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IFT Notes for Level I CFA® Program

R32 Measures of Leverage

Part 1


 

1.  Introduction

The total costs of a company can be broken down into two parts: fixed costs and variable costs. Fixed costs do not vary with output (the number of units produced and sold), whereas variable costs vary with output.

Leverage is the use of fixed costs in a company’s cost structure. It has two components:

  • Operating leverage: Fixed operating costs such as depreciation and rent create operating leverage.
  • Financial leverage: Fixed financial costs such as interest expense create financial leverage.

For highly leveraged firms, that is firms with a high proportion of fixed costs relative to total costs, a small change in sales will have a big impact on earnings.

2.  Leverage

Let’s look at an example to understand the impact of leverage.

Example

Consider two companies, HL and LL, with the same revenue and net income but a different cost structure.

Operating PerformanceIncome Statement
HLLLHLLL
No. of units sold100100Revenue100100
Sales price per unit11Operating costs7075
Variable cost per unit0.20.6Operating Income3025
Fixed operating cost5015Financing Expense105
Fixed financing cost105Net Income2020

How is the cost structure different?

What is the impact on net income if sales numbers change?

Solution:

Net income for different units of sold
HLLLHLLLHLLL
No. of units sold10010000120120
Fixed operating costs501550155015
Variable costs2060002472
Operating costs707550157487
Operating Income3025-50-154633
Interest expense105105105
Net Income2020-60-203628

Let us plot the net income for different levels of sales (units sold) for HL and LL.

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As you can see, the loss is magnified when revenue is zero and the profit is also magnified when revenue increases by a marginal amount for HL relative to LL. When 100 units are sold, the net income is the same for both the companies. The effect of both loss and profit is higher for a high leverage firm.

Leverage increases volatility of a company’s earnings and cash flows and also increases the risk of lending to or owning a company.  The valuation of a company and its equity is affected by the degree of leverage. The higher a company’s leverage, the higher is its risk, which requires a higher discount rate to be applied in valuation.

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3. Business and Sales Risks

3.1.     Business Risk and Its Components

Business risk is the risk associated with operating earnings. All firms face the risk that revenues will decline, which will in turn, affect operating earnings. Business risk consists of two components: sales risk and operating risk.

Business risk and its two components are depicted in the picture below:

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3.2.     Sales Risk

Sales risk is the variability in profits due to uncertainty of sales price and volume (product demand and revenue uncertainty).

4. Operating Risk and the Degree of Operating Leverage

Operating risk is the risk due to operating cost structure. It is greater when fixed operating costs are higher relative to variable operating costs.

Degree of operating leverage is a quantitative measure of operating risk. It is the ratio of the percentage change in operating income to the percentage change in units sold. It measures how sensitive a company’s operating income is to changes in sales. For example, a DOL of 2 means that a 1 percent change in units sold results in a 2 percent change in operating income.

DOL =\frac{Percentage\ change\ in\ operating\ income}{Percentage\ change\ in\ units\ sold}

 

It can be shown that DOL =\frac{Q\left(P-V\right)}{Q\left(P-V\right)-F}
where:
Q = number of units
P = price per unit
V = variable operating cost per unit
F = fixed operating cost
P – V = per unit contribution margin
Q (P – V) = contribution margin

Example

Given the following data, compute DOL for HL and LL.

 HLLL
Number of units sold100100
Sales price per unit11
Variable cost per unit0.20.6
Fixed operating cost5015
Fixed financing cost105

Solution:

For HL:

Q = 100; P = 1; V = 0.2; F = 50

DOL for HL:\frac{100\ *\ 0.8}{100\ *\ 0.8\ -\ 50}  = 2.67

For LL:

Q = 100; P = 1; V = 0.6; F = 15

DOL for LL:\frac{100\ *\ 0.4}{100\ *\ 0.4\ -\ 15} = 1.6

5. Financial Risk, the Degree of Financial Leverage and the Leveraging Role of Debt

Financial risk is the risk associated with how a company finances its operations. A company may choose to finance using debt or equity. Greater the use of debt, greater is the company’s financial risk.

Degree of financial leverage is a quantitative measure of financial risk. For example, if DFL is 2, then a 5 percent increase in operating income will most likely result in a 10 percent increase in net income.

DFL =\frac{Percentage\ change\ in\ net\ income}{Percentage\ change\ in\ operating\ income}

 

It can be shown that DFL =\frac{Q\left(P-V\right)-F}{Q\left(P-V\right)-F-C}

where

Q = number of units

P = price per unit

V = variable operating cost per unit

F = fixed operating cost

C = fixed financial cost

P-V = per unit contribution margin

Q (P – V) = contribution margin

Example

Given the following data, compute DFL for HL and LL.

