Leverage effect

The leverage effect , also called leverage effect ([ ˈlevəɹədʒ ], from English leverage for 'leverage'), describes generally situations in which small changes in a variable lead to large fluctuations in the result. Especially in finance, the term is used in the areas of capital structure (for example, of a company , financial leverage ), cost structure ( operating leverage ) and derivatives .

Capital structure

The leverage effect is understood here as the leverage effect of the financing costs of the debt on the return on equity . The return on equity of an investment can be increased by using outside capital . This applies if the investor can borrow capital on more favorable terms than the return on total capital achieved.

Calculation method

If the return on total capital ( internal rate of return of the investment) is higher than the interest rate on borrowed capital , the higher the level of indebtedness (ratio of borrowed and equity capital), the greater the return on the capital employed (also called return on equity ). ${\displaystyle r_{GK}}$ ${\displaystyle r_{FK}}$ ${\displaystyle V}$ ${\displaystyle r_{EK}}$

Under the premise that the interest rate on borrowed capital is constant even with a high level of indebtedness , the following formula applies: ${\displaystyle \left({\tfrac {FK}{EK}}\right)}$

${\displaystyle r_{\mathit {EK}}=r_{\mathit {GK}}+V\cdot (r_{\mathit {GK}}-r_{\mathit {FK}})}$

This means that - provided that outside capital requires less interest than the return on total capital - a higher level of indebtedness provides a higher return on equity.

Leverage risk

There are incentives to increase the level of debt - especially if the gap between the return on total capital and the interest rate on borrowed capital decreases. The consequence of an increased level of indebtedness is an increase in the risk - especially if the repayment of the borrowed capital occurs before the investment expires. As the level of debt rises, even small variations in the interest rate on borrowed capital or the overall profitability of the project can produce large fluctuations in the return on equity.

example 1

Diagram for example 1

A company can achieve a return of 10% on the capital employed on a project . The total capital employed amounts to € 1,000 and was financed half by equity and half by debt (i.e. € 500 each). The profit before interest is therefore € 100. The interest on borrowed capital that the company has to pay the lender is 2% (€ 500 × 0.02 =) € 10. The company receives the profit (€ 90). The return on equity is therefore 18% (€ 90 / € 500), with this profit only being related to the equity of € 500 used. ${\displaystyle r_{GK}}$

The leverage effect is the difference between the return and the interest expense, i.e. € 90 (€ 100 - € 10) or 18% on the equity invested.

Example 2

Diagram for example 2

The same company ( r _GK 10%, debt interest rate r _FK 2%) now reduces the equity share in the project from € 500 to € 200. The gap is covered by outside capital with the unchanged FK interest rate. So the debt is now € 800.

From the unchanged gross profits of € 100, € 16 (€ 800 × 0.02) must now be paid for interest. The rest of the profit amounts to 84 €, which was generated with only 200 € of equity invested. The equity return is now 42% (€ 84 / € 200). The released € 300 (of € 500 from example 1) must now be invested at least at the FK interest rate in order to compensate for the gap in absolute profit (€ 6 = € 90 - € 84 = € 300 × 0.02).

Example 3

Diagram for example 3

Now we are fundamentally changing the conditions for outside capital - suddenly an interest rate of 12% has to be paid for outside capital (previously 2%). From the gross profit of € 100 you suddenly have to pay € 96 (€ 800 × 0.12) in FK interest. The company leaves € 4 (€ 100 - € 96), which corresponds to an equity return of only 2% (€ 4 / € 200).

Conclusions

The basic assumption for example 2 is that the return on total investment is greater than the FK interest rate. In such a constellation, it makes sense to replace your own capital with outside capital if possible. You can also deduct the interest paid from taxes , which results in an additional tax advantage from the debt ( tax shield ). Interest means expense, which reduces the profit, which has to be taxed. However, this has been neglected in the above examples.

If the total return on capital would be less than the interest rate for borrowed capital, then it would make more sense to refrain from investing and to invest the equity at FK interest (return on capital, for example through securities investments). This would generate more income and there would also be no investment risk. With this assumption, it becomes clear that the leverage effect only has a positive effect as long as the LC interest rate is below the return on total capital.

Example 3 shows that with more expensive borrowed capital or with collapsing returns, the total return can also turn negative depending on the leverage.

