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The assumed mortgage: a residential cash equivalency case study.

This may be an inappropriate time to think about the value of assumable financing. After all, mortgage interest rates are low,(1) and most of the outstanding loans on existing properties are at or above current interest rates. In today's financing environment, there is little to be gained by a loan assumption. However, there was a time in the not-too-distant past when mortgage interest rates were very high and a low interest rate assumable mortgage had a great deal of value.(2) When interest rates again cycle upward, today's relatively low mortgage interest rates could add value to the real estate in situations where a loan is assumable. Therefore, this may actually be an opportune time to prepare to deal with the value of assumable financing and to brush up on the topic of cash equivalency.

In order to address valuation problems encountered during the high interest rate cycle of the early 1980s, the American Institute of Real Estate Appraisers (which in 1991 merged with the Society of Real Estate Appraisers to form the Appraisal Institute) adopted Guide Note 2, "Cash Equivalency in Value Estimates in Accordance with Standards Rule 1-2 (b)," to the Code of Professional Ethics and Standards of Professional Appraisal Practice on November 2, 1986. This Guide Note emphasizes that:

[T]he stun of the value of owner equity and the face amount of the balance(s) of the mortgage(s) may or may not be equal to the free and clear value of the property... If sufficient data to permit a direct market comparison is not available, the cash equivalency of existing or proposed financing can be estimated by discounting the contractual terms at current market rates... However, such mathematical methods should be weighed against other market indications.(3)

The same language exists in the Guide Note today, as last amended on January 28, 1994. Guide Note 2 says it is unacceptable to fail to analyze and make adjustments for favorable financing when comparing a favorably financed sale to the property being appraised. In addition, the Uniform Standards of Professional Appraisal Practice (USPAP) defines market value in terms of cash.

At least two practical questions arise from the Guide Note's directives and the USPAP market value definition. First, when sufficient market data does not exist to allow extraction of an adjustment for favorable assumable financing by direct market comparison, how does an appraiser calculate a satisfactory mathematical adjustment? Second, how does an appraiser calculate cash equivalency when a relevant historical sale of the subject property involved a loan assumption? Except for a book chapter (by William Brueggeman and Jeffrey Fisher) that recognizes the need to consider the effect of a second mortgage to avoid overestimating the value of an assumed loan, the appraisal literature provides less than fully satisfactory answers.(4)

The Literature

The Appraisal of Real Estate, 11th edition, provides two examples of mathematical calculations of cash equivalent prices. Both examples relate to owner financing of the entire mortgage amount and address a seller mortgage with no balloon payment and a seller mortgage with a balloon payment.(5) The text states, "Transactions involving mortgage assumptions can be adjusted to cash equivalency with the same method applied to seller-financed transactions."(6) In addition, the text refers to two published articles on the topic.

David Lennhoff's article discusses problems in the definition of the term "cash equivalency" and makes the point that cash equivalency does not necessarily mean "all cash."(7) Instead, the definition allows for "typical" financing. This point of view is presented in The Appraisal of Real Estate, which notes, "When a comparable sale price is used...the sale generally should reflect typical market terms, or be adjusted to reflect a cash equivalent price."(8)

An article by Halbert Smith and John Corgel offers a mathematical model that hinges on the assumption that nonmarket financing is subject to a short, five-year discount period.(9) They assert that any benefit of nonmarket financing more than five years from the date of sale is given very little, if any, weight by the parties to the transaction. Their result is consistent with then-contemporary empirical studies that show that buyers generally pay less than the "full value" of assumption financing.(10) There is, however, a theoretical problem with the assumption that below-market financing benefits more than five years beyond the date of sale have little or no value as an explanation for buyers paying less than the full value of the loan assumption benefit. The theoretical problem is summed up by Terrence Clauretie and G. Stacy Sirmans, who point out that "a buyer could capture the value of the remaining payment savings upon resale and thus should be willing to pay for the entire value at purchase."(11)

At least part of the disconnect between mathematical estimates of the value of nonmarket financing and prices observed in the market may be due to the past use of inappropriate mathematical estimates of nonmarket financing value. Nearly all the mathematical models of the value of assuming a favorable mortgage promulgated to date fail to deal effectively with the need, especially in the residential market, for a second junior mortgage to bridge the gap between the assumed loan and the buyer's equity. (The exception is Brueggeman and Fisher.) In an article by David Dale-Johnson et al., the authors note that properties sold with an assumed first mortgage also often include a second junior loan.(12) They correctly assert that including a junior mortgage reduces the value of an assumable loan because the interest rate on the junior loan is usually higher than the market interest rate on a conventional senior loan. Since empirical statistical models, by their nature, deal with central tendency, any significant incidence of junior mortgage financing being coupled with a loan assumption would result in a reduced empirical estimate of assumed financing value.

