Operational Approach to Financial Decision: formula sheet

Key formulas

Cost of irredeemable debt (before tax)

Kd = I ÷ NP

I = annual interest; NP = net proceeds (face value adjusted for premium, discount and issue cost). Use market price if the question asks for it.

Cost of irredeemable debt (after tax)

Kd (after tax) = Kd × (1 − t)

t = tax rate. Equivalent form: I × (1 − t) ÷ NP.

Cost of redeemable debt (approximate)

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

RV = redemption value; n = years to maturity. Multiply by (1 − t) for after-tax cost. Use YTM/IRR if exact value is asked.

Cost of irredeemable preference shares

Kp = PD ÷ NP

PD = annual preference dividend. No tax adjustment. Dividend distribution tax is not considered unless the question states it.

Cost of redeemable preference shares (approximate)

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

Same logic as redeemable debt, without tax.

Cost of equity: dividend yield method

Ke = D1 ÷ P0

Use only when dividends are expected to stay constant.

Cost of equity: dividend growth (Gordon) model

Ke = D1 ÷ P0 + g, where D1 = D0 × (1 + g)

D1 is next year's dividend. Use net proceeds if floatation costs are given. g is the constant growth rate.

Cost of equity: earnings yield method

Ke = E1 ÷ P0

E1 = expected EPS; works when all earnings are assumed paid out or the question asks for it.

Cost of equity: CAPM

Ke = Rf + β × (Rm − Rf)

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

Cost of retained earnings

Kr = Ke (simple case)

With personal tax and brokerage: Kr = Ke × (1 − personal tax rate) × (1 − brokerage cost), only if the question gives these.

WACC

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

Weights must add up to 1 (or 100%). Use the same weighting basis for all sources.

Weight of a source

Wi = Value of that source ÷ Total value of all long-term sources

Value is book value or market value, as the question needs.

After-tax cost of debt (irredeemable)

Kd = [I × (1 − t)] ÷ NP, or Kd = Interest rate × (1 − t) if issued at par

NP is net proceeds. t is the tax rate. Interest saves tax, so use the after-tax figure.

Cost of preference capital (irredeemable)

Kp = Preference dividend ÷ Net proceeds

No tax adjustment, because dividend is not tax deductible.

Cost of equity (dividend growth approach)

Ke = (D1 ÷ P0) + g

D1 = D0 × (1 + g). P0 is current market price or net proceeds.

Cost of equity (CAPM)

Ke = Rf + β × (Rm − Rf)

Use when risk-free rate, beta and market return are given.

Cost of retained earnings

Kr = Ke (ignoring issue costs and personal tax)

Use Ke unless the question gives an adjustment.

Marginal cost of capital

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

Uses the cost of new funds and the proposed mix, not the existing balance sheet mix.

Contribution

Contribution = Sales − Variable cost

Fixed cost is not deducted here.

EBIT

EBIT = Contribution − Fixed operating cost

Interest is not deducted yet.

Degree of operating leverage

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

Fixed operating cost excludes interest.

Degree of financial leverage

DFL = EBIT ÷ EBT = EBIT ÷ (EBIT − Interest)

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

Degree of combined leverage

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

EBT is EBIT less interest.

EPS

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

Use to verify leverage results.

EPS

EPS = [(EBIT − I) × (1 − t) − PD] ÷ N

I = interest, t = tax rate, PD = preference dividend, N = number of equity shares.

Indifference point (both plans taxed, no preference shares)

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

The tax factor cancels. Solve for EBIT.

Simplified indifference EBIT

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

Valid without preference dividend. N₂ > N₁; plan 1 has more debt and fewer shares.

Indifference point with preference dividend

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

Do not cancel the tax factor. Preference dividend is paid after tax.

Financial break-even point

FBEP = I + PD ÷ (1 − t)

EBIT at which EPS is zero for one plan.

Value of the firm

V = S + D

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

NI approach: value of equity

S = (EBIT − I) ÷ Ke = Earnings available to equity ÷ Ke

I = interest = Kd × D. Ke and Kd are constant.

Overall cost of capital

Ko = EBIT ÷ V

Used in NI to find Ko once V is known; in NOI Ko is given.

NOI approach: value of the firm

V = EBIT ÷ Ko

Then S = V − D and Ke = (EBIT − I) ÷ S.

MM Proposition I (no taxes)

Vu = Vl = EBIT ÷ Ko

Value is independent of capital structure. Ko is the same at every debt level and equals the cost of equity of the all-equity firm, Ke(u).

MM Proposition II (no taxes)

Ke = Ko + (Ko − Kd) × (D ÷ S)

Cost of equity rises linearly with debt-equity ratio.

MM with corporate tax: value

Vl = Vu + (t × D)

t = tax rate; t × D is the present value of the interest tax shield (debt assumed permanent).

MM with tax: cost of equity

Ke = Ko(u) + (Ko(u) − Kd) × (1 − t) × (D ÷ S)

Ko(u) is the cost of capital of the unlevered firm (its Ke).

Weighted average cost of capital

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

The optimal structure is where this is lowest. Use after-tax cost of debt.

