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The effect of the listing price on cash equivalence.

It is widely accepted that seller financing affects the sale prices of real estate. When a seller provides a buyer with financing having more favorable terms than are available from a third party, the value attributed to this financing may be paid to the seller through a higher selling price. The result is that the sale price of a parcel of real estate reflects not only the value of the property, but also the value of the financing. If an adjustment is not made the property thus will be overvalued when a sale price that reflects favorable seller financing is used as a proxy for market value. Unfortunately for the appraisal community, no definitive answers have been provided that indicate how seller-financed sales, or in particular assumption financing, should be adjusted.

The purpose of this article is to determine whether a listing price sets a ceiling on the amount of the financing premium that is capitalized into the price of a house. The evidence presented is based on residential sale date from Champaign, Illinois, consisting of sales that occurred from 1979 to mid-1984. Two linear multiple regression models are developed in order to compare an unadjusted cash equivalence adjustment (CEA) premium with an adjusted CEA (ADJCEA) premium that reflects listing price.

A discussion of the cash equivalence adjustment approach is provided in the following section, and the reasons that the listing price of a house may impose a ceiling on the financing premium are examined. An empirical test of the theory that listing price is significant is then presented.



The cash equivalence adjustment (CEA) approach has been a topic in the literature at least since Ken Garcia suggested its use in 1972. (1) The CEA approach was not empirically tested, however, until the early 1980s. In one of the most widely cited studies, G. Stacy Sirmans et al. (2) found that, on average, only 32.2 of the CEA financing premium is capitalized in the sale price of a house purchased with an assumption loan.

More recently, Mark A. Sunderman et al. (3) found that the proportion of the CEA financing premium capitalized in the sale price varies according to the loan-to-price ratio of the assumption loan. In response to the concerns raised by these authors and others, (4) most appraisal guidelines now recognize that the computationally estimated CEA must be considered in the context of empirical evidence from market transactions. For example, The Appraisal of Real Estate, ninth edition, states that

There are precise, mathematical calculations for analyzing cash equivalency, but the financing adjustments derived with these calculations must be rigorously tested against market evidence. More often than not, the cash discount indicated by the calculations is not specifically recognized by buyers and sellers. Furthermore, conditions of sale may reveal other noneconomic interests on the part of buyers or sellers. Therefore, appraisers must use cash equivalency calculations with caution and remember that the final adjustment is always derived from the market. (Emphasis added.) (5)

The CEA financing premium is defined as the present value of the monthly savings that accrue to a buyer who assumes the seller's existing loan with a below-market interest rate rather than obtaining conventional financing at the current market interest rate. This is shown mathematically in Sunderman et al. (6) as follows:

P = []([]L - []L) (1) where P = Financing premium [a.sub.rt] = Present worth of one per period; r indicates the discount rate and t indicates number of periods [f.sub.rt] = Mortgage constant; r indicates the mortgage rate and t indicates number of periods i = Current mortgage rate available on conventional first mortgages k = Contract rate on the assumption n = Periods remaining on the assumption L = Balance due on the assumption (or the book value)

The positive features of CEA include its directness, the relative ease of computation, and its adaptability to different forms of favorable financing. With minor modifications of the model, it is possible to allow for a second mortgage as well as for a difference in the number of remaining payments between the assumption and the conventional mortgage. Another advantage of the CEA approach is that, in most cases, the information needed to calculate the financing premium is readily available.

The remainder of this article demonstrates that, on average, consideration of listing price in calculating CEA for assumption-financed sales yields an estimate of the financing premium that is supported by empirical evidence from market transactions.


If the simplistic assumption is made that the value of an assumed loan is fully capitalized into the sale price of a single-family house, that sale price should equal the sum of the market value of the house and the value of the assumption financing. When placing an offer to buy, a potential buyer should consider both of these values. These values should also be considered by the seller in arriving at a listing price for the property. If a seller sets too low a price for a house, a ceiling is placed on the value of the financing premium that can be capitalized into the sale price. Thus, although the buyer may believe the house (including the financing) is worth more than its listing price, a higher offer will not occur. (7)

To account for this problem, the following adjustments to CEA are suggested:

[Mathematical Expression Omitted]

where ADJCEA = Adjusted version of CEA SP = The sales price of the house LP = The listing price of the house MV = The market value of the house SP and LP are observed, CEA can be calculated and MV is unknown; however, it is possible to predict MV with a hedonic regression model. (8) The parameters of the regression can be estimated using only the conventional sales. With this estimated model, MV can now be predicted for each of the sales with assumption financing. With MV, SP, and LP the value of ADJCEA can be calculated. Then it is possible to test whether the listing price sets a ceiling on the proportion of the calculated financing premium capitalized into the sale price.


