Cash Equivalency Example #3
Now we'll use some of this information to put together another Cash Equivalency example to see how it would relate to an actual appraisal report. Let's say, you were appraising a house and you found a sales comparable that was sold with an assumable mortgage loan. An assumable mortgage means that a buyer can "assume" or take over the mortgage loan when buying the house instead of having to get a new loan to pay off the existing mortgage. Basically, the buyer just makes the remaining payments on the existing mortgage. This makes the sale of the house more flexible and easier to find potential buyers who may be willing to pay a higher price for the convenience of being able to assume the existing loan. The buyer will not have to go through the hassle and expense of getting a new mortgage and pay the points, bank fees, and maybe even a higher interest rate. Assumable loans were easy to get years ago but today they are hard to find.
Now back to our example: The recorded sales price of the house was $100,000. The mortgage loan that was assumed by the buyer was the same loan and terms that we've used in our examples; $80,000 loan at a 12% interest rate for a 30 year term. The seller of the house has been making loan payments for 10 years on this mortgage loan before the buyer assumes it. We already found out, (from our prior examples) that the monthly mortgage payment is $822.88. However, at the time of the sale when the buyer assumed this loan, the market interest rates were 16.5% for conventional financing mortgages.
We first need to determine what the remaining loan principal balance is at the time the new buyer assumes the mortgage. This loan in our example has a principal balance remaining after 10 years of making loan payments of:
$822.88/0.011011 = $74,732.54
or
$9,874.56/0.132132 = $74,732.54
Using both methods, we come up with the same answer. The loan principal balance that is outstanding after 10 years of loan payments will be $74,732.54.
Next we need to figure out what the down payment amount was that the buyer had to pay to purchase this house. We find this by simply subtracting the balance of the assumable loan from the total sales price.
$100,000  $74,732.54 = $25,267.46
The amount of the buyer's down payment is determined to be $25,267.46.
As I said, the seller has been making payments on this loan for 10 years. The loan interest rates that the banks are charging at the time of the sale, have gone up from 12% to 16.5%. The 16.5% is now the market interest rate. We need to now determine what the book value of this loan was at the time that the loan was assumed by the buyer.

Book Value = Monthly Loan Payment/ITAO at CRRT

ITAO at CRRT = The Installment To Amortize One dollar at the Contract Rate for the Remaining Term of the loan.
The seller has been making payments on the loan for 10 full years. So we need to find out the remaining term of this loan.
30  10 = 20 years remaining
Now we'll figure out what this loan is worth at the market interest rate which is 16.5% in our example. You have to compare apples to apples, so we use the same ITAO remaining loan term, which is 20 years in our example.

ITAO at MRRT = The Installment To Amortize One dollar at the Market Rate for the Remaining Term of the loan.
If you check the tables, the ITAO for a loan term of 20 years at 16.5% interest is 0.014289. Now we'll find what the remaining loan balance is with 20 years remaining on this loan, at the market interest rate and the contract monthly loan payment. Remember we can do this two ways, using either the ITAO column figure or the Rm column figure. We'll use the ITAO column figure. Since we are using the monthly ITAO, then we must use the monthly loan payment to find the remaining loan balance at 20 years.
$822.88/0.014289 = $57,588.35
We now have determined what the current loan balance is at the contract interest rate of 12%. We've also found what the loan balance would be with the contract monthly loan payment, at the market interest rate of 16.5%. Now we will figure out what the loan is worth to the lender today. We do this by dividing the market rate figure by the contract rate figure.
$57,588.35/$74,732.54 = 0.77
Our answer is 0.77 which is the same as 77%. This indicates that the existing loan, at a 12% interest rate, is only worth 77% of what the exact same loan would be worth in today's market of 16.5% interest. That's a discount of 23% (100%  77% = 23%). This simply means, that if the seller's banker lent the equivalent of the unpaid loan balance to someone in today's market, the bank would get an additional 23% profit over what they are getting from the seller for the same loan amount! So the $74,732.54 outstanding loan balance at the contract interest rate of 12%, is only worth $57,588.35 in today's market at the current market interest rate of 16.5%.
Now since we are using this sale as a comparable for one of our appraisals, we have to make a cash equivalency adjustment to the sales price of the comp. We do this because the loan that was assumed by the buyer has a lower interest rate than a loan that a typical buyer would obtain, at the time that the sale of the comparable took place. An adjustment is needed because the recorded sales price does not reflect an "arms length" transaction. This is because the buyer had received a lower than normal interest rate loan to buy the house which probably caused them to pay a higher sales price due to the favorable terms.
We can figure out the adjustment to make by subtracting the recorded sales price of the comparable, from the adjusted sales price. The adjusted sales price takes into account the low interest rate loan. To do this, we first need to decide what the adjusted sales price is. This is calculated by adding the buyer's down payment to the market rate of the loan balance assumed.
$57,588.35 + $25,267.46 = $82,855.81
The adjusted sales price of the comparable in our example is $82,855.81. Meaning that this is what the house actually sold for because of the low interest rate of the loan assumed by the buyer. The $100,000 recorded sales price of that sales comparable then is not an "arms length" transaction.
Now we need to determine the adjustment to make in the appraisal report. We do this by simply subtracting the adjusted sales price of the comparable from the recorded sales price. Remember that you have to round out your adjustment amounts because real estate appraising is not an exact science.
$82,855.81  $100,000 = $17,144.19
The rounded adjustment in the appraisal report that we would make to the recorded sales price of the comparable in our example is $17,150.
Now do you see why I had to teach you all of this math? I hope so. Believe me, I wouldn't have included all of these math examples in the book unless it was a necessary part of teaching the techniques and methods of real estate appraising. The math calculations can get boring but there will be times when you need to know this stuff for an appraisal report.