The Dale-Johnson et al. perspective is developed here to show how introducing a junior loan into the model can substantially reduce the value of nonmarket financing, which significantly narrows the gap between mathematical estimates of assumed financing market value and empirically observed assumed financing values in the market.(13)


Consider the sale of a fictitious single-family residence on 15 Maple Street, Anywhere, USA. The sale price was $115,000 paid by assumption of an existing 7% loan, a junior mortgage bridging the gap between the balance owed on the assumed loan and an 80% loan-to-value ratio, and cash equal to 20% of the purchase price. The assumed loan was 5 1/2 years old at the time of closing, and all past payments of $465.71 had been made on time. The original loan balance was $70,000, and the loan term was 30 years with monthly payments. based on this information, the assumption amount is calculated to be $65,396.89.

Typical conventional senior mortgage terms at the time of the current sale are a 10% interest rate, 80% loan-to-value ratio, and a 30-year term with monthly payments. The amount of the junior mortgage is $26,603.11 ($115,000 x 0.80 - $65,396.89). Because it is a second mortgage, it carries a 13% interest rate and a 20-year term with monthly payments.

Cash Equivalency, Ignoring the Junior Mortgage

Absent the junior mortgage, the cash equivalent price would be $115,000 minus the difference between the amount owed on the assumed loan on the date of assumption and the present value of the assumed mortgage payments discounted at the market interest rate for conventional loans (10% in this example). Because there are 294 payments remaining (24 1/2 years), the present value of the assumed loan is computed as the present value of an annuity in the standard way, as follows:(14)

[Mathematical Expression Omitted] (1)

The discount for nonmarket financing is $65,396.89 - $51,013.46 = $14,383.43, and the cash equivalent price is $115,000 - $14,383.43 = $100,616.57.

This is the traditional way of handling a cash equivalency problem, consistent with the example problem found in The Appraisal of Real Estate and demonstrated in an article by G. Stacy Sirmans, C. F. Sirmans, and Stanley Smith.(15) The $14,383 discount represents the "full value" of assumption financing to which the literature typically refers. The dilemma is that the market has not recognized the full $14,383.43 adjustment for cash equivalency derived from equation 1, in part because of a failure to include the impact the typical need of a junior loan has on the cash equivalent calculation.

Cash Equivalence, Considering the Junior Mortgage

Although the solution becomes more complex when the junior mortgage is considered, the result is much more in line with market evidence. To calculate the cash equivalency adjustment under this scenario, the payments on the $26,603.11 junior loan and on a typical conventional loan must be computed first. Given the stated terms, the payment on the junior loan at a 13% interest rate is $311.68 and the payment on a $92,000, conventional, 80% loan-to-value ratio loan at a 10% interest rate is $807.37. Now the payment savings for the assumption financing versus conventional financing can be calculated as follows:

Payment Savings

Months 1-240: $807.37 - 465.71 - 311.68 = $29.98

Months 241-294: $807.37 - 465.71 - 0 = $341.66

Months 295-360: $807.37 - 0 - 0 = $807.37

Now the appraiser can use the standard present value of an annuity and the discounting formulas to compute the value of the payment savings at the time of sale and a cash equivalent price, including the junior mortgage's effect. For the sake of simplicity, the present value of payment savings calculations are presented in parts, as follows:

Months 1-240

[Mathematical Expression Omitted] (2)

Months 241-294

[Mathematical Expression Omitted] (3)

Months 295-360

[Mathematical Expression Omitted] (4)

The sum of the present values of payment savings from equations 2, 3, and 4 ($8,689.09) is the estimated value of the loan assumption, including the effect of the junior mortgage required to make the purchase possible. The value estimate is 60% of the $14,383.43 amount calculated without considering the effect of a junior mortgage, and is much more in line with the values of assumable financing uncovered in empirical studies.

