CMA Intermediate · Financial Management and Business Data Analytics

Leverage Analyses and EBIT - EPS Analysis: formula sheet

Full chapter guide

Key formulas

Degree of Operating Leverage (DOL): 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): DFL = EBIT ÷ EBT = % change in EPS ÷ % change in EBIT; EBT = EBIT − Interest. If preference shares exist, use DFL = EBIT ÷ [EBIT − Interest − Preference dividend ÷ (1 − t)], where t is the tax rate.
Degree of Combined Leverage (DCL): DCL = DOL × DFL = % change in EPS ÷ % change in sales. Without preference shares: DCL = Contribution ÷ EBT. With preference shares: DCL = Contribution ÷ [EBIT − Interest − Preference dividend ÷ (1 − t)]; Contribution ÷ EBT applies only when there is no preference dividend. When preference shares exist, the denominator must be EBT less the pre-tax equivalent of the preference dividend, that is, Preference dividend ÷ (1 − t).
EBIT: EBIT = Sales − Variable cost − Fixed operating cost; Interest is not deducted to reach EBIT.
EPS: EPS = (EBT − Tax − Preference dividend) ÷ Number of equity shares; Used when you need to prove leverage by recomputing profits.
Contribution: Contribution = Sales − Variable costs = Sales × P/V ratio; Use variable costs of all kinds, including variable selling and administration costs.
EBIT: EBIT = Contribution − Fixed operating costs; Do not deduct interest. Interest comes after EBIT.
Degree of operating leverage: DOL = Contribution ÷ EBIT; Valid at one given level of sales. EBIT must be positive.
DOL from percentage changes: DOL = % change in EBIT ÷ % change in sales; Use this to check the answer or when two sales levels are given.
DOL and fixed cost: DOL = 1 + (Fixed operating costs ÷ EBIT); Follows from Contribution = EBIT + Fixed costs. DOL is always more than 1 when fixed costs exist.
Effect on EBIT: % change in EBIT = DOL × % change in sales; Applies to a change from the sales level at which DOL was computed.
EPS: EPS = [(EBIT − Interest) × (1 − t) − Preference dividend] ÷ Number of equity shares; t is the tax rate. Preference dividend is deducted after tax.
DFL (only interest): DFL = EBIT ÷ (EBIT − Interest) = EBIT ÷ PBT; Use when there are no preference shares. Tax rate does not matter here.
DFL (with preference dividend): DFL = EBIT ÷ [EBIT − Interest − Preference dividend ÷ (1 − t)]; Gross up the preference dividend by dividing by (1 − t). Use the same tax rate as in the question.
DFL from percentage changes: DFL = % change in EPS ÷ % change in EBIT; Gives the same answer as the formula above for a small or exact change from the base EBIT.
Financial break-even EBIT: EBIT at which EPS = 0: Interest + Preference dividend ÷ (1 − t); At this EBIT, earnings for equity are nil and DFL is undefined.
Effect of a change in EBIT: % change in EPS = DFL × % change in EBIT; Use to forecast EPS quickly from a given EBIT change.
Degree of Operating Leverage: DOL = Contribution ÷ EBIT; Contribution = Sales − Variable cost. EBIT = Contribution − Fixed operating cost.
Degree of Financial Leverage: DFL = EBIT ÷ (EBIT − Interest); With preference shares: DFL = EBIT ÷ [EBIT − Interest − Preference dividend ÷ (1 − t)].
Degree of Combined Leverage: DCL = DOL × DFL = Contribution ÷ (EBIT − Interest); EBIT cancels out in the product. Use PBT as the denominator when there is no preference dividend.
DCL from percentage changes: DCL = % change in EPS ÷ % change in sales; Valid as a measure at the base level of sales.
Forecast change in EPS: % change in EPS = DCL × % change in sales; New EPS = Old EPS × (1 + % change in EPS).
EPS for a plan: EPS = [(EBIT − I) × (1 − t) − PD] ÷ N; I = total interest under the plan (old plus new debt), t = tax rate, PD = preference dividend, N = number of equity shares after the plan.
Indifference point (no preference shares): EBIT = (N2 × I1 − N1 × I2) ÷ (N2 − N1); Plan 1 has N1 shares and interest I1; plan 2 has N2 shares and interest I2. Works when the tax rate is the same in both plans, as the (1 − t) factor cancels.
Indifference point (general, with preference): (EBIT − I1 − PD1 ÷ (1 − t)) ÷ N1 = (EBIT − I2 − PD2 ÷ (1 − t)) ÷ N2; Gross up the preference dividend by dividing by (1 − t), then solve for EBIT.
Financial breakeven EBIT: EBIT = I + PD ÷ (1 − t); EPS is zero at this EBIT. It is the x-axis intercept of the plan's line on the chart.
Number of new shares: New shares = Amount raised ÷ Issue price per share; Add to existing shares to get N.
EPS: EPS = [(EBIT − I) × (1 − t) − PD] ÷ N; I = total interest, t = tax rate, PD = preference dividend, N = number of equity shares. Preference dividend is not tax-deductible.
Indifference point (with taxes, no preference): (EBIT − I₁)(1 − t) ÷ N₁ = (EBIT − I₂)(1 − t) ÷ N₂; The (1 − t) cancels, so the tax rate does not affect the answer when there is no preference dividend.
Indifference point (general, with preference): [(EBIT − I₁)(1 − t) − PD₁] ÷ N₁ = [(EBIT − I₂)(1 − t) − PD₂] ÷ N₂; Use this when a plan has preference shares. Tax rate then matters.
Simplified solution (no preference, no tax effect): EBIT = (N₂ × I₁ − N₁ × I₂) ÷ (N₂ − N₁); Plan 1 has fewer shares (N₁ < N₂) and more interest. I₁ and I₂ are total interest under each plan.
Financial break-even point: FBEP = I + PD ÷ (1 − t); EBIT at which EPS = 0 for one plan.
Decision rule: EBIT > indifference point: choose more debt. EBIT < indifference point: choose more equity.; Holds when the debt plan has the higher fixed charge and fewer shares.