Cost structure

A similar leverage as the (fixed) interest on the (variable) return on equity effect exists between the fixed costs and the return on sales. Based on the financial leverage effect mentioned above, the term operating leverage is used here . The profit lever

• measures the relationship between the fixed and variable costs of a company,
• is greatest in companies with high fixed costs and low variable unit costs,
• shows how a percentage change in sales volume affects profit.

${\displaystyle {\text{Gewinnhebel}}={\text{Deckungsbeitrag}}/{\text{Gewinn}}}$

The leverage effect resulting from operational fixed costs on the total costs of a company (fixed costs plus variable costs). The fixed costs increase profitability when business is good and the workload is high, but entail considerable risks when business is bad and the workload is low, as the fixed charge remains. The fixed costs inherent in production thus have a disproportionate impact of fluctuations in sales on net profit.

Profit lever = percentage change in EBIT / percentage change in sales

due to a change in sales volume.

${\displaystyle {\mathit {OL}}(x)={\frac {\frac {(P-K_{\mathrm {var} })\cdot \Delta x}{(P-K_{\mathrm {var} })x-K_{\mathrm {fix} }}}{\frac {P\cdot \Delta x}{P\cdot x}}}}$

• x: Current sales volume ( single-product company )
• P: Unit revenue
• K _var : variable unit costs
• K _fix : fixed costs

${\displaystyle {\mathit {OL}}(x)={\frac {(P-K_{\mathrm {var} })}{(P-K_{\mathrm {var} })-{\frac {K_{\mathrm {fix} }}{x}}}}}$

Example: Company A and B

${\displaystyle k_{\mathrm {var} }(A)<k_{\mathrm {var} }(B)\quad {\text{und}}\quad K_{\mathrm {fix} }(A)>K_{\mathrm {fix} }(B)\quad \Rightarrow \quad {\text{Operating Leverage: }}{\mathit {OL}}_{A}(x)>{\mathit {OL}}_{B}(x)}$

Operating and financial leverage of companies in the DAX

implication

The relative EBIT of companies reacts more strongly than that of the company to changes in . Therefore, companies have a higher variability of returns compared to companies . In connection with the estimate of the beta factor in the fundamental technical analysis, it can be concluded that must be. ${\displaystyle A}$ ${\displaystyle B}$ ${\displaystyle \Delta x/x}$ ${\displaystyle A}$ ${\displaystyle B}$ ${\displaystyle \beta (A)>\beta (B)}$

The following shows the various levers for companies in the Dax in 2018. The financial leverage is manageable for most companies. The greater risks usually result from high operating leverage. Deutsche Telekom and E.ON appear to be particularly vulnerable. E.ON also shows very high fluctuations in sales. It can therefore be expected that the Group's net income for the year will continue to develop in a very volatile manner in the future.

Derivatives

In the case of derivatives , leverage is also used if relatively large positions in the underlying can be taken with little capital investment . This means that the percentage change in profits and losses on a derivative is greater than the corresponding change in the respective underlying.

"Simple" leverage (without any additional name) is usually used to describe the subscription ratio , i.e. how many warrants an investor can buy for the current price of the respective underlying . It results from dividing the current price of the underlying by the current price of the option. If the option relates to a multiple or a fraction of the underlying, this factor must be taken into account in the calculation.

${\displaystyle {\text{Hebel}}={\frac {\text{aktueller Aktienkurs}}{\text{aktueller Optionspreis}}}\cdot {\text{Ratio}}}$

This leverage in the sense of the subscription ratio does not indicate by how many percent the value of a call option or put option increases if its base value increases in price or becomes cheaper by one percent. It is therefore only an indicator for the investor's level of investment . The so-called effective leverage , also known as the key figure Omega , depicts exactly this leverage effect. Mathematically, the effective leverage (the omega) corresponds to the product of the delta and the (simple) leverage.

See also

• Modigliani-Miller theorem
• Leverage ratio

Web links

• Derivation of the formula for the leverage effect and for the leverage risk
• Explanation of the leverage effect in the FAZ.NET stock exchange dictionary

Individual evidence

1. ↑ Peter Seppelfricke : company analyzes . Schäffer-Poeschel, 2019, ISBN 978-3-7910-4435-4 ( schaeffer-poeschel.de [accessed January 7, 2020]).