# Level 1 CFA® Exam:

Leverage

Let's start with the basics.

Leverage increases the volatility of a company’s earnings and cash flows. The greater the company's leverage, the greater its risk and the discount rate used for the company’s valuation.

The company’s cost structure affects the level of leverage. Costs are divided into:

- variable costs and
- fixed costs.

Variable costs are costs that fluctuate with the level of production and sales. These could for example be costs of materials or shipping charges. Fixed costs are not dependent on the level of production and sales, which means that they must be covered irrespective of the number of units sold.

The table below presents 2 companies with different cost structures:

Pear Inc. | Cherry Inc. | |
---|---|---|

Number of units produced and sold | 50,000 | 50,000 |

Sales price per unit | USD 8 | USD 8 |

Variable cost per unit | USD 5 | USD 2 |

Fixed costs | USD 70,000 | USD 250,000 |

Compute the net income for both companies in 2 scenarios:

Scenario 1: sales increase up to 100,000 units

Scenario 2: sales decreases down to 40,000 units

(...)

We can distinguish 4 types of risk:

- business risk,
- sales risk,
- operating risk and
- financial risk.

### Business Risk

Business risk is the risk associated with operating earnings which, in turn, depend on revenues. As we know, revenues are influenced by a large number of factors, such as economic and demographic factors, legal regulations, etc., hence the presence of business risk. Typically, companies operating in the same industry have a similar level of business risk.

Business risk consists of 2 components. The first is sales risk when the price or quantity of products or services is different than expected. The other component of business risk is operating risk. It depends on the ratio of fixed costs to variable costs. The higher it is, that is the greater the share of fixed costs in total costs, the greater the operating risk of a company.

### Sales Risk

Let’s say more about sale risk. The greater the standard deviation of the number and price of the units sold, the greater the sales risk. In the case of Pear Inc. and Cherry Inc. used in Example 1 the expected sales, price, and costs are equal. If, for instance, the standard deviation of units sold by Pear Inc. amounted to 1,000 units, and the price deviation equaled USD 3, and if in the case of Cherry Inc. it was 2,000 units and USD 5, respectively, the sales risk would be much higher in the case of Cherry Inc. We would say then that Cherry Inc. is characterized by a wider distribution of operating profit.

A high level of fixed operating costs makes it difficult to adjust a company’s operating costs to changes in sales and increases operating risk. Notice that cost structure can vary even among companies engaged in similar business activities, and so can operating risk.

What is important in the context of costs is elasticity. It is a measure of the sensitivity of changes in one item to changes in another. The degree of the operating leverage (DOL), which is a measure of operating risk, is based on this concept. DOL is the ratio of the percentage change in operating income to the percentage change in units sold. This is reflected in this formula that you can use in your level 1 CFA exam:

\(DOL = \frac{\%\Delta\text{ operating income}}{\%\Delta\text{ units sold}}\)

- \(DOL\) - degree of operating leverage
- \(\%\Delta\) - percentage change

How should we interpret DOL?

If DOL equals 1.3 and sales increase by 4 percent, then the operating profit will grow by \(1.3\times4\%=5.2\%\). Note that if sales didn’t increase but decreased by 4 percent, then the operating profit would fall by 5.2 percent.

An important category of the income statement item here is operating income which can be calculated using this formula:

\(\text{operating income}=Q\times(P-V)-O\)

The operating income equals the product of the number of units sold (\(Q\)) and the difference between the price per unit (\(P\)) and the variable cost per unit (\(V\)) less fixed operating costs (\(O\)).

\(P-V\) - per unit contribution margin,

\(Q\times(P-V)\) - contribution margin,

The following formula helps you with level 1 CFA exam questions where you need to calculate the degree of the operating leverage:

\(DOL = \frac{Q\times (P-V)}{Q\times (P-V) - O}\)

- \(DOL\) - degree of operating leverage
- \(Q\) - number of units
- \(P\) - price per unit
- \(V\) - variable operating cost per unit
- \(O\) - fixed
__operating__cost - \(Q\times (P-V)\) - contribution margin

Cherry Inc. produced and sold 50,000 units of a product at the price of USD 5 each. The variable cost per unit was USD 3, and the operating fixed costs were estimated at USD 60,000. The degree of the operating leverage is equal to…?