To conduct an empirical test of the effect that listing price has on the proportion of CEA paid by a buyer, an appropriate data set and model are needed. First the data set is described, after which the model is discussed, followed by presentation of the empirical results.


The data are derived from Multiple Listing Service (MLS) comparable books on sales of single-family detached houses located in a section of southwestern Champaign, Illinois, known as the Southwood area. The sample consists of 103 sales using assumption financing and 283 sales using conventional financing in the period from January 1979 to August 1984. Summary statistics for the variables are presented in Table 1. In addition to these variables, a schedule of the prevailing interest rates available (at the time of sale) on conventional mortgages with an amortization of 30 years and a loan-to-value ratio of 0.80 was compiled. For sales using assumption financing, the balance due, the remaining term, and the interest rate on the assumption were also compiled.

Specification of the model

Specification of the model includes selection of the dependent and explanatory variables to be included in the model, determination of the overall functional form, and specification of the form of certain variables, particularly the date-of-sale and the finance variables.

The actual sale price is used as the dependent variable because the primary concern is the effect that assumption financing has on the sale price of a house. This is consistent with previous research that uses a regression model. Explanatory variables are selected on the basis of: 1) an attempt to incorporate all the physical, locational, financing, and date-of-sale (to allow for changes in market conditions) variables that would be required to minimize specification bias; 2) results of previous studies; and 3) availability of data.

The form of the date-of-sale variable is that suggested by Thomas B. Bryan and Peter F. Colwell, who note that "Each date of sale is defined as a linear combination of the end points of the year in which the sale occurs. Thus, the B(y) variables are the proportionate weights." (9) There is a B(y) variable for each year in which sales occurred, with B signifying the beginning of the year and y symbolizing a year. For example, if a sale occurred in September 1983, B83 is 0.25, B84 is 0.85 and all other B(y) variables are zero. Because the sale was closer to the beginning [TABLE DATA OMITTED] of 1984 than to the beginning of 1983, B84 is larger and is given more weight than B83. This approach allows the rate of change in prices to be different for each year.

The linear functional form for the model is rationalized in part on the basis that the sample is relatively homogeneous. A linear approximation of a small segment of what may be a nonlinear function is therefore reasonable. Further, a linear model is chosen because it allows direct comparison with models developed for previous research and it is easier to interpret the coefficient of the financing premium variables. When a linear model is used, the model can be stated as follows:

SP[H.sub.j] = {b}[H.sub.0] + {b}[H.sub.1]X[H.sub.1j] + {b}[H.sub.2]X[H.sub.2j] + ... + {b}[H.sub.k]X[H.subkj] + {m}[H.sub.j] (3) where

SP[H.sub.j] = Sale price of the j[] property X[H.sub.1j] to X[H.sub.kj] = Expanatory variables defined in Table 1 {b} = Parameters to be estimated {m}[H.sub.j] = The random error term

The financing variables used are the calculated CEA premium and the calculated ADJCEA premium. For the conventionally financed sales, the financing-premium variable (either CEA or ADJCEA) is set equal to zero. For assumption sales, the CEA variable equals the calculated value using equation (1) and the ADJCEA variables equals the calculated value using equation (2). If the coefficient on the financing variable turns out to be insignificantly different from zero, this would imply that none of the calculated financing premium was capitalized into the sale price. If the coefficient turns out to be insignificantly different from unity, however, this would imply that 100% of the calculated financing premium was capitalized. The focus of the empirical results is the coefficients of these two financing premiums, CEA and ADJCEA.

Empirical results

The empirical results are presented for two different models. Model 1 includes the calculated CEA premium as a variable, while Model 2 includes the calculated ADJCEA premium as a variable. These results are shown in Table 2.

