Leverage Analysis: Operating, Financial, and Combined
Prerequisites
Before studying this chapter, please click and review these topics:
- 🔗 Capital Structure - Meaning - Understanding debt vs equity
- 🔗 Capital Structure Theories - Financial risk concept
- 🔗 Specific Cost of Capital - Cost of debt
1. What is Leverage?
Leverage (from the word "lever") means using a small force to lift a heavy object.
In Finance: Using fixed-cost funds (debt or fixed operating costs) to magnify the effect of changes in sales on profits.
Types:
- Operating Leverage (Business Risk)
- Financial Leverage (Financial Risk)
- Combined Leverage (Total Risk)
2. OPERATING LEVERAGE (DOL)
2.1 Definition
Operating Leverage measures the sensitivity of Operating Profit (EBIT) to changes in Sales.
It arises due to fixed operating costs (rent, salaries, depreciation) that don't change with sales volume.
2.2 Degree of Operating Leverage (DOL) Formula
DOL = % Change in EBIT / % Change in Sales
OR
DOL = Contribution / EBIT
OR
DOL = (Sales - VC) / (Sales - VC - FC)
Where:
- VC = Variable Costs
- FC = Fixed Costs
- EBIT = Earnings Before Interest and Tax
- Contribution = Sales - Variable Costs
2.3 Interpretation
DOL = 2.5 means:
- If sales increase by 10%, EBIT will increase by 25% (10% × 2.5)
- If sales decrease by 10%, EBIT will decrease by 25%
Higher DOL → Higher Business Risk → Higher volatility in EBIT
2.4 Numerical Problem (Exam Format)
Problem: Calculate DOL from the following data:
Sales: ₹5,00,000
Variable Costs: ₹3,00,000
Fixed Operating Costs: ₹1,20,000
Solution:
Step 1: Calculate Contribution
Contribution = Sales - Variable Costs
Contribution = ₹5,00,000 - ₹3,00,000
Contribution = ₹2,00,000
Step 2: Calculate EBIT
EBIT = Contribution - Fixed Costs
EBIT = ₹2,00,000 - ₹1,20,000
EBIT = ₹80,000
Step 3: Calculate DOL
DOL = Contribution / EBIT
DOL = ₹2,00,000 / ₹80,000
DOL = 2.5
Answer: Degree of Operating Leverage is 2.5.
Interpretation: A 10% change in sales will cause a 25% change in EBIT.
3. FINANCIAL LEVERAGE (DFL)
3.1 Definition
Financial Leverage measures the sensitivity of Earnings Per Share (EPS) to changes in Operating Profit (EBIT).
It arises due to fixed financial costs (interest on debt, preference dividend).
3.2 Degree of Financial Leverage (DFL) Formula
DFL = % Change in EPS / % Change in EBIT
OR
DFL = EBIT / (EBIT - Interest)
OR (if preference shares exist):
DFL = EBIT / [EBIT - Interest - (Pref Div / (1-T))]
Where:
- EBIT = Earnings Before Interest and Tax
- Interest = Interest on Debt
- Pref Div = Preference Dividend
- T = Tax Rate
3.3 Interpretation
DFL = 1.5 means:
- If EBIT increases by 10%, EPS will increase by 15% (10% × 1.5)
- If EBIT decreases by 10%, EPS will decrease by 15%
Higher DFL → Higher Financial Risk → Higher volatility in EPS
3.4 Numerical Problem (Exam Format)
Problem: Calculate DFL from the following:
EBIT: ₹2,00,000
Interest on Debt: ₹50,000
Tax Rate: 30%
Solution:
Step 1: Apply DFL Formula
DFL = EBIT / (EBIT - Interest)
DFL = ₹2,00,000 / (₹2,00,000 - ₹50,000)
DFL = ₹2,00,000 / ₹1,50,000
DFL = 1.33
Answer: Degree of Financial Leverage is 1.33.
Interpretation: A 10% change in EBIT will cause a 13.3% change in EPS.
4. COMBINED LEVERAGE (DCL)
4.1 Definition
Combined Leverage measures the total effect of both operating and financial leverage - the sensitivity of EPS to changes in Sales.
4.2 Degree of Combined Leverage (DCL) Formula
DCL = DOL × DFL
OR
DCL = % Change in EPS / % Change in Sales
OR
DCL = Contribution / (EBIT - Interest)
4.3 Interpretation
DCL = 4 means:
- If sales increase by 10%, EPS will increase by 40% (10% × 4)
- Combines both business and financial risk
4.4 Numerical Problem (Exam Format)
Problem: Calculate DCL using the following data:
Sales: ₹10,00,000
Variable Costs: ₹6,00,000
Fixed Operating Costs: ₹2,00,000
Interest: ₹80,000
Solution:
Step 1: Calculate Contribution
Contribution = Sales - Variable Costs
Contribution = ₹10,00,000 - ₹6,00,000
Contribution = ₹4,00,000
Step 2: Calculate EBIT
EBIT = Contribution - Fixed Costs
EBIT = ₹4,00,000 - ₹2,00,000
EBIT = ₹2,00,000
Step 3: Calculate DOL
DOL = Contribution / EBIT
DOL = ₹4,00,000 / ₹2,00,000
DOL = 2.0
Step 4: Calculate DFL
DFL = EBIT / (EBIT - Interest)
DFL = ₹2,00,000 / (₹2,00,000 - ₹80,000)
DFL = ₹2,00,000 / ₹1,20,000
DFL = 1.67
Step 5: Calculate DCL
DCL = DOL × DFL
DCL = 2.0 × 1.67
DCL = 3.34
Alternative Method:
DCL = Contribution / (EBIT - Interest)
DCL = ₹4,00,000 / ₹1,20,000
DCL = 3.33 (minor rounding difference)
Answer: Degree of Combined Leverage is 3.34.
