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The valuation of owner-financed residential mortgages.

In the fourth quarter of 1991, individuals owned $454 billion or 16% of the one- to four-family residential mortgages outstanding. A significant segment of these mortgages was generated through owner-financed transactions. For a variety of reasons, including estate tax and income tax purposes, these mortgages must be valued.

Finance theory indicates that the value of any asset is the present value of the cash flows generated by that asset discounted at the appropriate discount rate. Within this context, the valuation of a mortgage seems straightforward. Three issues cause this problem to be more complicated than might be expected: the potential for prepayment, the choice of the discount rate, and the adjustment for the lack of liquidity.

The first step in the valuation process is to project the size and the number of the cash flows. The promised cash flows from an owner-financed mortgage are known; however, the actual payments are not known because a borrower could choose to prepay. The second step is to choose the appropriate discount rate. This rate should reflect both the current level of return on securities with similar cash flows and the default risk of the individual borrower. Once the discount rate is chosen, the present value of the projected cash flows can be calculated.

These first two steps are similar to the process of valuing mortgages in the secondary market. Mortgages trading in the secondary market, however, are highly liquid while the owner-financed mortgages are not. In the final step, an adjustment must be made because the owner-financed mortgage's lack of liquidity reduces its value.

In this article, the proposed framework for the valuation of an owner-financed mortgage is applied to a specific example. The choices of prepayment assumptions, discount rate, and liquidity adjustment are explained within the context of that example.


In 1987, Mr. Smith sold his house to Ms. Jones. To finance the purchase of the house, Smith made a $50,000-first-mortgage loan to Jones. Five years later, Smith hires our appraisal firm to estimate the fair market value of the mortgage. The valuation date is June 1, 1992. The appraiser is given the following information:

* Origination date: March 1, 1987

* Maturity date: February 28, 2007

* Principal: $50,000

* Contract rate: 10.5%

* Monthly payment: $499.19

Cash flows and prepayment risk

Jones promises to pay the remaining 177(1) payments on the mortgage; however, she could decide to pay off the entire remaining principal prior to maturity. Her decision to prepay would affect the number and the size of the payments to be valued. The probability that prepayment will occur can be assessed on the basis of the individual circumstances of the mortgagor as well as the prepayment experience of similar mortgages.

In the case of an owner-financed mortgage, an appraiser is likely to have specific knowledge of the borrower as well as knowledge of local market conditions. This knowledge may allow an accurate estimate of the probability of prepayment. In this example, knowledge of Jones's circumstances indicates a low probability of prepayment. The cash flows are projected to be $499.19 per month over the remaining life of the loan--177 payments.

If an appraiser does not have specific knowledge concerning the individual borrower's prepayment probability, broader market experience of prepayment may be used. In Mortgage-Backed Securities: Products, Analysis, Trading,(2) William W. Bartlett cites the assumption of prepayment in 12 years as the "universal standard." This would be in line with the assumption used in the Federal Reserve Bulletin, which reports average net yields on Government National Mortgage Association (Ginnie Mae) pass-through securities, assuming prepayment in 12 years. An appraiser would be justified in expecting earlier prepayment if the market interest rate is significantly below the contract rate on the mortgage. A borrower would be more likely to refinance to obtain a lower interest rate. If market rates are above the contract rate, the borrower may still prepay but the chances are slimmer.(3)

Discount rate

The appropriate discount rate for an owner-occupied mortgage is the safe rate plus a default risk premium. The safe rate is estimated by the return on government-guaranteed, mortgage-backed securities. The default risk premium is estimated using the difference between the rate on A-rated corporate bonds and the rate on Treasury bonds.

The return on Ginnie Mae pass-through securities provides a good estimate of the safe rate for mortgage securities. Both the owner-financed mortgage and the Ginnie Mae pass-throughs are fully amortized debt, collateralized by real property. The pass-throughs have the additional advantages of a federal government guarantee and an active secondary market.

