# LO 54.5: Describe the relationship between leverage and a firm’s return profile,

LO 54.5: Describe the relationship between leverage and a firms return profile, calculate the leverage ratio, and explain the leverage effect.
A firms leverage ratio is equal to its assets divided by equity (total assets / equity). That is:
L = A = (E + D)
E E
D E
For an all-equity financed firm, the ratio is equal to 1.0, its lowest possible value. As debt increases, the leverage ratio (i.e., multiplier) increases. For example, a firm with \$100 of assets financed with \$50 debt and \$50 equity has a leverage ratio equal to 2.0 (\$100/\$50 = 2).
Return on equity (ROE) is higher as leverage increases, as long as the firms return on assets (ROA) exceeds the cost of borrowing funds. This is called the leverage effect. The leverage effect can be expressed as:
rE = LrA – ( L ~ 1 )rD
where: rA = return on assets r = return on equity rD = cost of debt L = leverage ratio
It may help to think of this formula in words as follows:
ROE = (leverage ratio x ROA) [(leverage ratio 1) x cost of debt] For a firm with a zero cost of debt, return on equity is magnified by the leverage factor; however, debt is not free. Thus, return on equity (ROE) increases with leverage, but the cost of borrowing, because there is more debt, also increases. The L 1 factor multiplies the cost of debt by the proportion of the balance sheet financed with debt. For example, with a leverage ratio of 2, 50% of the balance sheet is financed with debt and 50% with equity. So for every \$2 of assets, \$1 comes from shareholders and \$1 comes from borrowed funds. We multiply the cost of debt by 1 in this case. If the leverage ratio is 4, 25% is financed with equity and 75% is financed with debt. Thus, for every \$4 of assets, \$1 is equity and \$3 is borrowed funds. In the formula, we multiply the cost of debt by 3. The higher the leverage factor, the bigger the multiplier but also the higher the debt costs. Leverage amplifies gains but also magnifies losses. That is why leverage is often referred to as a double-edged sword.
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Topic 54 Cross Reference to GARP Assigned Reading – Malz, Chapter 12
The effect of increasing leverage is expressed as:
9 < r / <9L = rA – rD
where: < 9 r = change in retained earnings &L = change in the leverage ratio
This formula implies that, given a change in the leverage ratio, ROE changes by the difference between ROA and the cost of debt.
The equity in the denominator of the leverage ratio depends on the entity. If it is a bank, it may be the book value of the firm. It might also be calculated using the market value of the firm. The net asset value (NAV) of a fund is the appropriate denominator for a hedge fund. The NAV reflects the current value of the investors capital in the fund.
Example: Computing firm ROE (total assets = \$2)
Martin, Inc., a U.S. manufacturing company, has an ROA equal to 5%, total assets equal to \$2, and equity financing equal to \$1. The firms cost of debt is 2%. Calculate the firms ROE.
rE = L r A – ( L – 1)rD
rP = [(2 / 1) x 5%] – [(2 – 1) x 2%] = 8%
Example: Computing firm ROE (total asset = \$4)
Martin, Inc., a U.S. manufacturing company, has an ROA equal to 5%, total assets equal to \$4, and equity financing equal to \$1. The firms cost of debt is 2%. Calculate the firms ROE.
rE = LrA ~ ( L – 1)rD
rE = [(4 /1) X 5%] – [(4 –
1) X 2%\ = 14%
Given a cost of debt of 2%, increasing the leverage factor from 2 to 4 increased the firms ROE from 8% to 14%.
2018 Kaplan, Inc.
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Topic 54 Cross Reference to GARP Assigned Reading – Malz, Chapter 12
Leverage is also influenced by the firms hurdle rate (i.e., required ROE). For example, assume a firms hurdle rate (i.e., ROE) is 10%, ROA equals 6%, and its cost of debt equals 2%. The firm will choose a leverage ratio of 2.0. That is:
ROE = (2 x 6%) – (1 x 2%) = 10%
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