Capital Structure: formula sheet

Key formulas

Capital structure (long-term funds)

Capital structure = Equity share capital + Preference share capital + Reserves and surplus + Long-term debt

Short-term liabilities are excluded. Including them gives the financial structure.

Financial structure

Financial structure = Capital structure + Short-term liabilities

It equals the entire liabilities side of the balance sheet.

Debt-equity ratio

Debt-equity ratio = Long-term debt ÷ Shareholders' funds

A common measure of the mix. Use the definition given in the question.

Capitalisation

Capitalisation = Total long-term capital employed

It is an amount, not a ratio. Do not call it the mix.

Cost of debt (irredeemable), after tax

Kd = [I ÷ NP] × (1 − t)

I = annual interest, NP = net proceeds (issue price less floatation cost), t = tax rate. If debt is issued at par with no cost, Kd = interest rate × (1 − t).

Cost of debt (redeemable), approximate

Kd = [I + (RV − NP) ÷ n] ÷ [(RV + NP) ÷ 2] × (1 − t)

RV = redemption value, n = years to maturity. Apply (1 − t) to the whole result, as shown here, only if the interest-based method treats the premium and discount as tax-deductible; follow the question's convention.

Cost of preference shares (irredeemable)

Kp = PD ÷ NP

PD = annual preference dividend. No tax adjustment, because dividend is paid out of after-tax profit.

Cost of preference shares (redeemable), approximate

Kp = [PD + (RV − NP) ÷ n] ÷ [(RV + NP) ÷ 2]

Same logic as redeemable debt but without tax.

Cost of equity: dividend growth model

Ke = (D1 ÷ P0) + g

D1 = expected dividend next year = D0 × (1 + g). P0 = current market price (or net proceeds for new issue). g = constant growth rate.

Cost of equity: CAPM

Ke = Rf + β × (Rm − Rf)

Rf = risk-free rate, Rm = expected market return, (Rm − Rf) = market risk premium, β = beta.

Cost of equity: earnings yield

Ke = E1 ÷ P0

Used when the question gives EPS and price and assumes no growth.

Cost of retained earnings

Kr = Ke

Use the same formula as equity, with P0 as market price and no floatation cost.

WACC

WACC = Σ (Weight × Cost) = (E×Ke + P×Kp + D×Kd + R×Kr) ÷ Total capital

Use the same weighting basis (book or market) for all sources. Weights add up to 1.

Contribution

Contribution = Sales − Variable cost

Fixed costs are not deducted here.

EBIT

EBIT = Contribution − Fixed operating cost

Fixed operating cost excludes interest.

EBT

EBT = EBIT − Interest

Interest is the fixed financial cost.

Degree of Operating Leverage (DOL)

DOL = Contribution ÷ EBIT = % change in EBIT ÷ % change in sales

Works only when EBIT is positive. DOL is undefined at EBIT = 0 (the break-even point).

Degree of Financial Leverage (DFL)

DFL = EBIT ÷ EBT = % change in EPS ÷ % change in EBIT

If preference shares exist, DFL = EBIT ÷ [EBIT − Interest − Preference dividend ÷ (1 − t)], where t is the tax rate.

Degree of Combined Leverage (DCL)

DCL = DOL × DFL = Contribution ÷ EBT = % change in EPS ÷ % change in sales

Shows the total risk: business plus financial.

Percentage change

% change in EBIT = DOL × % change in sales; % change in EPS = DFL × % change in EBIT = DCL × % change in sales

Use these to forecast profit changes.

EPS

EPS = (EBIT − Interest − Tax − Preference dividend) ÷ Number of equity shares

Tax = (EBIT − Interest) × tax rate. Preference dividend is paid after tax and is not deductible.

Indifference point (no preference shares)

(EBIT − I₁)(1 − t) ÷ N₁ = (EBIT − I₂)(1 − t) ÷ N₂

I = interest, N = number of equity shares, t = tax rate. The (1 − t) cancels, so you can solve on pre-tax figures.

Indifference point solved directly

EBIT = (I₂ × N₁ − I₁ × N₂) ÷ (N₁ − N₂)

Valid when there is no preference dividend. Plan 1 and Plan 2 can be taken in either order.

Indifference point with preference shares

[(EBIT − I₁)(1 − t) − PD₁] ÷ N₁ = [(EBIT − I₂)(1 − t) − PD₂] ÷ N₂

Write it as [(EBIT − I₁)(1 − t) − PD₁] ÷ N₁ = [(EBIT − I₂)(1 − t) − PD₂] ÷ N₂. PD = preference dividend. Here t does not cancel.

Financial break-even point

Financial break-even EBIT = Interest + Preference dividend ÷ (1 − t)

EBIT at which EPS is zero. With no preference shares it equals interest.

Value of the firm

V = S + D

S = market value of equity, D = market value of debt.

NI approach: value of equity

S = (EBIT − Interest) ÷ Ke

Ke and Kd are constant. Interest = Kd × D.

