Sources of finance and their relative costs: formula sheet

Key formulas

Theoretical ex-rights price (TERP)

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

N is the number of old shares in the ratio and n is the number of new shares. For a 1 for 4 issue, use 4 old and 1 new.

Value of a right per new share

Value of right per new share = TERP − issue price

This is the gain on each new share bought.

Value of a right per existing share

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

Or equivalently: cum-rights price − TERP. Both give the same answer.

Funds raised

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

Issue costs are usually deducted from proceeds, and they do not enter the TERP unless the question says so.

Earnings per share after issue

New EPS = total earnings ÷ (old shares + new shares)

Adjust earnings if the funds raised are expected to earn a return.

Gearing (debt to equity)

Debt ÷ Equity

Use the definition the question gives. Another common form is Debt ÷ (Debt + Equity).

Interest cover

Profit before interest and tax ÷ Interest

A common covenant measure. A low result signals risk to lenders.

Annual interest on a bond

Nominal value × Coupon rate

Interest is paid on nominal (par) value, not market value.

Value of irredeemable debt

Market value = Annual interest ÷ Required return

Treats the interest as a perpetuity.

Tax shield on interest

Interest × Tax rate

Interest is tax deductible, so the after-tax cost of debt is lower.

Conversion ratio

Conversion ratio = Nominal value of bond ÷ Conversion price

Gives the number of ordinary shares received per bond. If the question states the ratio, use it directly.

Future share price

Future share price = Current share price × (1 + g)ⁿ

g is the expected annual growth rate and n the years to conversion. Use this to forecast the price at the conversion date.

Current conversion value

Current conversion value = Current share price × Conversion ratio

Use this in the conversion premium. It is not used for the conversion decision.

Future conversion value

Future conversion value = Forecast share price at conversion date × Conversion ratio

Compare with the redemption value. The holder takes the higher of the two.

Floor value

Floor value = PV of interest + PV of redemption value, discounted at the cost of similar straight debt

This is the minimum value of the bond as debt. Use the gross (pre-tax) interest and discount at the investor's required pre-tax return on similar straight debt. Do not use after-tax interest or the company's after-tax cost of debt.

Conversion premium

Conversion premium = Market price of bond − Current conversion value

It can be given per share: market price ÷ ratio − current share price.

Cost of irredeemable preference shares

Kp = Annual preference dividend ÷ Ex-div market price

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

Cost of convertible debt

Cost = IRR of: current price (outflow at t0), interest after tax (t1–n), and the higher of redemption or future conversion value (t n)

Apply tax relief to the interest, then find the IRR by interpolation using two discount rates.

Annual cost of trade credit (forgoing a discount)

[100 ÷ (100 − d)]^(365 ÷ (N − D)) − 1

d = discount % ; D = discount period in days ; N = normal payment days. This gives the compound annual cost. A simple version is d ÷ (100 − d) × 365 ÷ (N − D).

Lease versus buy decision rule

Choose the option with the lower present value of net costs

Discount at the after-tax cost of borrowing, since leasing is a substitute for debt. Include tax relief on lease payments or on capital allowances.

After-tax cost of debt

Kd (1 − T)

Use this as the discount rate in lease versus buy. T = tax rate.

Factor advance

Advance = invoice value × advance %

Interest is charged on the amount advanced, and a service fee is charged on total invoice value.

Dividend valuation model (constant growth)

P0 = D0(1 + g) ÷ (ke − g)

P0 must be the ex-div price. It holds only when ke > g and growth is constant.

Cost of equity from DVM

ke = [D0(1 + g) ÷ P0] + g

D0 is the dividend just paid. Use D1 directly if given.

Dividend growth from history

g = (D latest ÷ D earliest)^(1 ÷ n) − 1

n is the number of growth periods, which is one fewer than the number of dividends.

Gordon growth estimate

g = b × r

b is the retention rate. r is the return on retained funds, often ROCE or return on equity.

CAPM

ke = Rf + β(Rm − Rf)

(Rm − Rf) is the equity risk premium. If you are given Rm, subtract Rf first.

Ex-div adjustment

Ex-div price = cum-div price − dividend about to be paid

Make this adjustment before using the DVM.

Irredeemable debt, post-tax

Kd = I × (1 − T) ÷ P0

I is annual interest, T is the tax rate, P0 is the ex-interest market value of the debt. Use the market price, not nominal value.

Redeemable debt, IRR

P0 = Σ [I(1 − T) ÷ (1 + r)^t] + Redemption ÷ (1 + r)^n

Solve for r. Cash flows at time 0 are −P0. Use ex-interest prices. Tax is assumed paid in the same year unless the question says otherwise.

IRR by interpolation

IRR = L + [NPV at L ÷ (NPV at L − NPV at H)] × (H − L)

L and H are two trial rates. One NPV should be positive and one negative. Keep the trial rates close together, ideally 1 to 2 points apart.

