Capital Structure and Capital Stacking: formula sheet

Key formulas

Capital structure

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

Only long-term sources. Exclude current liabilities.

Financial structure

Financial structure = Capital structure + Short-term liabilities

Whole liabilities side of the balance sheet.

Debt-equity ratio

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

Common measure of how much debt is used in the mix.

Optimal structure rule

Optimal capital structure: WACC is minimum and firm value is maximum

The two conditions go together, for a given level of operating earnings.

Weighted average cost of capital

WACC = Σ (Weight of each source × Cost of that source)

Use after-tax cost of debt = Interest rate × (1 − tax rate).

Value of firm (general)

V = S + D

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

NI approach: equity value

S = (EBIT − Interest) ÷ Ke; Ko = EBIT ÷ V

Ke and Kd constant. Ko falls as D rises. This is the no-tax form, so the weighted average of Ke and Kd equals Ko. With tax, use after-tax Kd: Ko = Ke × S ÷ V + Kd × (1 − t) × D ÷ V.

NOI approach: firm value

V = EBIT ÷ Ko; S = V − D

Ko and Kd constant. Value does not change with leverage.

NOI approach: cost of equity

Ke = Ko + (Ko − Kd) × (D ÷ S)

Ke rises linearly with D/S. Equivalent to Ke = (EBIT − Interest) ÷ S. This equivalence holds in the no-tax setting.

MM Proposition I (no tax)

V(levered) = V(unlevered) = EBIT ÷ Ko

Holds under perfect markets, no taxes, same risk class and riskless debt.

MM Proposition II (no tax)

Ke = Ku + (Ku − Kd) × (D ÷ E)

Ku = cost of equity of the unlevered firm. Ko stays equal to Ku.

MM Proposition I (with tax)

V(levered) = V(unlevered) + t × D

t = corporate tax rate. Assumes perpetual debt. t × D is the value of the interest tax shield.

MM Proposition II (with tax)

Ke = Ku + (Ku − Kd) × (1 − t) × (D ÷ E)

Ke rises more slowly than without tax.

WACC with tax (MM)

Ko = Ku × (1 − t × D ÷ V); also Ko = Ke × S ÷ V + Kd × (1 − t) × D ÷ V

Ko falls as leverage rises, so the optimum under MM with tax is the maximum debt. The weighted-average check must use after-tax Kd.

Unlevered value with tax

V(unlevered) = EBIT × (1 − t) ÷ Ku

Used as the base in the with-tax proposition.

Degree of Operating Leverage

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

Contribution = Sales − Variable cost. EBIT = Contribution − Fixed operating cost. DOL is measured at a given sales level.

Degree of Financial Leverage

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

EBT = EBIT − Interest. With preference shares: DFL = EBIT ÷ [EBIT − Interest − Preference dividend ÷ (1 − t)].

Degree of Combined Leverage

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

Use EBT, not EBIT, in the denominator of the direct form.

Earnings per share

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

Tax is on EBT. Preference dividend is paid after tax.

Fixed costs link

Operating fixed cost = Contribution − EBIT; Interest = EBIT − EBT

Use these to find missing figures from a given DOL or DFL.

EPS for a financing plan

EPS = [(EBIT − Interest) × (1 − t) − Preference dividend] ÷ Number of equity shares

t is the tax rate. Preference dividend is paid after tax and is not tax-deductible. Interest includes interest on existing debt plus new debt.

Indifference point (general condition)

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

Solve for EBIT*. Plans 1 and 2 are any two alternatives. I is interest, PD is preference dividend, N is number of equity shares.

Indifference point (no preference dividend)

(EBIT* − I₁) ÷ N₁ = (EBIT* − I₂) ÷ N₂, so EBIT* = (I₂N₁ − I₁N₂) ÷ (N₁ − N₂)

The tax rate cancels out when both plans have no preference dividend and the same tax rate. Do not use this shortcut if any plan has preference shares.

Financial break-even EBIT

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

EBIT at which EPS is zero for one plan.

Decision rule

Expected EBIT > EBIT* → choose plan with fewer shares; Expected EBIT < EBIT* → choose plan with more shares

Holds when the plans compared have different share counts and fixed charges, as in a debt-versus-equity choice. Confirm by computing EPS at the expected EBIT.

After-tax cost of debt

Kd (after tax) = Kd × (1 − t)

Use this in WACC. Interest is tax-deductible; dividends are not.

WACC

WACC = Σ (Wi × Ki) = (E × Ke + P × Kp + D × Kd after tax) ÷ (E + P + D)

Weights are proportions of total capital. Use market value weights when given; otherwise use the weights the question states.

Cost of equity (dividend growth)

Ke = D1 ÷ P0 + g

D1 is next year's expected dividend, P0 is the current market price.

Cost of equity (CAPM)

Ke = Rf + β × (Rm − Rf)

Use when beta and market data are given.