Overall cost of capital (any approach)

Ko = EBIT ÷ V

Equivalent to the weighted average of Ke and Kd at market-value weights, with no taxes.

NOI approach: value of the firm

V = EBIT ÷ Ko

Ko is given and constant. Then S = V − D.

NOI approach: cost of equity

Ke = (EBIT − Kd × D) ÷ (V − D)

Ke rises with leverage.

MM Proposition I (no taxes)

Vu = Vl = EBIT ÷ Ko

Value does not depend on leverage.

MM Proposition II (no taxes)

Ke = Ko + (Ko − Kd) × (D ÷ S)

Cost of equity rises linearly with the debt-equity ratio.

MM with corporate tax

Vl = Vu + (t × D)

t = tax rate. t × D is the present value of the interest tax shield, assuming permanent debt.

Capital gearing ratio

Gearing = (Preference share capital + Debentures + Long-term loans) ÷ Equity shareholders' funds

Equity funds = equity share capital + reserves and surplus. State the definition you use. Some questions use equity share capital only.

Debt-equity ratio

Debt-equity = Long-term debt ÷ Shareholders' funds

Related but narrower measure, since it leaves out preference capital when preference is shown within shareholders' funds.

Trading on equity test

Favourable if ROI (EBIT ÷ capital employed) > interest rate on debt

Compare after tax when asked: ROI × (1 − t) against interest × (1 − t), or compare EPS directly.

Earnings per share

EPS = (EBIT − Interest − Tax − Preference dividend) ÷ Number of equity shares

Use this to show the effect of trading on equity under different financing plans.

Classification of gearing

High gearing: fixed-cost capital > equity. Low gearing: fixed-cost capital < equity

A direct rule for theory and short numerical questions.

Quick revision

• Capital structure is the mix of long-term debt, preference and equity funds.
• Degree of operating leverage = Contribution ÷ EBIT.
• Degree of financial leverage = EBIT ÷ EBT, where EBT = EBIT − interest.
• Degree of combined leverage = DOL × DFL = Contribution ÷ EBT.
• Operating leverage comes from fixed operating costs; financial leverage comes from fixed financing costs.
• EPS = (EBIT − interest − tax − preference dividend) ÷ number of equity shares.
• The indifference point is the EBIT at which two financing plans give the same EPS.
• Above the indifference EBIT, the plan with more debt gives higher EPS; below it, the equity plan does.
• Interest on debt is tax deductible, so the after-tax cost of debt is lower than its stated rate.
• The theories differ on whether the financing mix changes the value of the firm.
• Capital gearing is the ratio of fixed-cost capital to equity capital; high gearing means more financial risk.
• A good structure balances cost, risk, control and flexibility.

Common mistakes

• Treating capital structure and financial structure as the same thing. Fix: Say that capital structure includes only long-term funds, while financial structure includes short-term liabilities as well.
• Confusing capital structure with capitalisation. Fix: Capital structure is the proportion of sources. Capitalisation is the total amount. Write one line for each.
• Applying the tax adjustment to preference dividend or equity. Fix: Only interest on debt is tax-deductible. Preference dividend and equity dividend come from after-tax profit, so no adjustment.
• Using the face value instead of net proceeds or market price in the denominator. Fix: Compute NP first: issue price less floatation cost. For existing equity use current market price P0.
• Using sales instead of contribution in DOL. Fix: DOL always has contribution (sales − variable cost) in the numerator.
• Deducting interest while finding EBIT. Fix: Interest is a financial cost. It comes off only after EBIT, to reach EBT.
• Forgetting existing interest or existing shares Fix: Always build totals: old plus new for both interest and shares. Tabulate them first.
• Treating preference dividend as tax deductible Fix: Deduct tax on EBIT less interest only. Subtract preference dividend after tax.
• Treating NI and NOI as giving the same result. Fix: Remember: NI keeps Ke constant and Ko falls. NOI keeps Ko constant and Ke rises.
• Using EBIT instead of EBIT − interest to value equity under NI. Fix: Under NI, equity value is (EBIT − interest) ÷ Ke. Only the NOI approach starts from total EBIT.

Exam tips

• For 'distinguish' questions, write a point-by-point comparison with at least three points: coverage, nature and use.
• For 'features of a sound capital structure', give five or six features with a one-line reason each, and finish with a short conclusion.
• In numericals, show your classification of each liability as long-term or short-term. It earns marks even if the total is wrong.
• State the ratio definition you use, since books define shareholders' funds and debt slightly differently.
• Link the topic to later chapters in one line: cost of capital, leverage and capital structure theories decide how the mix is chosen.
• Write the formula before substituting numbers. Examiners award marks for the correct formula even if arithmetic slips.
• Show the net proceeds calculation as a separate line whenever floatation cost, discount or premium is given.
• Always state your assumption, such as 'book value weights used' or 'retained earnings cost taken equal to Ke', when the question is silent.