Mortgage Loans and Real Estate Financing
Using Borrowed Funds To Finance Property Investments
This is an excerpt from the book Real Estate Investing for Double-Digit Returns by Petros S. Sivitanides, Ph.D. 
Using mortgages or borrowed funds (debt) to finance the purchase of a property or a development project can significantly increase the rate of return of an investment under certain conditions. As you will see below in the numerical examples, the investor's return skyrockets with financial leverage when the property appreciates after its purchase. The same would be true if the property is bought below market value and sold at market value. Using loans to partially finance a real estate investment is referred to as leverage. By default, a real estate investment that does not involve the use of borrowed funds in general, is referred to as unleveraged. Wurtzebach and Miles (1994) indicate that the use of debt will increase the return of a real estate investment if the mortgage constant, which reflects the cost of financing in percentage terms, is smaller than the unleveraged return offered by the investment. Otherwise, leverage will have a negative effect. The mortgage constant (MC) applies to fixed-rate loans (as opposed to adjustable-rate loans) and represents the percentage of the original amount borrowed by the investor that needs to be paid periodically in order to completely repay the principal (the original loan amount) and interest over the term of the loan. The formula for calculating the constant for a fixed-rate loan is: The term interest rate refers to the loan rate, and n refers to the term of the loan in number of periods. For example, if one wants to estimate the monthly mortgage constant, n would represent the term of the loan in months. Thus depending on the type of period, the MC can reflect the monthly, quarterly, or annual percentage of the loan that needs to be paid during each period. Notice that the MC has nothing to do with the amount of the loan, just the rate. For example, for a loan at an interest rate of 6% and term of 20 years, the annual MC would be: The second element needed in order to evaluate whether leverage will enhance returns is the unleveraged income return expected from the investment. This is calculated as the ratio of Net Operating Income (NOI) over the purchase price, or total investment cost in the case of development: Consider, for example, that you purchase an apartment with an annual NOI of $30,000 for $300,000. Enticed by the low interest rates, you want to examine whether a loan at an interest rate of 6% and term of 20 years, which as calculated above, has an annual mortgage constant of 8.72%, will have a positive or negative effect on the return of your investment. In order to answer your question, you first need to calculate the unleveraged return of the investment as: Thus, the unleveraged income return of the investment is 10%, which is higher than the mortgage constant, in this case 8.72%. This suggests that under the particular assumptions, with respect to the loan rate and the unleveraged return of the investment, borrowing will indeed help the investor achieve a higher return, assuming that NOI will not decrease during the holding period. Since we are focusing on properties with prospects for strong rent increases, the chances of decreasing NOI are, in theory, small.
The comparison of the unleveraged return with the mortgage constant can help the investor evaluate whether leverage will increase the rate of return of the investment, but not by how much. In order to evaluate how much, we need to calculate the investment’s leveraged return, which takes into account the borrowed funds and the payment made periodically to service the debt (debt service). The one-period, leveraged income return of an investment can be calculated as follows:
Notice that the formula above estimates the one-period leveraged not the multi-period leveraged return that takes into account the value or sales price of the property at the end of the holding period. In order to demonstrate the effect of positive leverage on the return of a real estate investment, let’s continue our example with the apartment that was purchased for $300,000, assuming that the investor financed 30% of the purchase price with a 20-year loan at a 6% fixed interest rate. The calculations are shown below: These calculations show that by financing 30% of the purchase price, the return on equity invested, which is the amount of the investor’s own money used for carrying out the purchase, increased from 10% (the return of the investment without using any borrowed money) to 10.5%. This increase in this case is quite small. One major reason for this is that the investor financed only a small percentage of the purchase price with borrowed funds.