EPS

EPS = [(EBIT − Interest) × (1 − t) − Preference dividend] ÷ Number of equity shares

Compute it for each financing plan at the same EBIT.

EBIT-EPS indifference point

(X − I1)(1 − t) ÷ N1 = (X − I2)(1 − t) ÷ N2, so X = (N2 × I1 − N1 × I2) ÷ (N2 − N1)

X is EBIT. The shortcut holds when the tax rate is the same and there is no preference dividend. Above X the plan with more debt gives higher EPS; below X the equity-heavy plan does.

ROE with leverage

ROE = [ROI + (ROI − i) × D ÷ E] × (1 − t)

i is the interest rate, ROI is pre-tax return on total capital. Debt raises ROE only when ROI > i.

Value of firm and WACC

Firm value = Market value of equity + Market value of debt

For a given EBIT, a lower WACC means a higher firm value.

Priority of claims (waterfall)

Senior debt → Junior/subordinated debt → Mezzanine → Preference capital → Equity

Cash or sale proceeds are paid in this order. A lower layer receives money only after every layer above it is paid in full. Exact ranking of instruments depends on their terms.

Risk-return hierarchy

Risk and expected return: Senior debt < Mezzanine < Equity

Cost of each layer rises as you go down the stack.

Layer share of total funding

Layer % = Amount of the layer ÷ Total capital × 100

Used to show the composition of the stack.

Weighted average cost of the stack

WACC = Σ (Weight of layer × Cost of layer)

Weights use the amount of each layer. Use after-tax cost for debt layers where interest is tax-deductible.

Cover for a layer

Cushion below a layer = Total of all layers beneath it

A layer is safer when more capital sits below it to absorb losses.

Quick revision

• Capital structure is the mix of long-term debt, preference and equity capital used to finance the firm.
• Optimal structure maximises firm value and minimises the weighted average cost of capital.
• DOL = Contribution ÷ EBIT; it measures the effect of sales changes on EBIT.
• DFL = EBIT ÷ (EBIT − Interest); with preference dividend, use EBIT ÷ [EBIT − Interest − Pref. dividend ÷ (1 − t)].
• DCL = DOL × DFL = Contribution ÷ (EBIT − Interest).
• Financial leverage helps EPS only when return on assets exceeds the cost of debt.
• 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.
• The net income approach says value rises with debt; the net operating income approach says capital structure does not change value.
• Modigliani-Miller without taxes says structure is irrelevant; with corporate tax, debt gives a tax shield.
• Interest is tax-deductible, so after-tax cost of debt = Interest rate × (1 − tax rate).
• Capital stacking arranges funding sources in layers by cost, risk and priority.

Common mistakes

• Treating capital structure and financial structure as the same. Fix: Capital structure = long-term sources only. Financial structure also includes short-term liabilities.
• Including trade payables or bank overdraft in capital structure. Fix: Take only equity, preference, reserves, debentures and long-term loans.
• Treating Ko as constant in the NI approach, or Ke as constant in the NOI approach. Fix: Memorise: NI fixes Ke and Kd; NOI fixes Ko and Kd. Write this beside the solution before starting.
• Using EBIT instead of net income to value equity in the NI approach. Fix: In NI, S = (EBIT − interest) ÷ Ke. EBIT ÷ Ko gives total firm value only in NOI.
• Using EBIT instead of EBT in the denominator of DCL. Fix: Remember DCL = Contribution ÷ EBT. Cross-check with DOL × DFL.
• Using sales instead of contribution in DOL. Fix: DOL always needs contribution. Subtract variable cost first.
• Forgetting existing interest or existing shares Fix: Always start by listing existing capital. Total interest = old + new. Total shares = old + new.
• Deducting preference dividend before tax Fix: Deduct tax first on EBIT − interest, then subtract preference dividend from the profit after tax.
• Using pre-tax cost of debt in WACC Fix: Always write Kd × (1 − t) as the first line of your working. Do not tax-adjust Ke or Kp.
• Choosing the plan with the highest EPS and stopping Fix: Higher EPS from debt comes with higher financial risk. Mention risk, and compare WACC or interest cover where data is given.

Exam tips

• Write the one-line difference between capital structure and financial structure whenever the question asks for meaning; it is a frequent MCQ.
• In theory answers, give factors with one-line reasons. Five to seven well-explained factors earn better than a long bare list.
• Keep the figures separate: show capital structure, then proportions, then the ratio. Each line can earn a step mark.
• For MCQs, check whether the item named is long-term or short-term before deciding if it belongs in capital structure.
• In MCQs, identify the theory from one phrase: Ko constant means NOI or MM without tax; value rises with debt means NI or MM with tax.
• In numericals, write the theory's assumption in the first line. Examiners give step marks for stating what is constant.
• For comparison questions, a short table of V, Ke and Ko at each debt level makes the pattern clear and earns presentation marks.
• In theory answers, include the assumptions of MM: perfect capital markets, no taxes (in the base case), same risk class, riskless debt, no transaction costs and full payout.