally (simple view): Internal cash = Retained profit + Depreciation ± Working capital change; Use only when the question asks for cash available. Depreciation is added back as a non-cash charge.
Theoretical ex-rights price (TERP): TERP = (N × cum-rights price + n × issue price) ÷ (N + n); N old shares and n new shares. Use the number of shares in the rights ratio, e.g. 1 new for every 4 held.
Value of a right (per new share): Value of right = TERP − issue price; This is what a right to buy one new share is worth. Per old share, divide by the ratio.
Value of a right (per existing share): Value per existing share = cum-rights price − TERP; The fall in price for each share already held.
Dividend growth model (cost of equity): Ke = D1 ÷ P0 + g; D1 = next dividend, P0 = current ex-dividend price, g = constant growth rate. Assumes constant growth.
CAPM cost of equity: Ke = Rf + β × (Rm − Rf); Rf is the risk-free rate, Rm the market return, β the equity beta.
Bonus issue: Price after bonus = old price × old shares ÷ total shares after bonus; Total value is unchanged, so the price falls in proportion.
Cost of non-redeemable preference shares: Kp = Dividend ÷ Price; No tax adjustment, as preference dividends are not tax deductible.
Gearing (debt-to-equity): Gearing = Debt ÷ Equity; Another common form is Debt ÷ (Debt + Equity). State which one you use.
Interest cover: Interest cover = Profit before interest and tax ÷ Interest expense; A low value means the company may struggle to meet interest. Lenders often set a minimum in covenants.
Value of a bond: Price = Σ C ÷ (1 + i)^t + R ÷ (1 + i)^n; C is the coupon, R the redemption payment, n the number of periods, i the yield per period.
Conversion ratio: Conversion ratio = Nominal value of bond ÷ Conversion price; This gives the number of shares received per bond.
Conversion value: Conversion value = Conversion ratio × Current share price; Assuming no arbitrage, a convertible's value is at least the greater of its conversion value and its straight bond value.
Post-tax cost of debt (approximate): Kd after tax = Kd × (1 − tax rate); Applies when interest is fully tax-deductible and the company pays tax.
Conversion ratio: Number of shares per bond = Nominal value of bond ÷ Conversion price; Use the conversion price stated in the question. Check whether it is set per bond or per share.
Conversion value: Conversion value of one bond = Share price × Conversion ratio; Compare with the bond's straight value and redemption value. A holder converts if conversion value is higher than redemption value.
Conversion premium: Premium = Market price of bond − Conversion value; Premium per bond; divide by conversion value to give a percentage if asked.
Floor value of a convertible: Floor value = PV of interest and redemption at the rate for a similar non-convertible bond; The market price should not fall far below this. The excess over floor value is the price of the conversion option.
Warrant exercise payoff: Payoff per share = Share price − Exercise price, if positive; otherwise 0; Exercise only if the share price at exercise is above the exercise price.
Lease versus buy: Compare PV of after-tax lease rentals with PV of after-tax cost of buying, discounted at the after-tax cost of borrowing; Choose the lower present value of cost. Include tax allowances and the scrap value when buying.
Simple annual interest-rate comparison: Annual cost of instalment credit ≈ solve for r in: Cash price = PV of instalments at r; Use trial rates or interpolation. A flat rate understates the true cost because the balance falls over time.
Debt to equity ratio: Debt ÷ Equity; Equity means shareholders' funds (book value unless the question says market value). Debt is usually long-term borrowings.
Gearing ratio (debt to capital): Debt ÷ (Debt + Equity); Also written as a percentage. Always state whether debt includes preference shares and short-term borrowings.
Interest cover: Profit before interest and tax (PBIT) ÷ Interest payable; A higher figure means a safer position. It is a multiple, not a percentage.
Tax shield on interest: Tax shield = Interest × Tax rate; Applies where interest is tax deductible and the company has enough taxable profit to use it.
After-tax cost of debt: Pre-tax cost of debt × (1 − tax rate); Use for WACC when interest is deductible.
Return to equity under gearing: Profit after interest and tax ÷ Equity; Rises with gearing when return on assets exceeds the cost of debt, and falls when it does not.
Cost of equity (dividend growth model): Ke = D1 ÷ P0 + g; D1 is next year's dividend, P0 is the current ex-dividend share price, g is the constant annual dividend growth rate. Valid when growth is constant and g < Ke.
Cost of equity (CAPM): Ke = Rf + β × (Rm − Rf); Rf is the risk-free rate, β is the equity beta, (Rm − Rf) is the market risk premium.
After-tax cost of debt (irredeemable): Kd = i × (1 − t); Here i is the pre-tax cost of debt (the yield, or interest ÷ market price), and t is the corporate tax rate. Assumes the company pays tax and gets relief at once.
Cost of redeemable debt: Solve: P0 = Σ I × (1 − t) ÷ (1 + Kd)^n + R ÷ (1 + Kd)^N; Kd is the IRR of the after-tax cash flows: market price paid in, after-tax interest and redemption value paid out. Use two trial rates and interpolate.
Cost of irredeemable preference shares: Kp = D ÷ P0; D is the fixed annual preference dividend and P0 is the market price. No tax adjustment.
WACC: WACC = (E × Ke + D × Kd + P × Kp) ÷ (E + D + P); E, D and P are market values of equity, debt and preference shares. Kd must be the after-tax cost.