Quick revision

Operating leverage arises from fixed operating costs; financial leverage from fixed financing charges.
DOL = Contribution ÷ EBIT.
DFL = EBIT ÷ EBT when there is no preference dividend.
With preference dividend, convert it to a pre-tax amount by dividing by (1 − tax rate).
DCL = DOL × DFL = Contribution ÷ EBT.
DOL shows the percentage change in EBIT for a 1% change in sales; DFL does the same for EPS against EBIT; DCL for EPS against sales.
Leverage figures hold only at the given level of sales or EBIT, and change when that level changes.
EPS = (EBIT − Interest − Tax − Preference dividend) ÷ Number of equity shares.
Indifference point: the EBIT at which two financing plans give the same EPS.
Above the indifference point, the plan with more fixed financing charges usually gives higher EPS; below it, the equity plan does.
Higher DCL means higher risk, so check the interpretation line in every answer.

Common mistakes

Deducting interest before computing DOL. Fix: DOL uses only operating items. Interest comes below EBIT and affects DFL, not DOL.
Using sales instead of contribution in the DOL formula. Fix: Always write Contribution = Sales − Variable cost first, then divide by EBIT.
Dividing EBIT by contribution instead of contribution by EBIT. Fix: Remember that DOL is always above 1 when fixed costs exist. If you get less than 1, you have inverted it.
Deducting interest before finding EBIT for DOL. Fix: DOL uses EBIT only. Interest affects financial leverage, not operating leverage.
Subtracting preference dividend without grossing it up Fix: Always divide preference dividend by (1 − t) before putting it in the DFL denominator.
Grossing up interest as well Fix: Interest is already before tax. Use it as it is. Only preference dividend needs the adjustment.
Using EBIT instead of Contribution in the numerator of DCL. Fix: DCL always has Contribution on top. EBIT on top gives DFL.
Subtracting fixed operating cost twice or forgetting it when finding EBIT. Fix: Always write the layout: Contribution − Fixed cost = EBIT, then − Interest = PBT.
Ignoring existing interest when adding new debt Fix: Always write total interest = old interest + new interest for each plan before building the table.
Deducting preference dividend before tax Fix: Preference dividend is paid out of profit after tax. Deduct it after PAT, and gross it up by (1 − t) when solving for the indifference point.

Exam tips

In the 2-mark MCQs, expect a quick calculation of DOL, DFL or DCL, or a statement-type question on which leverage links which two variables. Learn the link: sales to EBIT, EBIT to EPS, sales to EPS.
In written answers, draw the income statement format first. It earns step marks even if the final ratio is wrong.
Always add a one-line interpretation, such as what a DCL of 2.67 means for risk. ICMAI-style answers reward this.
Show the check DOL × DFL = Contribution ÷ EBT. It catches errors and shows the examiner you understand the link.
Read the question for preference shares and tax. These change DFL and DCL and are a common trap.
Always show the statement of sales, variable cost, contribution, fixed cost and EBIT. Marks are given for each line.
In MCQs, check which cost is fixed and which is variable before dividing. Distractor options often use sales or PBT.
Write a one-line interpretation. ICMAI answers expect you to link DOL to business risk.