# 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 that you may potentially earn more EPS and ROE as EBIT increases, but also risk a greater negative impact should EBIT come in lower. Yes, it is true that as management projects EBIT to exceed the crossover point, increasing leverage may be warranted. Still, the degree of leverage actually chosen is a decision function of management based on its own (and shareholders’) risk profile(s), as well industry characteristics and relative capital costs.

Plot your solutions on a new graph: EBIT on the horizontal axis and ROE on the vertical. You now have four lines, whereas earlier we had only two DOL cases and two lines (for 0/100 and 50/50 leverage), and we did not then know the precise value for EBIT at the Crossover Point. Again, the EPS and ROE points will be congruent if you plot all the lines. The 80/20 DOL line is the steepest because it is the riskiest. With more leverage, you potentially get more EPS and ROE – if EBIT works out as predicted. Do you have the stomach to bear the negative effects if projections fall far short?

With a steeper, more risky line, you get more movement along the vertical axis for every change along the horizontal than with a less steep line. If we get a change along the horizontal, we will get more of an increase in the vertical than with a shallower line. However, take note that it works in both directions. A steeper line will also get more downward movement. This makes the steeper line riskier. The 80/20 mix is riskiest and the numbers also bear that out!

Were we instead solving for an “EPS Table” – rather than the “ROE Table” as above, we would use a different formula, but not much different. Here it is: EPS = NI / NOSO (where “NOSO” is the number of shares outstanding). Once again NI = [(EBIT – i) (1 – T)].

Question: What if either interest rates and/or taxes increased or decreased?

1. If taxes went up, the ROE would go down.
2. If rates went up, Net Income would go down.