(...)

The principle is that when a company has a positive DOL, the DOL decreases when the number of products sold increases. Why is that? Because as the number of products sold increases, the proportion of variable costs, in terms of value, in the structure of total cost increases, too. So, the proportion of the fixed costs in total cost decreases and, as we know, it results in a decrease in operating risk.

What is also important is that in the case of a negative operating profit, the degree of operating leverage will also be negative.

Remember that operating profit is most sensitive to changes in sales volume if sales are close to the operating breakeven point. The operating breakeven point is the number of units sold at which the company's operating income is zero.

Cherry Inc. produced and sold 30,000 units of a product at the price of USD 5 each. The variable cost per unit was USD 3, and the operating fixed costs were estimated at USD 60,000. The degree of operating leverage in the case of selling 30,000 units is…?:

(...)

Sales increased from 100,000 to 120,000. Calculate the percentage change in operating income assuming that the operating leverage is 1.43.

(...)

Our examples illustrate that the two types of business risk, that is sales risk and operating risk, have a strong impact on a company’s activity and their level is highly dependent on the industry in which the company operates.

However, when it comes to operating risk, the management may control it to a certain extent. Let’s consider a case when a company wants to buy new equipment. Whether a product is made using an old or a modern machine has no effect on the sales volume. However, this new equipment can affect the cost structure, and more specifically, the ratio of fixed costs to variable costs. It is an analyst’s job to forecast how such an operation will influence costs and consequently the company’s operating risk.

Companies that spend most of their funds on research and development of their products but spend relatively little funds on their production and distribution are characterized by a high degree of operating leverage. This is due to a high proportion of fixed costs in the cost structure. Such companies include computer and pharmaceutical companies. The opposite of such companies are companies that generate mainly variable costs which depend on the volume of sales, so the degree of their operating leverage is quite low. These are mainly companies operating in the retail sector.

Let us now move on to the financial risk and ways of quantifying it with the degree of financial leverage (DFL). Financial risk is the risk associated with how a company finances its operations.

(...)

We can quantify the financial risk with the degree of financial leverage that is given by this CFA exam formula:

\(DFL = \frac{\%\Delta\text{ net income}}{\%\Delta\text{ operating income}}\)

- \(DFL\) - degree of financial leverage
- \(\%\Delta\) - percentage change

If the DFL increases, so does the sensitivity of net income to operating income, and thus the financial risk is greater. In other words, the DFL tells us how much a change in operating income affects net income.

Let's take a close look at the degree of financial leverage using the following example.

Let's assume that the degree of financial leverage of Cherry Inc. is 1.6 and the company's operating profit has increased by 3%. What is the change in the net income of the company?

(...)

As was said before, using more debt financing results in higher financial leverage, that is higher sensitivity of net income to changes in operating income. So what is the formula used for calculating the degree of financial leverage? It is similar to the DOL formula and it looks like this:

\(DFL = \frac{Q\times (P-V)-O}{Q\times (P-V)-O-F}\)

- \(DFL\) - degree of financial leverage
- \(Q\) - number of units
- \(P\) - price per unit
- \(V\) - variable operating cost per unit
- \(O\) - fixed
__operating__cost - \(F\) - fixed
__financial__cost - \(Q\times (P-V)\) - contribution margin

The degree of financial leverage is equal to revenue minus variable costs minus fixed operating costs divided by the contribution margin less fixed operating and financial costs.

Note: Fixed financial costs are for instance interest that a company must pay on the incurred debt. Please note that in the DFL formula, \(F\) doesn’t stand for debt but rather for the cost connected with the debt, usually the interest. In your exam, you may have to solve a question where you will have fixed financing costs given. Or in the question there can be given only the value of the debt and the interest in terms of percentage and your task will be to calculate the fixed financing costs, that is the interest in terms of value.