Quick revision

Internal finance: retained profits and depreciation. External finance: new shares, loans, bonds, leases.
Retained profits are not free: shareholders expect a return on them.
Ordinary shareholders are paid last on winding up and carry the most risk.
A rights issue offers new shares to existing shareholders in proportion to their holdings, usually at a discount.
A bonus issue turns reserves into shares and raises no new cash.
Debt interest is usually tax-deductible, which lowers its after-tax cost.
Secured debt ranks ahead of unsecured debt if the company fails.
Convertibles and warrants are hybrids linked to future equity.
A finance lease transfers most risks and rewards of ownership to the lessee; an operating lease does not.
Higher gearing raises the risk of financial distress and makes equity returns more volatile.
WACC = weighted sum of each source's cost, using market value weights where possible.
Use the after-tax cost of debt in WACC when interest is tax-deductible.

Common mistakes

Calling depreciation a source of new funds. Fix: Say it is a non-cash charge. It does not create cash. Cash comes from profits and operations.
Treating retained earnings as free finance. Fix: Retained earnings have an opportunity cost: shareholders could have received the dividend and reinvested it. Their cost is the cost of equity.
Thinking a discounted rights issue makes existing holders worse off. Fix: Compare total wealth. The shares fall to TERP, but the holder owns more shares or sells the rights. A holder who takes up or sells the rights is no worse off.
Using the issue price as the new share price after the rights issue. Fix: Calculate TERP as a weighted average. It lies between the issue price and the cum-rights price.
Saying debentures are always unsecured. Fix: In IAI-style answers, treat debentures as secured on assets and unsecured loan stock as unsecured. State your assumption if the question is unclear.
Thinking interest is optional in a poor year. Fix: Interest is a legal obligation. Dividends are at the board's discretion. Missed interest is a default.
Saying converting a bond raises new cash for the company. Fix: On conversion, debt is replaced by shares and no cash comes in. Cash comes in when a warrant is exercised, because the holder pays the exercise price.
Calling a lease a finance lease just because it is long. Fix: Look at the share of the asset's life covered and who bears the risks and rewards of ownership. Substance matters more than the label.
Using debt ÷ equity when the question asks for debt ÷ (debt + equity). Fix: Write the definition first, then compute. Debt ÷ equity is always larger than debt ÷ capital.
Calculating interest cover with profit after interest. Fix: Use profit before interest and tax in the numerator unless told otherwise.

Exam tips

In MCQs, check the word 'internal' or 'external' first. Retained earnings and asset sales are internal. New shares and loans are external.
In written answers, always compare at least cost, risk and control for each source. Lists alone earn few marks.
Tie your recommendation to the company in the question: listed or unlisted, high or low gearing, stable or volatile profits.
Mention the matching principle whenever term of finance is discussed.
State your gearing definition if you quote a ratio.
Show the TERP working in full. Marks are given for method even if the arithmetic slips.
In MCQs on rights issues, check which price the question gives: cum-rights or issue price.
In written answers, compare ordinary and preference shares on dividend, voting, risk, tax and cost. Use a short bullet for each.