Ignoring the effect of a needed junior loan, the cash equivalent price computes to $100,617, which is $115,000 minus the $14,383 adjustment derived from equation 1. When the junior financing effect is included, the cash equivalent price computes to $106,311, which is the $115,000 sale price minus the $8,689 adjustment for the value of the assumed loan derived from equations 2, 3, and 4. In addition, the $106,311 amount can be partitioned into a $23,000 cash down payment, the $51,013 present value of the assumed loan, and the $32,298 present value of the monthly $311.68 junior loan payment obligation discounted at the 10% interest rate otherwise payable on an 80% loan-to-value first mortgage absent the loan assumption.


While these calculations can be done easily on a financial calculator (see the appendix), creating a spreadsheet template will speed up the calculation and preserve the model for future use. A spreadsheet model also provides a convenient way to test the sensitivity of the assumption financing value to changes in the financial market and real estate market conditions (such as the interest rate spread between conventional first mortgages and junior mortgages, loan-to-value ratio, and the price paid for the property). Table 1 represents the spreadsheet template developed, including the results for the 15 Maple Street example.(16) The shaded areas are the outputs from the model, and the unshaded areas are the required input cells.

The spreadsheet model was used to test the sensitivity of assumption financing, including a junior mortgage, to variation in the interest rate spread between conventional first mortgages and junior mortgages, loan-to-value ratio, and the price paid for the property. The results of the sensitivity test are summarized in table 2.

The bold values in table 2 show the $8,689 value of assumed financing derived in the sample case ($115,000 price, 0.80 loan-to-value ratio, and 3% interest rate spread). The remaining values in each "Assumed Financing Value" column show the sensitivity of the value of assumed financing to changes in a given variable with the other two variables held constant. Clearly, the terms of the assumed financing and the ratio of the assumed loan to the purchase price have a dramatic impact on the value of the assumed loan. Also, it should be noted that the value of the assumed loan reaches the $14,383 amount calculated ignoring the junior mortgage only when the junior mortgage effect is reduced to zero (A/P ratio = 80% of price, loan-to-value ratio = 0.57, and interest rate spread = 0).
TABLE 1 Value of Assumable Financing

Value of Assumable Financing $8,689.09

Original Loan Information

Original amount: $70,000.00
Original term: 30
Original interest rate: 7.00%
Monthly payment: ($465.71)
Original loan age (months): 66
Balance on original loan: $65,396.89

Second Mortgage Requirement

Sales price: $115,000.00
Loan-to-value ratio: 0.80
Amount financed: $92,000.00
Assumed mortgage: $65,396.89
Second mortgage amount: $26,603.11
Term: 20
Rate spread: 3.00%
Interest rate: 13.00%
Monthly payment: ($311.68)

Conventional Loan Information

Loan amount: $92,000.00
Term: 30
Interest rate: 10.00%
Monthly payment: $807.37

Payment Savings

Months 1-240: $29.98
Months 241-294: $341.65
Months 295-360: $807.37

Months 1-240: $3,106.52
Months 241-294: $2,020.71
Months 295-360: $8,689.09


It is also possible for an assumable loan to have no value or to have a negative value. For example, at an interest rate spread of 3.87%, a price of $130,000 (A/P ratio = 0.503), and a loan-to-value ratio of 0.90, the value of the assumable loan is reduced to zero. In this extreme case, the cash equivalent value is the same as the sale price. If any of these three variables exceeds these limits, the value of the assumable loan becomes negative and the buyer is better off financing the purchase with a new, first mortgage and paying off the old mortgage at closing. As table 2 shows, the value of assumable financing erodes quickly when the combined effects of principal reduction and property value appreciation reduce the ratio of the assumable mortgage amount to the sales price (the A/P ratio in table 2). Consequently, the expected value of the remaining payment savings upon resale will be much lower in markets where housing prices are expected to increase over time than in a static or declining market.


The real estate literature has struggled with the disconnect between the calculated "full value" of a favorable assumable loan and empirical studies of market prices paid for these loans, showing discounts of 36%-70%. However, measures of assumable financing value that have ignored the need for a junior mortgage to bridge the gap between the assumable loan amount and the buyer's equity overestimate the value of assumable financing.

Absent sufficient data to extract an adjustment from the market, it is appropriate to incorporate the effect of junior mortgages into mathematical calculations in order to comply with Guide Note 2, be consistent with the USPAP definition of market value, and provide more realistic estimates of cash equivalency.