Cherry Inc. sold 200,000 units USD 4 each and the variable cost per unit equals USD 2. If fixed financial cost amounts to USD 40,000 and fixed operating cost is 20,000 the degree of financial leverage equals…?

(...)

The operating income of With Friends Co. in 2021 amounted to USD 15 million. In the same year, the company issued bonds at par for USD 100 million. The yield to maturity of those bonds is 7% and the company's fixed operating costs equal USD 5 million. What is the degree of financial leverage (DFL)?

(...)

The degree of financial leverage, just like the degree of operating leverage, changes at different amounts of units sold. What's more, the greater the amount of fixed obligations, the greater the sensitivity of net income to changes in operating income.

The degree of financial leverage is often a choice left to the company’s management. Therefore, the degree of financial leverage may be different among companies in the same industry.

Companies with more tangible assets may use higher degrees of financial leverage. Why is that? It happens so because these assets may serve as collateral for liabilities. More tangible assets result in higher security of the claim, which translates into more certainty that the borrowed capital will be returned. Companies with substantial tangible assets include companies with land or equipment that can be used to collateralize liabilities.

Now, let's see how financial leverage affects ROE.

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The degree of total leverage (DTL) is a measure of the sensitivity of net income to changes in the number of units sold by 1%.

\(DTL = \frac{\%\Delta\text{ net income}}{\%\Delta\text{ units sold}}\)

- \(DTL\) - degree of total leverage
- \(\%\Delta\) - percentage change

The degree of total leverage (DTL) may also be calculated by multiplying the degree of operating leverage (DOL) by the degree of financial leverage (DFL):

\(DTL = DOL \times DFL = \frac{Q\times (P-V)}{Q\times (P-V)-O-F}\)

- \(DTL\) - Degree of Total Leverage
- \(DOL\) - Degree of Operating Leverage
- \(DFL\) - Degree of Financial Leverage
- \(Q\) - number of units sold
- \(P\) - price per unit
- \(V\) - variable cost per unit
- \(O\) - fixed
__operating__cost - \(F\) - fixed
__financial__cost - \(Q\times (P-V)\) - contribution margin

DTL is equal to the contribution margin divided by contribution margin less fixed operating and fixed financial costs.

The number of units sold of Silvers Co. amounts to 50,000, each sold at USD 6 with a variable cost per unit of USD 3. If the fixed operating cost is USD 10,000 and the fixed financial cost is USD 20,000 then the degree of total leverage is closest to…?

(...)

The degrees of the operating leverage and financial leverage are equal to 2.3 and 2.7, respectively. What is the value of the degree of total leverage?

(...)

The degrees of operating, financial and total leverage of Shoelaces Inc. are given below:

- DOL = 1.5
- DFL = 1.8
- DTL = 2.7

The price of the product is USD 10 and its variable cost per unit is USD 5. If fixed operating costs are USD 7.4 million and the company has issued bonds at par for USD 56 million, then the company's revenue is equal to…?

(...)

- Leverage increases the volatility of a company’s earnings and cash flows.
- Variable costs are costs that fluctuate with the level of production and sales.
- Fixed costs are not dependent on the level of production and sales.
- Business risk is the risk associated with operating earnings which, in turn, depend on revenues.
- Sales risk is when the price or quantity of products or services is different than expected. The greater the standard deviation of the number and price of the units sold, the greater the sales risk.
- Operating risk depends on the ratio of fixed costs to variable costs.
- In the case of operating leverage, the higher fixed operating costs, the higher sensitivity of operating income to changes in the number of units sold.
- In the case of financial leverage, the higher fixed financial costs, the higher sensitivity of net income to changes in operating income.
- Total leverage combines those two effects and tells us how net income will change if the number of units sold rises by 1%.