Preference shares

Kp = D ÷ P0

D is the annual preference dividend, P0 is the ex-dividend market price. No tax adjustment.

Bank loan, post-tax

Kd = Interest rate × (1 − T)

Use when the loan is at par and the interest rate is the cost. Without issue costs or a discount this needs no IRR.

Convertible conversion value

Conversion value = P0 × (1 + g)^n × number of shares per bond

Here P0 is the current share price and g is the share price growth rate. Compare this with the redemption value and use the higher in the IRR.

WACC

WACC = [E ÷ (E + D + P)] × Ke + [D ÷ (E + D + P)] × Kd(1 − T) + [P ÷ (E + D + P)] × Kp

E, D, P are market values of equity, debt and preference shares. Drop P if there are none.

Cost of equity (dividend growth model)

Ke = [D0 × (1 + g) ÷ P0] + g

D0 is the dividend just paid. P0 is the ex-dividend share price.

Cost of equity (CAPM)

Ke = Rf + β × (Rm − Rf)

Rm − Rf is the equity risk premium. Use the data given.

After-tax cost of irredeemable debt

Kd = [i × (1 − T)] ÷ P0

i is annual interest, P0 is the ex-interest market price of the debt.

Cost of redeemable debt

Kd = the IRR of: − market price now, + interest × (1 − T) each year, + redemption value at the end

Use two discount rates and interpolate.

Cost of preference shares

Kp = preference dividend ÷ market price

No tax adjustment, as dividends are not tax deductible.

Market value of equity

E = number of shares × share price

Use ex-dividend prices.

Quick revision

• Rights issue: new shares offered to existing shareholders in proportion, usually at a discount to market price.
• Equity is riskier for investors than debt, so it has a higher required return.
• Interest on debt is usually tax-deductible, so cost of debt is calculated after tax.
• Dividend valuation model with growth: Ke = D0(1 + g) ÷ P0 + g, where P0 is ex-dividend price.
• CAPM: Ke = Rf + β × (Rm − Rf).
• Irredeemable preference share cost = dividend ÷ market price; there is no tax adjustment.
• Cost of redeemable debt is the IRR of the cash flows: price now, post-tax interest, redemption value.
• Convertible: compare the redemption value with the conversion value, and use the higher in the cost calculation.
• WACC = Σ (market value weight × cost of each source).
• Use market values for weights, not book values, where they are given.
• Leasing: operating leases keep the asset with the lessor; finance leases pass most risks and rewards to the lessee.
• Match the finance to the need: long-term assets with long-term finance, working capital with short-term finance.

Common mistakes

• Using the ratio the wrong way round, for example treating 1 for 4 as 1 old and 4 new. Fix: Write 'old : new' on your working before you start. 1 for 4 means one new share for every four held.
• Using the average of the market price and the issue price as the TERP. Fix: TERP is a weighted average. The weights are the number of old and new shares.
• Calculating bond interest on market value instead of nominal value. Fix: Interest = nominal value × coupon rate. Market value matters only for valuation and cost of debt.
• Saying secured debt is always cheaper for the company in every sense. Fix: Mention the cost too: assets are tied up, which limits future borrowing, and default allows the lender to seize them.
• Using the current share price to work out the conversion value at the conversion date. Fix: Grow the share price to the conversion date first, then multiply by the conversion ratio. Use the current price only for the current conversion value in the premium.
• Taking tax relief on preference dividends. Fix: Preference dividends are paid from after-tax profit. Cost = dividend ÷ price, with no tax adjustment.
• Using N instead of N − D as the extra credit period when costing a discount. Fix: The extra days you gain by not paying early are N − D. For 2/10 net 60, use 50 days.
• Discounting lease versus buy cash flows at the WACC. Fix: The lease replaces borrowing, so use the after-tax cost of debt unless told otherwise.
• Saying Islamic finance has no cost or return for the provider. Fix: State that returns exist but come from a mark-up, rentals or profit share tied to real assets, not from interest on money.
• Treating sukuk as ordinary bonds. Fix: Say sukuk give ownership rights in an underlying asset and returns come from that asset, not from interest.

Exam tips

• In objective questions, wrong options are often the answers from the common slips: a simple average, the wrong ratio, or the value per new share instead of per existing share. Check your result against the unit asked.
• Do the bundle method in the margin of your rough paper. It is quick and reduces ratio errors.
• In constructed-response answers, show the TERP working line by line. Marks are given for method even if the final figure is slightly wrong.
• For discussion parts, compare rights issues, placings and public offers on cost, speed, control and dilution, and tie each point to the company in the scenario.
• If a question asks about the effect on EPS or gearing, update the share count or debt level first and state your assumptions about how the funds are used.
• In OT questions, read every option fully. A single word such as 'floating' or 'irredeemable' often decides the answer.
• Always use nominal value for interest and market value for valuation. Check which one the question gives.
• For written questions, tie every advantage or disadvantage to the scenario. Generic lists score poorly.