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IFT Notes for Level I CFA® Program
IFT Notes for Level I CFA® Program

R34 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 Performance Income Statement
HL LL HL LL
No. of units sold 100 100 Revenue 100 100
Sales price per unit 1 1 Operating costs 70 75
Variable cost per unit 0.2 0.6 Operating Income 30 25
Fixed operating cost 50 15 Financing Expense 10 5
Fixed financing cost 10 5 Net Income 20 20

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
HL LL HL LL HL LL
No. of units sold 100 100 0 0 120 120
Fixed operating costs 50 15 50 15 50 15
Variable costs 20 60 0 0 24 72
Operating costs 70 75 50 15 74 87
Operating Income 30 25 -50 -15 46 33
Interest expense 10 5 10 5 10 5
Net Income 20 20 -60 -20 36 28

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 Risk and Financial Risk

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).

3.3.     Operating Risk

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.

  HL LL
Number of units sold 100 100
Sales price per unit 1 1
Variable cost per unit 0.2 0.6
Fixed operating cost 50 15
Fixed financing cost 10 5

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

3.4.     Financial Risk

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.

  HL LL
Number of units sold 100 100
Sales price per unit 1 1
Variable cost per unit 0.2 0.6
Fixed operating cost 50 15
Fixed financing cost 10 5

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%
EBIT NI ROE NI ROE
0 0 0 -10 -10%
20 20 10% 10 10%
40 40 20% 30 30%
60 60 30% 50 50%
80 80 40% 70 70%

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%).

3.5.     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.

  HL LL
Number of units sold 100 100
Sales price per unit 1 1
Variable cost per unit 0.2 0.6
Fixed operating cost 50 15
Fixed financing cost 10 5

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

3.6.     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}

Example

Given the following data, compute the breakeven and operating breakeven points for HL and LL.

HL LL
Number of units sold 100 100
Sales price per unit 1 1
Variable cost per unit 0.2 0.6
Fixed operating cost 50 15
Fixed financing cost 10 5

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


Corporate Finance Measures of Leverage Part 1