1. According to Bank Rate Monitor, on November 13, 1998, the typical interest rate was 6.71% on a conventional 30-year fixed-rate mortgage, 6.34% on a 15-year fixed-rate mortgage, and 5.54% on a one-year adjustable-rate mortgage.

2. based on data from Rates & Terms on Conventional Home Mortgages, Annual Summary (Federal Housing Finance Board, 1993), in 1982 the national average annual interest rate on a conventional single-family mortgage for a previously occupied home was 14.78%.

3. Appraisal Institute, Code of Professional Ethics and Standards of Professional Appraisal Practice, Guide Note 2, November 2, 1986, D4.

4. William B. Brueggeman and Jeffrey D. Fisher, "Cash Equivalency: Lower Loan Balance," Real Estate Finance and Investments, 10th ed. (Chicago, Illinois: Irwin, 1997).

5. Appraisal Institute, The Appraisal of Real Estate, 11th ed. (Chicago, Illinois: Appraisal Institute, 1996).

6. Ibid, 409.

7. David C. Lennhoff, "Defining the Problem," The Appraisal Journal (April 1986): 198-204.

8. The Appraisal of Real Estate, 21.

9. Halbert C. Smith and John B. Corgel, "Adjusting for Nonmarket Financing: A Quick and Easy Method," The Appraisal Journal (January 1984): 75-83.

10. G. Stacy Sirmans, C. F. Sirmans, and Stanley D. Smith, "Adjusting Comparable Sales for Assumption Financing," The Appraisal Journal (January 1984): 84-91; Karl L. Guntermann, "Financing and Selling Prices of Single-Family Homes," Research in Real Estate, v. 1, edited by C. E Sirmans (Greenwich, Connecticut: JAI Press, 1982), 255-273.

11. Terrence M. Clauretie and G. Stacy Sirmans, Real Estate Finance: Theory and Practice, 2d ed. (Upper Saddle River, New Jersey: Prentice Hall, 1996).

12. David Dale-Johnson, M. Chapman Findlay, Arthur L. Schwartz, Jr., and Stephen D. Kapplin, "Valuation and Efficiency in the Market for Creatively Financed Houses," AREUEA Journal (Winter 1985): 388-403.

13. Clauretie and Sirmans cite numerous studies showing actual assumed financing prices that range from 30% to 64% of the mathematically estimated value of assumption financing. Also, an article based on survey data implicitly demonstrates a relationship between prices that buyers were willing to pay for a low-interest rate assumed loan and the cost of junior loans. See James L. Doherty, "Favorable Financing Effects on Values of Single-Family Residences," The Appraisal Journal (July 1970): 398405.

14. This can also be derived on a financial calculator by setting the interest rate (i) to 0.10/12, the number of periods (N) to 294, the payment (PMT) to -$465.71, the future value (FV) to zero, and solving for present value (PV).

15. The Appraisal of Real Estate, 408; G. Stacy Sirmans, C. F. Sirmans, and Stanley D. Smith, "Cash Equivalency Valuation for Creative Financing Methods," The Appraisal Journal (July 1984): 425.

16. The template developed for this paper is in Excel 97, and can be provided by the author. E-mail requests are preferred.


Clark, David. "Cash Equivalency Adjustments in Depressed Real Estate Markets," The Appraisal Journal (October 1989): 544-550.

Clauretie, Terrence M., and Douglas S. Bible. "Cash Equivalency: Appraisers' Views and Applications," The Appraisal Journal (January 1987): 25-31.

DeLacy, P. Barton. "Cash Equivalency in Residential Appraising," The Appraisal Journal (January 1983): 81-88.

Sirmans, G, Stacy, C. F. Sirmans, and Stanley D. Smith, "Valuation of VA Assumable Loans," The Appraisal Journal (January 1987): 138-143.

Marvin L. Wolverton, MAI, PhD, is the Alvin J. Wolff Professor of Real Estate/Director of Real Estate Research at Washington State University, Pullman. He specializes in real estate appraisal, behavioral issues in real estate, and market segmentation. He earned a PhD in business administration with a real estate emphasis from Georgia State University, Atlanta. His research has been published in various real estate journals. Contact:
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Author:Wolverton, Marvin L.
Publication:Appraisal Journal
Date:Jan 1, 1999
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