Financing Decisions - Capital Structure: formula sheet

Key formulas

Value of firm (NI approach)

V = S + D, where S = (EBIT − Interest) ÷ Ke

Ke and Kd are constant. S is market value of equity and D is market value of debt.

Overall cost of capital

Ko = EBIT ÷ V

Under NI, Ko falls as debt rises. Use this to show the effect of added debt.

Value of firm (NOI approach)

V = EBIT ÷ Ko, and S = V − D

Ko is constant. First find V, then S by subtraction.

Cost of equity (NOI approach)

Ke = (EBIT − Interest) ÷ S

Ke rises as debt rises. Interest = D × Kd.

MM without taxes: value

V(levered) = V(unlevered) = EBIT ÷ Ko

Capital structure does not affect value. Ko is the same at every debt level.

MM without taxes: cost of equity

Ke = Ko + (Ko − Kd) × (D ÷ S)

Ke rises linearly with the debt-equity ratio.

MM with taxes: value

V(levered) = V(unlevered) + (t × D)

t × D is the tax shield on permanent debt. t is the corporate tax rate.

MM with taxes: cost of equity

Ke(levered) = Ke(unlevered) + (Ke(unlevered) − Kd) × (1 − t) × (D ÷ S)

Kd is the pre-tax cost of debt here. Ke rises with leverage, but less than without tax.

MM with taxes: WACC

Ko(levered) = Ko(unlevered) × (1 − t × D ÷ V)

WACC falls as debt rises, so a firm gains by using more debt.

Cost of irredeemable debt (before tax)

Kd = I ÷ NP

I = annual interest; NP = net proceeds (issue price less issue costs).

Cost of irredeemable debt (after tax)

Kd after tax = [I ÷ NP] × (1 − t)

t = tax rate. Use only if the company pays tax and the question gives a rate.

Cost of redeemable debt (approximation)

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

RV = redemption value; n = years to maturity. Multiply by (1 − t) for after-tax cost. Use NP, not face value, in the (RV − NP) term.

Cost of irredeemable preference shares

Kp = PD ÷ NP

PD = annual preference dividend. No tax adjustment.

Cost of redeemable preference shares (approximation)

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

Same structure as redeemable debt, without tax.

Cost of equity: dividend growth model

Ke = (D1 ÷ P0) + g

D1 = expected dividend next year = D0 × (1 + g). P0 = current market price; use net proceeds for new issue.

Cost of equity: CAPM

Ke = Rf + β × (Rm − Rf)

Rf = risk-free rate; Rm = market return; (Rm − Rf) = market risk premium.

Cost of equity: earnings model

Ke = E1 ÷ P0

Use when earnings do not grow; E1 = expected EPS.

Cost of retained earnings

Kr = Ke

Where the question asks for a tax or brokerage adjustment on shareholders' reinvestment, follow the data given.

Growth rate from retention

g = b × r

b = retention ratio; r = return on equity or on retained funds.

WACC

WACC (Ko) = Σ (Wi × Ki) = (E × Ke + P × Kp + D × Kd(1 − t) + R × Kr) ÷ Total capital

Wi is the weight of each source and Ki its cost. Weights must add up to 1 (or 100%). Use after-tax cost of debt.

After-tax cost of debt

Kd(1 − t) = Kd × (1 − tax rate)

Kd is the pre-tax cost. For irredeemable debt, Kd = Interest ÷ Net proceeds (or market price).

Book value weight

Weight of a source = Book value of that source ÷ Total book value of capital

Use balance-sheet figures at face or carrying value, as given.

Market value weight

Market value of a source = Market price per security × Number of securities; Weight = That value ÷ Total market value

If retained earnings are given with market value of equity, do not add them again; the market price already reflects them.

Marginal cost of capital

MCC = Σ (Proportion of new funds from each source × Cost of that new source)

Use the proportions of the new financing package or the target structure, and the current cost of new funds.

Contribution

Contribution = Sales − Variable cost

EBIT = Contribution − Fixed operating cost.

Degree of Operating Leverage (DOL)

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

Use fixed cost excluding interest. Valid at the given level of sales.

Degree of Financial Leverage (DFL)

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

EBT = EBIT − Interest. DFL = EBIT ÷ EBT applies only when there is no preference dividend. When preference shares exist: DFL = EBIT ÷ [EBIT − Interest − PD ÷ (1 − t)], where PD is the preference dividend and t is the tax rate.

Degree of Combined Leverage (DCL)

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

Fixed cost in DCL means operating fixed cost plus interest. With preference dividend, use the grossed-up DFL, so the denominator becomes EBT − PD ÷ (1 − t).

EPS

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

Use this to find EPS before and after a change.

Risk link

Operating leverage → business risk; Financial leverage → financial risk

Combined leverage reflects total risk.

EPS

EPS = [(EBIT − I)(1 − t) − PD] ÷ N

I = interest, t = tax rate, PD = preference dividend, N = number of equity shares. Use the total interest and shares after the new plan, including existing ones.

Indifference point (general)

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

E is the EBIT to solve for. Plan 1 and Plan 2 are the two financing plans compared.

Indifference point (no tax effect, no preference)

E = (I₂N₁ − I₁N₂) ÷ (N₁ − N₂)

Tax cancels out when there is no preference dividend, so this shortcut is valid then. Check it by putting E back into both plans.

