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firm's profits. Because there are 200,000 shares in this case, the EPS is — $2 as shown. Similarly, if EBIT were $400,000, EPS would be exactly zero.

The important thing to notice in Figure 17.1 is that the slope of the line in this second case is steeper. In fact, for every $400,000 increase in EBIT, EPS rises by $2, so the line is twice as steep. This tells us that EPS is twice as sensitive to changes in EBIT because of the financial leverage employed.

Another observation to make in Figure 17.1 is that the lines intersect. At that point, EPS is exactly the same for both capital structures. To find this point, note that EPS is equal to EBIT/400,000 in the no-debt case. In the with-debt case, EPS is (EBIT — $400,000)/200,000. If we set these equal to each other, EBIT is:

EBIT/400,000 = (EBIT — $400,000)/200,000 EBIT = 2 X (EBIT — $400,000) = $800,000

When EBIT is $800,000, EPS is $2 under either capital structure. This is labeled as the break-even point in Figure 17.1; we could also call it the indifference point. If EBIT is above this level, leverage is beneficial; if it is below this point, it is not.

There is another, more intuitive, way of seeing why the break-even point is $800,000. Notice that, if the firm has no debt and its EBIT is $800,000, its net income is also $800,000. In this case, the ROE is 10 percent. This is precisely the same as the interest rate on the debt, so the firm earns a return that is just sufficient to pay the interest.

Ross et al.: Fundamentals of Corporate Finance, Sixth Edition, Alternate Edition

VI. Cost of Capital and Long-Term Financial Policy

17. Financial Leverage and Capital Structure Policy

© The McGraw-Hill Companies, 2002

CHAPTER 17 Financial Leverage and Capital Structure Policy

### Break-Even EBIT

The MPD Corporation has decided in favor of a capital restructuring. Currently, MPD uses no debt financing. Following the restructuring, however, debt will be $1 million. The interest rate on the debt will be 9 percent. MPD currently has 200,000 shares outstanding, and the price per share is $20. If the restructuring is expected to increase EPS, what is the minimum level for EBIT that MPD's management must be expecting? Ignore taxes in answering.

To answer, we calculate the break-even EBIT. At any EBIT above this, the increased financial leverage will increase EPS, so this will tell us the minimum level for EBIT. Under the old capital structure, EPS is simply EBIT/200,000. Under the new capital structure, the interest expense will be $1 million x .09 = $90,000. Furthermore, with the $1 million proceeds, MPD will repurchase $1 million/20 = 50,000 shares of stock, leaving 150,000 outstanding. EPS will thus be (EBIT - $90,000)/150,000.

Now that we know how to calculate EPS under both scenarios, we set them equal to each other and solve for the break-even EBIT:

EBIT/200,000 EBIT

(EBIT - $90,000)/150,000 4/3 X (EBIT - $90,000) $360,000

Verify that, in either case, EPS is $1.80 when EBIT is $360,000. Management at MPD is apparently of the opinion that EPS will exceed $1.80.

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