# 5.5 Leverage and the Crossover Point

We observed above that the crossover point – on the horizontal axis – corresponds with certain values in terms of EBIT, ROE, and EPS – on the vertical axis. This point was noted for the comparison of no leverage, 50/50, and 25/75 (see footnote above) leverage cases. In fact, using these cases, we observed that any degree of leverage yielded the same crossover point! In other words, there is a certain proportionality, which pertains to this, and any, example.

To illustrate this point further, let’s imagine that the firm considers using 80% leverage (“80/20”) for this project. You will find that the vertical intercept is yet lower, that the line passes through the former crossover point, and that, overall, the line is steeper than the 50/50 leverage line. This is as it should be, because 80/20 leverage is riskier! When EBIT is “great,” i.e., to the right of the crossover point, EPS and ROE are more and more favorable the more leverage there is, but beware, this is also true in the reverse!

Let’s work-up the numbers using \$24,000 as our EBIT, as below. Next, let’s insert the new, 80% line in the diagram above. (Do this on your own, as before, using various EBIT values of, say, \$0, \$40, and \$80, and then calculating EPS and ROE. Once you have done this, insert the values into the graph on the prior pages.)

 Degree of Financial Leverage (\$000) D/E= 0/100 25/75 50/50 80/20 EBIT 24 24 24 \$24 Int. Exp. 00 (6) (12) (19.2) Taxes (9.6) (7.2) (4.8) (1.92) Net Inc. 14.4 10.8 7.2 2.88 ROE 14.4/200=.072 .072 7.2/100=.072 .072 EPS 14.4/10=\$1.44 \$1.44 7.2/5=\$1.44 \$1.44

Note: ROE and EPS are the same regardless of the degree of leverage!

Worksheet (for the above table): Assume that EBIT = \$24,000

 80/20 Leverage 25/75 Leverage Interest Expense (0.12)(\$200,000)(0.80)= \$19,200 (0.12)(\$200,000)(0.25) = \$6,000 Taxes (\$24,000 -19,200)(0.40)= \$1,920 (\$24,000 – 6,000)(0.40) = \$7,200 ROE (\$2,880) ÷ (\$200,000)(0.20)= 0.072 (\$10,800) ÷ (\$200,000)(0.75) = 0.072 EPS (\$2,880) ÷ (10,000s.)(0.20) = \$1.44 (\$10,800) ÷ (10,000s.)(0.75) = \$1.44

Notes:

• We have made a critical, “simplifying,” ceteris paribus assumption, namely that the firm’s interest rate does not go up with increased leverage. This may – or may not – be true!
•  EPS = (NI – Preferred Dividends) ÷ “NOSO”