After-tax cost of debt

Kd (after tax) = Interest rate × (1 − Tax rate)

Tax shield on interest is a key reason debt is cheaper.

Trading on equity condition

Favourable if ROCE (after or before tax, used consistently) > Cost of debt

If ROCE is lower than the cost of debt, leverage reduces return to equity.

Debt-equity ratio

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

A common measure of gearing. Compare with industry norms.

Degree of financial leverage

DFL = EBIT ÷ (EBIT − Interest)

Shows how sensitive EPS is to changes in EBIT. Higher DFL means higher financial risk.

Contribution

Contribution = Sales − Variable cost = Fixed cost + Profit

Per unit: Selling price per unit − Variable cost per unit.

P/V ratio

P/V ratio = (Contribution ÷ Sales) × 100

Also = (Change in profit ÷ Change in sales) × 100 when fixed cost is constant.

Break-even point in units

BEP (units) = Fixed cost ÷ Contribution per unit

Round up if the answer is fractional and whole units are needed.

Break-even point in rupees

BEP (₹) = Fixed cost ÷ P/V ratio

Equals BEP units × selling price per unit.

Sales for target profit

Required sales (₹) = (Fixed cost + Target profit) ÷ P/V ratio

In units: (Fixed cost + Target profit) ÷ Contribution per unit.

Margin of safety

MOS (₹) = Actual sales − BEP sales; MOS ratio = MOS ÷ Actual sales × 100

Also MOS (₹) = Profit ÷ P/V ratio.

Variable cost ratio

Variable cost ratio = 100% − P/V ratio

Useful to cross-check your P/V ratio.

Quick revision

• Cost of debt after tax = interest rate × (1 − tax rate), for irredeemable debt at par.
• Cost of redeemable debt (approximate) Kd = [I(1 − t) + (RV − NP) ÷ n] ÷ [(RV + NP) ÷ 2], where I is annual interest, t is the tax rate, RV is redemption value, NP is net proceeds and n is the number of years to redemption.
• Cost of equity can be found by the dividend growth method or by CAPM: Ke = Rf + β × (Rm − Rf).
• WACC = Σ (weight × cost of each source).
• Use the weights the question specifies (book, market or target) and apply the same basis to all sources; say which you use.
• Contribution = Sales − Variable cost.
• Degree of operating leverage = Contribution ÷ EBIT.
• Degree of financial leverage = EBIT ÷ (EBIT − Interest), or EBIT ÷ EBT when no preference dividend exists.
• Degree of combined leverage = DOL × DFL = Contribution ÷ EBT.
• At the indifference point, EPS is the same under both financing plans.
• Break-even point (units) = Fixed cost ÷ Contribution per unit.
• Margin of safety = Actual sales − Break-even sales. Margin of safety ratio = Margin of safety ÷ Actual sales.
• Net income approach says value rises with debt; Modigliani-Miller without taxes says capital structure does not affect value.

Common mistakes

• Forgetting the tax shield on debt Fix: Whenever a tax rate is given, multiply by (1 − t). Do not apply tax to preference or equity.
• Using D0 instead of D1 in the growth model Fix: Compute D1 = D0 × (1 + g) unless the question states the expected dividend directly.
• Using the pre-tax cost of debt in WACC. Fix: Always multiply the debt cost by (1 − t). Do not adjust preference or equity.
• Mixing book value and market value in the same calculation. Fix: Pick one basis for all sources. If market value of a source is not given, state your assumption clearly.
• Deducting fixed cost when finding contribution. Fix: Contribution = Sales − Variable cost only. Fixed cost comes off next to give EBIT.
• Including interest in fixed operating cost for DOL. Fix: Interest belongs to financial leverage. Keep it out of EBIT.
• Forgetting existing interest on old debt. Fix: Always add old interest to new interest for the total I of each plan.
• Using the shortcut formula when preference shares exist. Fix: With preference dividend, write full equations and keep (1 − t) on EBIT and interest; the dividend is not tax-deductible.
• Mixing up what is constant in NI and NOI. Fix: Remember: NI keeps Ke and Kd constant; NOI keeps Ko (and Kd) constant. Write this at the top of your answer.
• Using EBIT instead of EBIT minus interest to value equity under NI. Fix: Equity value always uses earnings after interest. EBIT is used only for the whole firm value V.

Exam tips

• Read whether the question wants cost on face value, net proceeds or market price, and write your basis in the answer.
• Show the formula first, then substitution. Marks are awarded for the method even if arithmetic slips.
• If both growth data and CAPM data are given, answer by the method the question names; if none, state your choice and why.
• Keep percentages to two decimals during working and round only at the end.
• Be ready for short notes on explicit versus implicit cost: explicit is a real cash cost like interest; implicit is an opportunity cost like retained earnings.
• Read whether the question asks for book value, market value or target weights. Writing the basis at the top of your answer shows the examiner you know the difference.
• Show a clear table with source, amount, cost and weighted cost. Even if one cost is wrong, you still earn method marks for the rest.
• Calculate each individual cost first, since the numerical often hides them in raw data such as issue price, flotation cost or growth rate.