In general, when positive leverage is possible, that is, when the mortgage constant of the loan is smaller than the investment’s unleveraged return, the greater the amount of the loan, the greater the increase in the investor’s leveraged return (on a before-tax basis). To demonstrate this point, let us assume the investor finances 80% of the purchase price with borrowed funds. Because the loan amount will be a higher percentage of the value of the property, the interest rate will be higher, since the lender assumes a greater risk.1 So let’s assume the investor secures a 20-year fixed-rate loan at 6.5% to finance 80% of the purchase price. The annual mortgage constant for this loan is 9.08%, which should have a positive effect on the investor’s return, since the unleveraged return is 10%. Let’s see how much better the leveraged return is compared to the unleveraged return under these new assumptions: This example demonstrates that, taking into account reasonable value gains, the use of leverage dramatically increases the investor’s return and profits (in percentage terms). As these calculations show, the combination of positive leverage, the high percentage of borrowing relative to the purchase price, and a decent increase in value significantly improve the investor’s return from 15% to 38.7%.
Notice that Formulas 3, 4, and 5 refer to the calculation of the one-period return. The calculation of the multi-period rate of return of an investment, which is referred to as internal rate of return (IRR), involves the use of a more complex mathematical formula, based on the discounted cash-flow approach. The model and the mathematics involved in its application are out of the scope of this book, but it is discussed briefly in a footnote.2 It suffices to say that the combination of positive leverage and increases in value can contribute to equally impressive increases of the investor’s return within a multi-period context as well. It should be emphasized, however, that, usually, the sooner the property-value gains are obtained, the greater the IRR. From a strategic point of view, this means that a property needs to be resold as soon as the investor has no reason to believe that significant value gains will be realized in the future. It should be noted that the technique described in this article for evaluating whether borrowing will enhance property investment returns, is simplistic and has deficiencies that may lead to erroenous conclusions, especially in the case of properties with fluctuating cash flows over their holding period. The deficiencies of this simplistic technique is that it does not account for changes in cash flow through time and the impact of property liquidation and potential capital gains or losses on invesment return. The most appropriate way to evaluate the effect of leverage on investment return is to run a full discounted cash flow (DCF) model and estimate expected return under alternative financial structure scenarios.
The bottom line conclusion is that finding properties with strong appreciation potential or properties that can be bought below market value and financing their purchase with borrowed funds can be highly profitable. Borrowing though, especially at high loan-to-value ratios is not riskless, and there should be a careful examination of these risks in any financing decision. Investors often use second mortgages in addition to first mortgages, in order to reduce their equity contribution and increase the effects of positive leverage. However, caution is needed when using such financing techniques as second mortgages are provided by lenders at considerably higher interest rates. The best way to obtain 100% financing of a property acquisition is perhaps the use of a blanket mortgage. 1 The percentage of the purchase price or value of the property that is financed with borrowed funds is referred to as loan-to-value ratio (LTV).
2 The discounted cash-flow approach estimates the periodic(annual, quarterly, etc.) total rate of return of a multi-period investment as the discount rate that equalizes the present value of future cash flows with the investor’s total cost or purchase price. This rate of return is referred to as internal rate of return (IRR). Notice that the periodicity reflected by the estimated internal rate of return will depend on the periodicity of the cash flows used to calculate it. For example, if annual cash flows are used, the estimated IRR will reflect the annual rate of return of the investment; if quarterly cash flows are used, the estimated IRR will reflect the quarterly rate of return of the investment. Greer and Farrell (1993) point out that there are two problems with respect to the IRR calculation. The first involves the assumption that all cash flows received during the period the investment is held are reinvested at the same rate as the IRR. For example, if the estimated IRR for a real estate investment is 20%, this return estimate incorporates the assumption that all cash flows received during the holding period are re-invested with a return of 20% until the liquidation of the property. This assumption may be unrealistic, since it is difficult to find real-world investment opportunities with a 20% return. If the re-investment rate of cash flows received during the holding period is lower than the estimated IRR, the true rate of return will be lower. The second issue with respect to the IRR calculation is that it may give multiple solutions if the cash-flow stream includes not only positive but also negative cash flows.
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