The default risk premium should reflect only differences in the risk of default; therefore, two bonds with similar payment structures are compared in order to estimate the premium. An owner-financed mortgage is an individual's liability and is not normally insured. While an individual may have a good payment record there is some probability that he or she may be unable to make future payments. In the event of default, the property would be available to satisfy the debt.

The combined safety offered by individuals with satisfactory credit histories and the collateral value of the property makes the default risk associated with the owner-financed note approximately equivalent to that of an A-rated corporate bond. Because of the government guarantee, the risk of default on the Ginnie Mae pass-throughs is similar to the default risk on U.S. Treasury securities. The Federal Reserve Bulletin for March 1992(4) reported the following yields:

* Ginnie Mae pass-through: 7.81%

* Thirty-year Treasury bond: 7.7%

* A-rated corporate bond: 8.82%

The difference between the corporate and the Treasury yields is used to estimate the default risk premium:

8.82% - 7.7% = 1.12%

This adjustment for default risk is added to the Ginnie Mae market rate (i.e., safe rate) to arrive at a risk-adjusted discount rate of

7.81 + 1.12 = 8.93%

This risk-adjusted discount rate is used to calculate the present value of the projected cash flows. The 177 monthly payments are discounted at the monthly rate of .744% (8.93%/12). The present value is $49,022.31. This present value is an estimate of the value of the mortgage assuming it has the same degree of marketability as a Ginnie Mae pass-through. Because it does not, the final step is to make an adjustment for the lack of liquidity.

Liquidity adjustment

The value of owner-financed mortgages is significantly reduced by their lack of liquidity. If information concerning recent sales of owner-financed mortgages in the local market is available, this information can be used to estimate the liquidity adjustment. Because their lack of liquidity is a result of the limited nature of the secondary market for these assets, however, such market information may be unavailable.

While no studies were found that compare the values of mortgages that will sell readily in the secondary market with those that will not, studies that compare the values of readily marketable common stock with values of stock having limited marketability are available. These studies provide information on the appropriate size of the adjustment caused by the lack of marketability. Table 1 summarizes the discounts for illiquidity cited in the literature.

Restricted stock, also known as letter stock, is restricted from immediate resale by federal security laws. Milton Gelman uses the purchases of letter stock by closed-end investment companies to estimate an appropriate discount for lack of marketability of closely held common shares in "An Economist-Financial Analyst's Approach to Valuing Stock of a Closely-Held Company."(5) In a study of four funds that specialize in restricted securities investments from 1968 through 1970, Gelman finds both a mean and median discount from market value of 33% for letter stock purchases from 89 publicly traded companies.

In "Discounts for Lack of Marketability for Closely-Held Business Interests," J. Michael Maher(6) studies the purchase of restricted common stocks by four mutual funds between 1969 and 1973. By comparing the market value of the restricted shares with the market value of unrestricted securities of the same class, Maher concludes that a proper discount for lack of marketability should be approximately 35%.

Thomas A. Solberg reviews court decisions regarding the discount applied in valuing restricted securities in "Valuing Restricted Securities: What Factors Do the Courts and the Service Look For?"(7) He notes a 17% to 44% range of discounts recognized by the courts in previous valuation cases regarding restricted securities.

A second asset with similar risk characteristics is closely held common stock. Several articles focus on the valuation of closely held common stock that represents a minority interest in the company. In "Why 25% Discount for Nonmarketability in One Valuation, 100% in Another?"(8) Robert E. Moroney examines the valuation of closely held shares with minority interests for estate and gift tax purposes. While noting that previous tax court decisions have upheld illiquidity discounts in the 50% range, Moroney feels that consideration of the dual factors of lack of marketability and minority interests dictates discounts of up to 75%.
TABLE 1 Summary of Discounts for Illiquidity

Author Security Discount

Gelman (1972) Restricted stock 33%
Maher (1976) Restricted stock 35%
Moroney (1977) Closely held stock 75%
Solberg (1979) Restricted stock 17-44%
Andrews (1988) Closely held stock 10-50%
Lyons and Wilczynski
(1989) Closely held stock 35-40%
Curtis (1991) Closely held stock 40-50%