Interpretation: A 10% change in sales will cause a 33.4% change in EPS.
5. Comparison of All Three Leverages
| Leverage Type | Measures | Formula | Depends On | Risk Type |
|---|---|---|---|---|
| Operating (DOL) | EBIT sensitivity to Sales | Contribution / EBIT | Fixed Operating Costs | Business Risk |
| Financial (DFL) | EPS sensitivity to EBIT | EBIT / (EBIT - I) | Fixed Financial Costs (Interest) | Financial Risk |
| Combined (DCL) | EPS sensitivity to Sales | DOL × DFL | Both Fixed Costs | Total Risk |
6. EBIT-EPS Analysis
6.1 Purpose
To determine the indifference point between two financing alternatives (debt vs equity).
At the indifference point, EPS is the same under both plans.
6.2 EPS Formula
EPS = [(EBIT - Interest)(1 - T) - Preference Dividend] / No. of Equity Shares
Where:
- EBIT = Earnings Before Interest and Tax
- T = Tax Rate
- Interest and Pref Div = Fixed charges
6.3 Indifference Point Formula
At indifference point, EPS from Plan 1 = EPS from Plan 2
[(EBIT - I₁)(1-T) - PD₁] / N₁ = [(EBIT - I₂)(1-T) - PD₂] / N₂
Solve for EBIT to find indifference point.
6.4 Numerical Problem (Exam Format)
Problem: ABC Ltd. needs ₹10,00,000 for expansion. Two plans:
- Plan A: Issue 10,000 equity shares at ₹100 each
- Plan B: Issue ₹10,00,000 in 10% debentures
Tax rate = 30%. Find: (i) EPS at EBIT = ₹2,00,000 under both plans (ii) Indifference point
Solution:
(i) EPS at EBIT = ₹2,00,000
Plan A (All Equity):
No. of shares = ₹10,00,000 / ₹100 = 10,000
Interest = ₹0
EPS = [(EBIT - I)(1-T)] / N
EPS = [(₹2,00,000 - 0)(1-0.30)] / 10,000
EPS = [₹2,00,000 × 0.70] / 10,000
EPS = ₹1,40,000 / 10,000
EPS = ₹14
Plan B (All Debt):
No. of shares = 0 (assume existing shares = 5,000 for comparison)
Interest = 10% of ₹10,00,000 = ₹1,00,000
EPS = [(₹2,00,000 - ₹1,00,000)(1-0.30)] / 5,000
EPS = [₹1,00,000 × 0.70] / 5,000
EPS = ₹70,000 / 5,000
EPS = ₹14
(ii) Indifference Point:
Set EPS of Plan A = EPS of Plan B
[(EBIT - 0)(0.70)] / 10,000 = [(EBIT - 1,00,000)(0.70)] / 5,000
Simplifying:
EBIT / 10,000 = (EBIT - 1,00,000) / 5,000
Cross multiply:
5,000 × EBIT = 10,000 × (EBIT - 1,00,000)
5,000 EBIT = 10,000 EBIT - 10,00,00,000
5,000 EBIT = 10,00,00,000
EBIT = ₹2,00,000
Answer:
- EPS under both plans at EBIT ₹2,00,000 = ₹14
- Indifference Point = ₹2,00,000 EBIT
Interpretation:
- If expected EBIT > ₹2,00,000 → Choose Plan B (Debt) for higher EPS
- If expected EBIT < ₹2,00,000 → Choose Plan A (Equity) for higher EPS
Exam Pattern Questions and Answers
Question 1: "Calculate DOL, DFL, and DCL." (6 Marks)
Given:
Sales: ₹8,00,000
Variable Cost: ₹4,80,000
Fixed Cost: ₹2,00,000
Interest: ₹40,000
Solution:
Contribution = ₹8L - ₹4.8L = ₹3.2L
EBIT = ₹3.2L - ₹2L = ₹1.2L
DOL = ₹3.2L / ₹1.2L = 2.67
DFL = ₹1.2L / (₹1.2L - ₹0.4L) = 1.2L / 0.8L = 1.5
DCL = 2.67 × 1.5 = 4.0
Answer: DOL = 2.67, DFL = 1.5, DCL = 4.0
Summary
Three Leverages:
- DOL = Contribution / EBIT (Business Risk)
- DFL = EBIT / (EBIT - I) (Financial Risk)
- DCL = DOL × DFL (Total Risk)
Higher Leverage = Higher Risk BUT Higher Reward potential
EBIT-EPS Analysis helps choose optimal financing mix
For leverage calculations (6 marks):
- Show Given data clearly
- Calculate Contribution first (Sales - VC)
- Then EBIT (Contribution - FC)
- Apply formulas step-by-step
- Round to 2 decimal places
Common Mistakes:
- Forgetting to subtract FC before calculating DOL
- Using wrong denominator in DFL (EBIT - I, not just EBIT)
- Not simplifying before cross-multiplication in indifference point
Memory Aid:
- DOL = "Down to EBIT" (Sales → EBIT)
- DFL = "Further Down to EPS" (EBIT → EPS)
- DCL = "Complete Down" (Sales → EPS)
Quiz Time! 🎯
Test Your Knowledge
Question 1 of 4
1. Operating leverage arises due to: