Sources of, and raising, business finance: formula sheet

Key formulas

Cost of giving up an early settlement discount (annual)

(1 + d ÷ (100 − d))^(365 ÷ (T − t)) − 1

d = discount %, T = normal credit days, t = discount days. The simple version is d ÷ (100 − d) × 365 ÷ (T − t). Use the compound version unless told otherwise.

Cost of one period of foregone discount

d ÷ (100 − d)

This is the periodic cost of paying late instead of taking the discount.

Matching principle

Long-term assets → long-term finance; fluctuating current assets → short-term finance

A rule of thumb, not a law. Aggressive and conservative policies depart from it deliberately.

Gearing (debt/equity)

Debt ÷ Equity (or Debt ÷ (Debt + Equity))

Say which version you use. Higher gearing means higher financial risk.

Theoretical ex-rights price (TERP)

TERP = [(N × cum-rights price) + (M × issue price)] ÷ (N + M)

N is the number of old shares and M is the number of new shares in the offer. A '1 for 4' issue means N = 4, M = 1.

Value of a right per new share

Value of right = TERP − issue price

This is what a right is worth for each new share bought. Use it when the question asks about selling rights.

Value of a right per existing share

Value per existing share = (TERP − issue price) × (M ÷ N)

Use when a shareholder sells rights relating to the shares already held.

Funds raised

Net funds = (new shares × issue price) − issue costs

Deduct issue costs when the question gives them.

Rights issue price from required funds

New shares = funds needed ÷ issue price

Then work out the ratio of new shares to old shares.

Earnings per share after issue

New EPS = Total earnings ÷ total shares after issue

Add any extra earnings from the new investment. Compare with old EPS to judge dilution.

Value of redeemable debt

Value = Σ [interest ÷ (1 + kd)^t] + redemption value ÷ (1 + kd)^n

kd is the investor's required yield. Use annuity and discount factors from the tables provided. This is also the straight debt value for a convertible.

Irredeemable debt (pre-tax and post-tax)

Value = interest ÷ kd; kd after tax = (interest × (1 − T)) ÷ market value

T is the corporate tax rate. Use this only for debt that is never repaid.

Conversion value of a convertible

Conversion value = share price × (1 + g)^n × number of shares per bond

g is the expected annual share price growth and n the years to the conversion date. For today's conversion value, use the current price with no growth.

Floor value of a convertible

Floor value = higher of (straight debt value, conversion value)

The market price should not fall below this. In practice it sits above it because the option has value.

Conversion premium

Premium = market price of convertible − current conversion value; as a % = premium ÷ conversion value

It measures how much extra an investor pays for the option to convert.

Preference shares

Value = dividend ÷ kp; kp = dividend ÷ market price

No tax adjustment, because preference dividends are not tax-deductible.

Lease versus buy

Compare PV of buying (outlay − PV of tax savings on allowances ± scrap) with PV of leasing (rentals − PV of tax saved on rentals)

Discount at the post-tax cost of borrowing: pre-tax rate × (1 − T). Choose the lower PV of cost.

Murabaha price

Selling price = cost to bank + agreed mark-up

Fixed at the outset and not increased for late payment. Payment can be deferred or in instalments.

Mudaraba profit and loss

Profit shared in agreed ratio; financial loss borne by the capital provider

The mudarib loses only time and effort unless they were negligent or breached the contract.

Musharaka profit and loss

Profit shared as agreed; loss shared in proportion to capital contributed

Both parties contribute capital and may manage the venture.

Ijara rentals

Lessor owns the asset and bears ownership risks; lessee pays rentals for use

Rentals can be fixed or linked to a benchmark rate. Ownership may transfer at the end.

Sukuk return

Holder receives a share of the income or profit from the underlying asset

Return depends on the asset's performance, not a promise of interest on a loan.

Dividend cover

Dividend cover = Earnings (profit after tax and preference dividends) ÷ Ordinary dividends

Higher cover means more profit is retained and the dividend is safer.

Payout ratio

Payout ratio = Ordinary dividends ÷ Earnings = 1 ÷ Dividend cover

Retention ratio = 1 − payout ratio.

Dividend per share

DPS = Total ordinary dividend ÷ Number of ordinary shares

Use shares in issue that rank for the dividend.

Dividend yield

Dividend yield = DPS ÷ Market price per share

Use the same date and basis for DPS and price.

Residual dividend

Dividend = Earnings − (Equity-funded part of investment)

Equity part = investment × equity share of the target financing mix. If the result is negative, no dividend is paid unless new equity is raised.

Growth from retention (Gordon)

g = b × r

b = proportion of earnings retained; r = return on new investment. Assumes constant b and r; syllabus use is as an estimate of dividend growth.

Quick revision

• Match the finance term to the asset life: short-term for working capital, long-term for non-current assets.
• Retained earnings are not free: shareholders expect a return on them.
• Rights issue: theoretical ex-rights price = (existing shares × cum-rights price + new shares × issue price) ÷ total shares.
• Value of a right per new share = theoretical ex-rights price − issue price.
• A rights issue at a deeper discount does not by itself make shareholders worse off if they take up or sell their rights.
• Debt is usually cheaper than equity because interest is tax-deductible and lenders face less risk.
• Debt adds financial risk through fixed interest and possible security or covenants.
• Finance leases put risks and rewards with the lessee; operating leases do not.
• Convertibles give lower interest now in return for possible dilution later.
• Islamic finance avoids interest (riba) and uses asset-backed or profit-sharing structures.
• Venture capital brings funds and expertise but needs an exit route and gives up some control.
• Dividend policy signals information; view it alongside investment needs and shareholder expectations.

Common mistakes

• Treating trade credit as free finance. Fix: Calculate the cost of losing the early settlement discount. It is often far higher than overdraft interest.
• Recommending equity because it has no fixed payments, ignoring its higher cost. Fix: State both sides: equity lowers financial risk but costs more and dilutes control.
• Using the issue price as the share price after the issue. Fix: The market price after the issue is TERP, a weighted average of old price and issue price.
• Mixing up N and M in the weighted average. Fix: '1 for 4' means one new share for every four held, so N = 4 and M = 1. Check TERP lies closer to the old price when N is larger.
• Discounting lease and buy cash flows at the pre-tax borrowing rate. Fix: Multiply the pre-tax rate by (1 − T) whenever the cash flows include tax effects. Say that you are doing so.
• Ignoring share price growth when calculating the conversion value at a future date. Fix: Grow the price at g for n years first, then multiply by the number of shares per bond. Use today's price only for the current conversion value.
• Calling the Murabaha mark-up interest. Fix: Say it is the profit on a genuine sale of an asset the bank owned first, not a charge for lending money.
• Confusing Mudaraba and Musharaka. Fix: Mudaraba: one party gives capital, the other gives management. Musharaka: both give capital and usually share management.
• Saying venture capital and business angels are the same thing. Fix: Angels are individuals using their own money, usually in smaller sums and earlier stages. Venture capital firms are organisations investing pooled funds, usually in larger sums with formal controls and a planned exit.
• Forgetting the exit route when discussing equity investors. Fix: Always mention how the investor will realise its investment, such as a flotation, a trade sale or a share buy-back.

Exam tips

• In OT questions, check the time period first. Many wrong options fail only on maturity matching.
• For written answers, use a short structure per source: cost, risk, flexibility, security. Then link to the scenario.
• Always give the discount cost calculation with working. Method marks matter in constructed response, and OT answers are all or nothing.
• Quote the company's stated position, such as high gearing or a small unlisted status, when recommending finance.
• Make a clear recommendation. Listing pros and cons without choosing loses marks.
• In objective questions, check that your TERP lies between the issue price and the old price. If it does not, you have mixed up N and M.
• Show the weighted-average working in constructed response answers. Method marks are available even if the arithmetic slips.
• When asked to discuss methods of issue, compare on cost, speed, control and the effect on existing shareholders. Do not just list definitions.