Robert P. Lyons and Michael J. Wilczynski indicate in "Discounting Intrinsic Value"(9) that discounts should apply for lack of marketability and minority interest. They advocate a 27% to 28% discount for minority control, and a 35% to 40% discount as a result of lack of marketability. In "Discounting Minority Stock Interests in Closely-Held Corporations: When and How Much?"(10) Andrew M. Curtis notes that in estate asset conflicts between taxpayers and the Internal Revenue Service, expert witnesses have recognized minority discounts of 40% to 50%. Edmund L. Andrews observes in "Take the Money and Run"(11) that valuations for private market stock placements have traditionally been discounted 10% to 50% from comparable public companies. Clearly, a significant discount for lack of marketability is appropriate in the asset valuation process.(12)

Based on the valuation literature and knowledge of the local market, a discount for illiquidity of 35% is applied to Smith's mortgage. Applying this 35% discount for lack of marketability, the owner-financed mortgage is valued as:

$49,022.31 x (1 - .35) = $31,864.50


The valuation of an owner-financed mortgage presents some interesting problems: the probability of prepayment, the default risk, and the lack of liquidity. Using readily available market interest rates and the literature on valuation of restricted and closely held corporate common stock, a method is presented here that may be easily implemented by appraisers to value owner-financed mortgages.

1. This assumes that the June 1 payment has not yet been made; thus, 177 monthly payments remain until maturity.

2. William W. Bartlett, Mortgage-Backed Securities: Products, Analysis, Trading (New York, New York: New York Finance Institute, 1989), 154.

3. For explanations of alternative methods used to estimate prepayment rates for pools of mortgage-backed securities, see ibid.; or Frank J. Fabozzi, Bond Markets, Analysis and Strategies, 2d ed. (Prentice-Hall, Inc., 1993).

4. Federal Reserve Bulletin, v. 78, no. 3 (March 1992): A24, A35.

5. Milton Gelman, "An Economist-Financial Analyst's Approach to Valuing Stock of a Closely-Held Company," The Journal of Taxation (June 1972): 353-354.

6. Michael Maher, "Discounts for Lack of Marketability for Closely-Held Business Interests," Taxes--The Tax Magazine (September 1976): 562-571.

7. Thomas A. Solberg, "Valuing Restricted Securities: What Factors Do the Courts and the Service Look For?" The Journal of Taxation (September 1979): 150-153.

8. Robert E. Moroney, "Why 25% Discount for Nonmarketability in One Valuation, 100% in Another?" Taxes--The Tax Magazine (May 1977): 316-320.

9. Robert P. Lyons and Michael J. Wilczynski, "Discounting Intrinsic Value," Trusts and Estates (February 1989): 22-27.

10. Andrew M. Curtis, "Discounting Minority Stock Interests in Closely Held Corporations: When and How Much?" The Journal of Taxation of Estates and Trusts (Spring 1991): 26-30.

11. Edmund L. Andrews, "Take the Money and Run," Venture (March 1988): 77-78.

12. For a comprehensive review of valuation discounts for various reasons allowed in tax court cases, see Donald M. Schindel, "Various Methods Exist for Establishing a Sustainable Value for Estate Assets," Estate Planning (September/October 1990): 258-264.

J. Howard Finch, PhD, is Max Finley Assistant Professor of Finance at the University of Tennessee at Chattanooga. He received his PhD from the University of Alabama.

Patricia Rudolph, MAI, PhD, is the Board of Visitors Research Professor of Finance at the University of Alabama. She received her PhD from the University of North Carolina, Chapel Hill.
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Author:Finch, J. Howard; Rudolph, Patricia
Publication:Appraisal Journal
Date:Jul 1, 1993
Previous Article:Management by objective for appraisal firms.
Next Article:Direct capitalization or discounted cash flow analysis?

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