San José State University
Department of Economics
& Tornado Alley
This page deals with the process of financial intermediation in which one organization, usually relatively large and secure, borrows funds to lend it to relatively smaller, less safe borrowers. The smaller borrowers pay a higher interest rate than the larger organization pays for the funds. This seems innately profitable but the crucial question is whether the smaller borrowers pay a sufficiently higher interest rate to compensate for the higher risk and the costs of servicing the loans.
The use of borrowed funds along with owned funds for investment is called leverage. The ratio of borrowed funds to own funds (or debt to equity) is called the leverage ratio.
Business organizations in all fields may make use of leverage. American corporations in the past overall had a leverage ratio of about 1.0; i.e., 1 to 1. This means that overall they used equal amounts of stockholder equity and funds borrowed by the sale of bonds. In more recent decades the leverage ratio of American corporations has been rising above 1.0. Corporations outside of the U.S., such as in Japan, have leverage ratios significantly higher than those in the U.S. Corporations in different industries within the U.S. may have leverage ratios significantly different from the U.S. average. Commercial banks, whose leverage ratio is the ratio of their liabilities to their net worth, have much higher leverage ratios than corporations in general. In the 1980's insured commercial banks had an average leverage ratio of slightly over 15 to 1. Credit unions typically have leverage ratios of zero.
Business enterprises leverage their capital because it offers the potential for increasing the average rate of return on their equity funds. Leverage will do this if the rate of return on the invested funds is significantly higher than the interest rate paid on the borrowed funds. In this case the difference accrues to the equity capital and can give a quite elevated rate of return on the equity funds.
An example illustrates the power of leverage. Suppose an organization has $1 million of equity funds and borrows $4 million at an interest rate of 8 percent. Its leverage ratio L is thus 4. If the $5 million in total funds is loaned or invested and brings a rate of return of 10 percent then it has earnings of $500,000. From this $500,000 it has to pay $320 thousand in interest, leaving $180 thousand as return on equity. On the $1 million of equity this $180 thousand is an 18 percent rate of return, a commendable rate of return. This is the positive side of leverage. But if due to unforeseen circumstances the rate of return on the invested funds falls to 6 percent then the organization has only $300 thousand in earnings and an interest bill of $320 thousand. This means the equity holders suffer a $20 thousand loss, a -2 percent rate of return.
Any variability in the rate of return on invested funds relative to the interest rate on the debt could get amplified by leverage. In the example a swing in the rate of return on invested funds from 2 percent above the interest rate to 2 percent below the interest rate caused a swing in the rate of return on equity from 18 percent (heaven) to -2 percent (hell). The 4 percent variation in the rate of return on invested funds produced a 20 percent swing in the rate of return on equity; a five to one ratio.
Now consider a much less extreme case of leverage. Suppose the organization borrows $500,000 to go with its $1 million of equity. Its leverage ratio is 0.5. If the interest rate on the debt is 8 percent and the rate of return on the overall assets is 10 percent then the organization has earnings of $150,000 and an interest bill of $40,000. This leaves $110,000 as earnings for the equity holders. On the $1 million this $110,000 constitutes an 11 percent rate of return. The leverage raised the rate of return for equity by 1 percent, from 10 percent to 11 percent. An adverse development that dropped the rate of return on assets from 10 percent to 6 percent would lower the earnings to $90,000. After the payment of $40,000 interest there is $50,000 left for the equity holders, a 5 percent rate of return. Thus the rate of return on equity fell from 11 percent to one percent below the 6 percent return; i.e., 5 percent. The rate of return on equity fell 6 percent as a result of the 4 percent drop in the rate of return on assets. The ratio of the swing in the rate of return on equity to the swing in the rate of return on assets is 1.5.
The general formula that applies is:
where again L stands for the leverage ratio and * for multiplication. In more compact symbols the above formula is:
(Note that this formula does not take into account the fixed overhead costs of a financial organization and the servicing costs on the individual loans or investments. These are of great practical significance to the financial organization but they obscure the general problem of leverage.)
The formula for the rate of return on equity and the above example illustrate the effect of leverage. For leverage ratios greater than 1.0 it amplifies the difference between the rate of return on assets and the interest rate on debt. But that difference can be negative as well as positive.
The graph below illustrates the effect of leverage. The graph shows hypothetical cycles in the rates of return on invested assets. At times the rate on assets falls below the interest rate on borrowed funds. For the case shown the leverage ratio is 1.5.
The average rate of return on assets is above the interest rate on borrowings and the average rate of return on equity is higher than the average rate of return on assets. The leverage brings this enhancement.
For the case in which the leverage ratio is a much smaller 0.5 the fluctuations in the rate of return on equity are much less. For leverage ratios less than 1.0 only a fraction of the difference is added to the rate of return on assets.
The return on assets does not necessarily ever fall below the interest rate on debt. Below is such a case:
In discussing anything concerning risk there is a problem that the word risk can mean many different things. In the financial economics risk commonly means the variability of the rate of return, whereas in bonds and loans where the earning are prescribed the relevant risk is default.
Risk is a particularly important issue for organizations which combine their own funds with funds that are borrowed. The contractual payments for the borrowed funds must be met and consequently any variability of the return on loaned funds can get amplified in its effect on the rate of return on the organization's own funds.
The general relationship that exists between the risk on the loaned funds (the invested funds) and the risk to the equity holders of the organization is:
where L is the leverage ratio (Borrowed Funds/Equity Funds).
In the first example above a swing in the rate of return on assets of 4 led to a 20 percent swing in the rate of return on equity. The leverage ratio for that case was 4. The swing in the rate of return on equity was (4+1)x4. In the second case the leverage ratio was 0.5 and the swing in the rate of return was 6 percent for a 4 percent swing in the rate of return on assets. The 6 percent is (0.5 + 1)x4, consistent with the formula.
The relationship between rate of return on equity and risk in the case of leverage is just a special case of the general relationship betweeen risk and return. The market establishes a relationship between the risk of an activity and its expected rate of return. This is illustrated by the following graph:
This is the tradeoff that businesses always face.
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