Financial break-even point

Financial break-even EBIT = I + PD ÷ (1 − t)

EBIT at which EPS = 0. With no preference shares it is just the total interest.

Return on equity

ROE = [(EBIT − I)(1 − t) − PD] ÷ Equity shareholders' funds

Use when the question asks for ROE along with EPS.

Decision rule

Expected EBIT > indifference EBIT → choose plan with more fixed-cost financing; Expected EBIT < indifference EBIT → choose the equity-heavy plan

Applies when comparing two plans. It maximises EPS, not value.

Financial structure vs capital structure

Financial structure = All liabilities (long-term + short-term) + equity; Capital structure = Long-term debt + preference + equity

Capital structure excludes current liabilities. Use this for the difference question.

Return on investment (pre-tax)

ROI = EBIT ÷ Total capital employed × 100

Compare with the pre-tax interest rate to judge the effect of debt.

Return on equity

ROE = (EBIT − Interest − Tax) ÷ Equity shareholders' funds × 100

Use net worth, and deduct preference dividend if preference shares exist and the question asks for equity return.

Effect of debt on ROE

If ROI > interest rate, ROE rises with more debt; if ROI < interest rate, ROE falls

Compare pre-tax ROI (EBIT ÷ capital employed) with the pre-tax interest rate. This holds when the tax rate is the same on both. On an after-tax basis, compare ROI × (1 − t) with interest rate × (1 − t); the conclusion is the same. Rule describes direction only.

Illustrative debt-service coverage measure (not a prescribed ICAI formula)

Debt-service coverage = Cash flow available for fixed charges ÷ (Interest + Principal repayment)

Use it only to illustrate the cash flow approach. The approach itself is a projection of cash flows against fixed obligations. A higher figure suggests the firm can carry more debt. If the question gives its own method, follow that.

Interest coverage ratio

ICR = EBIT ÷ Interest

A simple test of debt-servicing ability from earnings.

Quick revision

• Capital structure is the mix of long-term debt, preference and equity.
• Cost of debt after tax = Interest rate × (1 − tax rate).
• Cost of preference and equity are not tax-adjusted, since dividends are paid from post-tax profit.
• WACC = Σ (weight × cost of each source).
• Market value weights reflect current conditions; book value weights are easier to compute.
• DOL = Contribution ÷ EBIT.
• DFL = EBIT ÷ (EBIT − Interest), and with preference dividend the denominator also subtracts the grossed-up preference dividend.
• DCL = DOL × DFL. When there is no preference dividend, DCL = Contribution ÷ (EBIT − Interest). Otherwise subtract the grossed-up preference dividend too: DCL = Contribution ÷ [EBIT − Interest − Pref. Div ÷ (1 − t)].
• Indifference point is the EBIT at which two financing plans give the same EPS.
• Above the indifference EBIT, the plan with higher financial leverage (more debt or preference) gives higher EPS; below it, the plan with lower financial leverage (more equity) gives higher EPS.
• Under the NOI approach and MM without taxes, value does not depend on capital structure.

Common mistakes

• Using EBIT instead of EBIT less interest to value equity under the NI approach. Fix: Equity holders get only what remains after interest. S = (EBIT − Interest) ÷ Ke. Use EBIT in full only for V under NOI or for Ko.
• Mixing up what is constant under NI and NOI. Fix: NI: Ke is given, so you compute S first. NOI: Ko is given, so you compute V first. Write the constant at the top of your answer.
• Using face value instead of net proceeds in the denominator. Fix: Always compute net proceeds first. Interest is on face value; the denominator is cash actually received.
• Applying the tax shield to preference or equity. Fix: Only interest is tax-deductible. Preference and equity dividends are paid after tax, so no adjustment.
• Using pre-tax cost of debt in WACC Fix: Always write Kd(1 − t) first. Tax shield applies only to interest, not to dividends.
• Using book value of equity when market weights are asked Fix: Read the question for the word market. Compute price × number of shares for each security.
• Including interest in fixed cost when computing DOL. Fix: DOL stops at EBIT. Only fixed operating cost is deducted. Interest comes in only for DFL and DCL.
• Using Sales instead of Contribution in the numerator of DOL. Fix: Write Contribution = Sales − Variable cost first, then divide by EBIT.
• Using only new shares or only new interest, and ignoring existing shares or existing debt Fix: Build a small table for each plan with total interest and total shares. Existing items always go in.
• Deducting preference dividend before tax Fix: Preference dividend is not tax-deductible. Deduct it after tax: EPS = [(EBIT − I)(1 − t) − PD] ÷ N.

Exam tips

• Questions often ask you to compute at two or three debt levels and then comment. Always draw a small table and write the conclusion.
• In MCQs, first identify the theory from keywords: constant Ke means NI, constant Ko means NOI, tax shield means MM with taxes.
• Theory questions in the written part often ask you to compare NI and NOI, or to explain the MM assumptions and arbitrage. Learn the assumptions as a short list.
• Round Ko and Ke to two decimals and show the formula line before the numbers, as this earns step marks.
• Do not skip the interpretation. Name the optimal structure or state that debt does not matter, as the theory requires.
• Read each question for the words 'redeemable', 'net of tax' and 'just paid' before choosing a formula.
• In written answers, show net proceeds as a separate working line. It usually carries a step mark.
• If a question gives both dividend data and beta, compute what is asked. If unspecified, state your assumption and show the model used.