Model 1--CEA

Model 1 has a high explanatory power with an R[H.sup.2] adjusted for degrees of freedom of approximately 0.90. All physical-characteristic variables (building sytle is taken as a group and garage type is taken as a group) except lot area, subdivision-location variables (taken as a group), and date-of-sale variables (taken as a group) have coefficients that are considered statistically significantly different from zero at the 95% level of confidence. Further, for each of these variables the sign on the coefficient is as expected when there is a basis for a priori expectations. In addition, the CEA variables has a coefficient that is statistically significant.

The coefficient on the CEA variable indicates that, on average, approximately 18% of the calculated CEA financing premium is capitalized into the sale price of a house when an assumption is used. This indicates that the CEA formula, as shown in equation (1), overvalues the premium associated with an assumption; however, as this coefficient is statistically significantly different from zero it also indicates that there is some value attributed to an assumption.

Variance inflation factors were used to detect the presence of multicollinearity. These inflation factors, one for each explanatory variable, measure how much the variances of the estimated regression coefficients are inflated compared with the explanatory variables when they are not linearly related. The largest factor among the variables is used to indicate the severity of multicollinearity. A variance inflation factor (VIF) exceeding 10 is often an indication that multicollilnearity may be influencing the least squares estimates. (10) For Model 1, the highest VIF was 6.5531, while the mean VIF for the model was 2.4601. These magnitudes of the VIF indicate that this model is not significantly affected by multicollinearity.

Model 2--ADJCEA

Model 2 has an even higher explanatory power with an R[H.sup.2] adjusted [TABLE DATA OMITTED] for degrees of freedom of approximately 0.91. Based on the higher adjusted R[H.sup.2] and lower standard, error, the model with the adjusted financing premium variable (ADJCEA) appears to be the better-specified model.

A variance inflation factor test was also applied to Model 2. The highest VIF was 6.5531 and the mean VIF for the model was 2.4561, further indicating that multicollinearity is not a significant problem.

While it is clear that most variables that Model 1 and Model 2 have in common have coefficients with relatively similar magnitudes, some appear to be quite different. Of course, some variation in the coefficients is to be expected. Further, because the focus of this article is the financing premium variables, some variation in the coefficients of the nonfinance variables is not considered a major problem. The coefficients that are common to both models, however, should not be jointly significantly different from each other. To test this hypothesis, a variation of an F-test was used. (11) The results indicated that no stastically significant difference exists between the coefficients used in Model 1 and those used in Model 2, excluding the financing premium variables. In addition, in developing these models several different combinations of explanatory variables were tried, and the coefficients on the financing premium variables were found to remain quite stable.

Model 2 provides an interesting result; that is, that the coefficient on the ADJCEA variable is not statistically significantly different from unity. This indicates that this variable does not over- or undervalue the financing premium attributed to assumption financing. The calculated CEA, adjusted for listing price, thus may be about right on average. This may be accurate enough for such purposes as property tax assessment when a large number of properties must be appraised. In addition, owners of overassessed properties may use the appeal process.


The purpsoe of this article is to determine whether listing price imposes a ceiling on the amount of the financing premium that is capitalized into the price of the house. The major findings are as follows:

* When CEA was not adjusted for listing price, it was found that on average only about 18% of the financing premium was capitalized into the sale price.

* When CEA was adjusted for the listing price, the empirical results cannot exclude the posibility that 100% of the adjustment estimated is included in the sale price. (12) Therefore, it can be concluded that the listing price may set a ceiling on the amount of the financing premium capitalized into the sale price.

These results show that a simple computational CEA approach overvalues the premium associated with assumption-financed sales unless listing price is properly considered. According to these results, the simple computational CEA approach overvalues the premium to such a great extent that to make no adjustment is better than to make a CEA adjustment.

[1] Ken Garcia, "Sales Prices and Cash Equivalents, "The Appraisal Journal (January 1972): 1-10.

[2] G. Stacy Sirmans, Stanley D. Smith, and C. F. Sirmans, "Assumption Financing and Selling Price of Single-family Homes," The Journal of Financial and Quantitative Analysis (September 1983): 307-317.

