5.6 Leverage and Risk
Commonly, we think of risk as the possibility of losing money. While there is a great deal of sense in that assertion, we look at risk differently in traditional Finance.
In Finance, “risk” is defined as volatility of earnings or return, by which here it is meant EPS and ROE. Volatility! Volatility is two-directional. If risk – leverage – is great, then EPS and ROE will vary greatly – up or down – for a given change in EBIT. This movement corresponds to the slope of the various leverage lines. (A common, but not exclusive, measure of risk is the standard deviation of the variable.)
Let’s look at some numbers; fill in the blank cells. This way, we will be able to map out our entire set of Leverage lines. We will focus on ROE as before; EPS and ROE will be congruent as on the prior graph – on the vertical axis. An ROE Sample Solution is provided on the page below.
ROE Table
With Varying Levels of EBIT and Leverage
| Degree of Financial Leverage | |||||
| 0/100 | 25/75 | 50/50 | 80/20 | ||
| EBIT | 0 | 0% | (7.2%) | ||
| 24 | 7.2% | 7.2% | 7.2% | 7.2% | |
| 40 | 12% | 16.8% | |||
| 80 | 24% | 40.8% |
Notice how to the right of the crossover point, i.e., where EBIT = $24,000, leverage increases ROE increasingly, i.e., the vertical distance between the different plans’ lines widens! If you graph this on the prior page, you will note that all ROE lines pass through the crossover point, and that higher leveraged lines are steeper, representing greater risk.
In the foregoing case of financial leverage, the steeper the EPS/ROE line the greater the risk because there will be more movement along the vertical axis for any given change in the horizontal axis. 80/20 leverage is steeper than 50/50, which is steeper than 0/100. (The standard deviation of both ROE and EPS will be greater the steeper the line.) Again, and in other words, for any change in EBIT – left or right – we will have more volatility in EPS and ROE – more up or down. That is volatility! That is, what we, finance people, mean by “risk”!!
| Slope | Financial Risk | Where slope = Δy/Δx
=Δ ROE (or Δ EPS) / Δ EBIT |
| Shallow | Low | |
| Steep | High |
In order to fill in the table, you must set ROE as the outcome variable (the dependent variable) to the right of the equal sign in the ROE formula. We know that ROE = NI / Equity = [(EBIT – i) (1 – T)] / Equity. Interest expense will change as will the amount of Equity, but not the Tax Bracket (T), with changes in the Degree of Leverage. On the next page, we provide a sample solution for one cell in this table.
ROE Table
(Solutions)
| Degree of Financial Leverage (DOL) | |||||
| 0/100 | 25/75 | 50/50 | 80/20 | ||
| EBIT | 0 | 0% | (2.4%) | (7.2%) | (28.8%) |
| 24 | 7.2% | 7.2% | 7.2% | 7.2% | |
| 40 | 12% | 13.6% | 16.8% | 31.2% | |
| 80 | 24% | 29.6% | 40.8% | 91.2% |
With increased leverage, there is more movement up or down the vertical axis for every one-dollar decrement/increment in EBIT – along the horizontal. This means