 HLLL
Number of units sold100100
Sales price per unit11
Variable cost per unit0.20.6
Fixed operating cost5015
Fixed financing cost105

Solution:

For HL:

Q = 100; P = 1; V = 0.2; F = 50; C = 10

DFL for HL: \frac{100\ *\ 0.8-50}{100\ *\ 0.8\ -\ 50\ -\ 10} = 1.5

For LL:

Q = 100; P = 1; V = 0.6; F = 15; C = 5

DFL for LL: \frac{100\ *\ 0.4\ -\ 15}{100\ *\ 0.4\ -\ 15\ -\ 5} = 1.25

 

Effect of Financial Leverage on NI and ROE

Higher leverage leads to higher ROE volatility and potentially higher ROE levels. This is illustrated through a simple example. Consider two firms with the same operating income (EBIT), but different capital structures. While Firm 1 has no debt, capital structure of Firm 2 comprises 50% debt and 50% equity. The table below computes ROE for different levels of EBIT.

ROE = NI / equity

Firm 1: Assets = 200; Equity = 200 Debt = 0; Tax = 0%Firm 2: Assets = 200; Equity = 100; Debt = 100, Interest = 10%
EBITNIROENIROE
000-10-10%
202010%1010%
404020%3030%
606030%5050%
808040%7070%

Some inferences about the effect of financial leverage on NI and ROE:

  • For lower levels of EBIT, NI and ROE are negative for the high leverage firm.
  • Higher EBIT leads to potentially higher ROE levels, as seen in Firm 2 (high leverage firm).
  • ROE of firm 2 (high leverage firm) has a higher volatility and variability (-10% to 70%) relative to firm 1 (0 to 40%).

6. Total Leverage and the Degree of Total Leverage

Total leverage gives us the combined effect of both operating leverage and financial leverage. Degree of total leverage (DTL) measures the sensitivity of net income to changes in the number of units produced and sold.

DTL = \frac{Percentage\ change\ in\ net\ income}{Percentage\ change\ in\ units\ sold}
It can be shown that DTL = DOL * DFL = \frac{Q\left(P-V\right)}{Q\left(P-V\right)-F-C}

where

Q = number of units

P = price per unit

V = variable operating cost per unit

F = fixed operating cost

C = fixed financial cost

P-V = per unit contribution margin

Q (P – V) = contribution margin

Example

Given the following data, compute DTL for HL and LL.

 HLLL
Number of units sold100100
Sales price per unit11
Variable cost per unit0.20.6
Fixed operating cost5015
Fixed financing cost105

Solution:

For HL:

Q = 100; P = 1; V = 0.2; F = 50; C = 10

DTL for HL: \frac{100\ *\ 0.8}{100\ *\ 0.8\ -\ 50\ -\ 10} = 4

For LL:

Q = 100; P = 1; V = 0.6; F = 15; C = 5

DTL for LL: \frac{100\ *\ 0.4}{100\ *\ 0.4\ -\ 15\ -\ 5} = 2

7. Breakeven Points and Operating Breakeven Points

Breakeven point

Breakeven point is the number of units produced and sold at which net income is zero, the point at which revenues are equal to costs.

Breakeven point QBE =\frac{F+C}{P-V}

where:

F = fixed operating costs

C = fixed financial cost

V = variable cost per unit

P = the price per unit

Operating breakeven point

Operating breakeven point is the number of units produced and sold at which operating income is zero.

Operating breakeven point QOBE =\frac{F}{P-V}

All else equal companies that have high operating and financial leverage will have high break even points as compared to companies with low leverage. This is demonstrated in the following example.

The further away unit sales are from the breakeven point for high leverage companies, the greater the magnifying effect of this leverage.

Example

Given the following data, compute the breakeven and operating breakeven points for HL (high leverage) and LL (low leverage) companies.

HLLL
Number of units sold100100
Sales price per unit11
Variable cost per unit0.20.6
Fixed operating cost5015
Fixed financing cost105

Solution:

For HL:

F = 50; C = 10; P = 1; V = 0.2

QBE = \frac{F\ +\ C}{P\ -\ V} = \frac{50\ +\ 10}{1\ -\ 0.2}= 75
QOBE = \frac{F}{P-V}$ = 50/0.8 = 62.5

For LL:

F = 15; C = 5; P = 1; V = 0.6

QBE = \frac{F\ +\ C}{P\ -\ V} = \frac{15\ +\ 5}{1\ -\ 0.6} = 50
QOBE = \frac{F}{P\ -\ V} = 15/0.4 = 37.5

Instructor’s Note: Section 8 ‘The Risks of Creditors and Owners’ is not testable and hence not covered.