An analyst interpreting the past behavior of a firm's ROE or forecasting its future value must pay careful attention to the firm's debt-equity mix and to the interest rate on its debt. An example will show why. Suppose Nodett is a firm that is all-equity financed and has total assets of $100 million. Assume it pays corporate taxes at the rate of 40% of taxable earnings.

Table 19.4 shows the behavior of sales, earnings before interest and taxes, and net profits under three scenarios representing phases of the business cycle. It also shows the behavior of two of the most commonly used profitability measures: operating return on assets (ROA), which equals EBIT/assets, and ROE, which equals net profits/equity.

Table 19.4 Nodett's

Profitability over the Business Cycle

Sales |
EBIT |
ROA |
Net Profit |
ROE | |

Scenario |
($ Millions) |
($ Millions) |
(% per Year) |
($ Millions) |
(% per Year) |

Bad year |
80 |
5 |
5 |
3 |
3 |

Normal year |
100 |
10 |
10 |
6 |
6 |

Good year |
120 |
15 |
15 |
9 |
9 |

Nodett |
Somdett | ||||

EBIT |
Net Profits |
ROE |
Net Profit* |
ROEt | |

Scenario |
($ Millions) |
($ Millions) |
(%) |
($ Millions) |
(%) |

Bad year |
5 |
3 |
3 |
1.08 |
1.8 |

Normal year |
10 |
6 |
6 |
4.08 |
6.8 |

Good year |
15 |
9 |
9 |
7.08 |
11.8 |

*Somdett's after-tax profits are given by .6(EBIT - $3.2 million). tSomdett's equity is only $60 million.

*Somdett's after-tax profits are given by .6(EBIT - $3.2 million). tSomdett's equity is only $60 million.

Somdett is an otherwise identical firm to Nodett, but $40 million of its $100 million of assets are financed with debt bearing an interest rate of 8%. It pays annual interest expenses of $3.2 million. Table 19.5 shows how Somdett's ROE differs from Nodett's.

Note that annual sales, EBIT, and therefore ROA for both firms are the same in each of the three scenarios; that is, business risk for the two companies is identical. It is their financial risk that differs. Although Nodett and Somdett have the same ROA in each scenario, Somdett's ROE exceeds that of Nodett in normal and good years and is lower in bad years.

We can summarize the exact relationship among ROE, ROA, and leverage in the following equation:1

Equity

The relationship has the following implications. If there is no debt or if the firm's ROA equals the interest rate on its debt, its ROE will simply equal (1 minus the tax rate) times ROA. If its ROA exceeds the interest rate, then its ROE will exceed (1 minus the tax rate) times ROA by an amount that will be greater the higher the debt-to-equity ratio.

1 The derivation of equation 19.1 is as follows: Net profit

Equity

(ROA X Assets) - (Interest rate X Debt) Equity

= (1 — Tax rate) I ROA X v 4 ' .-— Interest Rate X -—— I

Equity Equity

Debt

Equity

CHAPTER 19 Financial Statement Analysis

This result makes intuitive sense: If ROA exceeds the borrowing rate, the firm earns more on its money than it pays out to creditors. The surplus earnings are available to the firm's owners, the equityholders, which increases ROE. If, on the other hand, ROA is less than the interest rate, then ROE will decline by an amount that depends on the debt-to-equity ratio.

To illustrate the application of equation 19.1, we can use the numerical example in Table 19.5. In a normal year, Nodett has an ROE of 6%, which is .6 (i.e., 1 minus the tax rate) times its ROA of 10%. However, Somdett, which borrows at an interest rate of 8% and maintains a debt-to-equity ratio of %, has an ROE of 6.8%. The calculation using equation 19.1 is

The important point to remember is that increased debt will make a positive contribution to a firm's ROE only if the firm's ROA exceeds the interest rate on the debt.

Note also that financial leverage increases the risk of the equityholder returns. Table 19.5 shows that ROE on Somdett is worse than that of Nodett in bad years. Conversely, in good years, Somdett outperforms Nodett because the excess of ROA over ROE provides additional funds for equityholders. The presence of debt makes Somdett more sensitive to the business cycle than Nodett. Even though the two companies have equal business risk (reflected in their identical EBITs in all three scenarios), Somdett carries greater financial risk than Nodett.

Even if financial leverage increases the expected ROE of Somdett relative to Nodett (as it seems to in Table 19.5), this does not imply that the market value of Somdett's equity will be higher. Financial leverage increases the risk of the firm's equity as surely as it raises the expected ROE.

CONCEPT CHECK ^ QUESTION 1

Mordett is a company with the same assets as Nodett and Somdett but a debt-to-equity ratio of 1.0 and an interest rate of 9%. What would its net profit and ROE be in a bad year, a normal year, and a good year?

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