[3] Mark A. Sunderman, Roger E. Cannaday, and Peter F. Colwell, "The value of Mortgage Assumption: An Empirical Test," The Journal of Real Estate Research (Summer 1990): 247-257.

[4] For exampe, see Vinod B. Agarwal and Richard A. Philips, "The Effects of Assumption Financing Across Housing Price Categories," The Journal of the American Real Estate and Urban Economics Association (Spring 1985): 48-57; John B. Corgel and Paul R. Goebel, "Financing Adjustments via Cash Equivalency: Evidence on Accuracy," The Real Estate Appraiser and Analyst (Spring 1983): 55-61; Eurico J. Ferreira and G. Stacy Sirmans, "Assumption Loan Value in Creative Financing," Housing Finance Review (April 1984): 63-80; M. C. Findlay and F. E. Fischer, "On Adjusting the Price of 'Creatively Financed' Residential Sales: Cash Equivalence F. E. Fischer, "On Adjusting the Price of 'Creatively Financed' Residential Sales: Cash Equivalence vs. FFVA," Housing Finance Review (January 1983): 63-80; and Stanley D. Smith, G. Stacy Sirmans, and C. F. Sirmans, "The Valuation of Creative Financing in Housing," Housing Finance Review (April 1984): 129-138.

[5] American Inst. of Real Estate Appraisers, The Appraisal of Real Estate, 9th ed. (Chicago: American Inst. of Real Estate Appraisers, 1987), 319.

[6] Sunderman et al., 248.

[7] There may be exceptions to this when there is an imbalance between supply and demand; for example, when there is a shortage of housing available in a certain price range and potential buyers start to bid against each other for a particular house. In examining the data set used in this study, it was determined that property was not being sold above its list price. This was accomplished by comparing sale price and listing price for houses in the relevant price range from Multiple Listing Service (MLS) comparable books used to generate the data set. In geographic areas or time periods when housing routinely sells for amounts in excess of the original listing price, the results of this study may not be appropriate. However, this would represent an exception rather than the rule.

[8] Although it is not discussed in this article, it would be possible to estimate market value by using a method other than a regression model. For example, the market value would be estimated by the adjustment-grid method.

[9] Thomas B. Bryan and Peter F. Colwell, "Housing Price Indexes," in C. F. Sirmans, ed., Research in Real Estate, v. 2 (1982), 57-84.

[10] For a discussion of variance inflation factors see John Neter, William Wasserman, and Michael H. Kutner, Applied Linear Regression Models (Homewood, Ill.: Richard D. Irwin, Inc., 1983), 391-392.

[11] This test involves calculating a predicted market value using the base models--Model I with the CEA variable excluded and Model 2 with the ADJCEA variable excluded--and comparing the sum of the squared prediction errors for each model. If the coefficients of these models are exactly the same, the ratio of these squared prediction errors could be expected to be one. Instability of the coefficients would increase this value. An F-test could then be used to determine significance.

[12] These results do not necessarily invalidate the results of other who have shown that factors such as loan-to-value, taxes, downpayment, expected holding period, as well as other influences, may explain why less than 100% of CEA is capitalized into the sale price of a house purchased with an assumption loan. These results show, however, that perhaps these other factors should be considered again in light of this suggested adjustment for listing price.

Mark A. Sunderman, PhD, is an assistant professor of finance at the University of Wyoming. He received a PhD in finance from the University of Illinois in Urbana-Champaign. His research primarily concerns real estate valuation and assessment administration, and he has published many articles on these topics.

Roger E. Cannaday, PhD, is an associate professor of finance at the University of Illinois at Urbana-Champaign. He received his PhD in business administration from the University of South Carolina. With a research emphasis on real estate valuation and market analysis, he has published articles in various real estate-related journals.

Peter F. Colwell, PhD, is an ORDER professor of real estate as well as the director of the Office of Real Estate Research at the University of Illinois in Urbana-Campaign. He received his PhD in economics from Wayne State University and specializes in the pricing of urban land. He has previously published several articles.

This research was funded in part through a University of Wyoming Faculty Development Award.
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Author:Sunderman, Mark A.; Cannaday, Roger E.; Colwell, Peter F.
Publication:Appraisal Journal
Date:Apr 1, 1992
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