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Calculating Yield on a Wrap-around Loan

The basic steps in calculating the yield on a wrap-around mortgage are as follows:

  1. First, calculate the mortgage payment using the wrap-around loan rate and amount just as any other loan.
  2. Next, calculate the amount the seller is actually lend to the buyer of the seller's own money.
  3. Finally, calculate the yield on the actual money the seller is lending.

Let's try it with a problem
Assume that the market interest rate is 12%. (The market interest rate of 12% is actually not used anywhere in the calculations. It is included to show that the wrap-around mortgage is beneficial to both the buyer and the seller. They buyer gets a mortgage substantially below the market rate--10.5% rather than 12%.) Assume that the seller has a $70,000 fully assumable first mortgage at the time of the sale that carries a contract interest rate of 8.25%. The loan has monthly mortgage payments of $563.66 for the next 25 years. Further assume that the buyer has $10,000 for the down payment, but needs to get a $90,000 loan. If the seller agrees to give the buyer a $90,000 wrap-around mortgage at 10.5%, what is the yield to the seller on that money lent?

Now let's compute the problem

  1. First, you calculate the mortgage payment using the wrap-around loan rate and amount just as any other loan.

    • Enter the proper payments per year. You first must type in the appropriate number (eg. monthly would be 12, quarterly would be 4, etc.), then push the orange SHIFT key , then the P/YR key .

      In our problem, first calculate the buyer's payment on the $90,000 wrap-around mortgage. Enter the proper payments per year, 12, and then push the orange SHIFT key , then the P/YR key .

       

    • The order of the next three steps is not important, but I recommend that you follow across the financial tour of your calculator from left to right. If you do this, then the next step would be to enter in the proper number of years. You first type the appropriate number, then push the orange SHIFT key , then the xP/YR key.

      In our problem, enter in the proper number of years, 25, then push the orange SHIFT key , then the xP/YR key.

     

    • Now, enter the appropriate interest rate per year. This is done by entering the appropriate annual interest rate as a whole number, not as a decimal (the calculator will convert it to decimal automatically), then pressing the I/YR key.

      In our problem, now enter the wrap-around interest rate per year, 10.5, and then pressing the I/YR key.

     

    • Next, enter the amount of the loan and the PV key.

      In our problem, next enter the amount of the loan , 90,000, and press the PV key.

     

    • Finally, all that is necessary is push the PMT key.
      In our problem, now push the PMT key. The display shows -849.76.

     

    • You then store this value in any storage register by pressing the orange SHIFT key key, the STO key, and then the number of the storage register desired. (most people will probably use register 1.)

      In our problem, you then store this value to the register 1 by pressing the orange SHIFT key key, the STO key, and then 1.

     

  2. Next, calculate the amount the seller is actually lend to the buyer of the seller's own money using the following steps: 

    • Enter the sales prices of the property and press the minus key, then enter the balance outstanding on the seller's old mortgage. Press the equals key to complete the subtraction. This amount is the amount of equity that the seller has in the property. If the seller sold the property outright and the buyer got a traditional mortgage loan instead of the wrap-around loan, this is the amount that the seller would receive at closing.

      In our problem, enter the sales prices of the property, 100,000, and press the minus key, then enter the balance outstanding on the seller's old mortgage, 70,000. Press the equals key to complete the subtraction. This amount, $30,000, is the amount of equity that the seller has in the property. If the seller sold the property outright and the buyer got a traditional mortgage loan instead of the wrap-around loan, this is the amount that the seller would receive at closing.

       

    • Now, subtract from that equity the amount that the buyer is putting down on the property by simply hitting the minus key, then enter the amount of the buyer's downpayment. Press the equals key to complete the subtraction. This is the amount of the seller's equity that is actually being lent to the buyer. The remainder of the equity is received at closing in the form of the buyer's downpayment.

      In our problem, now subtract from that equity, 30,000 the amount that the buyer is putting down on the property, 10,000, by simply hitting the minus key, then enter the amount of the buyer's downpayment, 10,000. Press the equals key to complete the subtraction. This 20,000 is the amount of the seller's equity that is actually being lent to the buyer. The remainder of the equity is received at closing in the form of the buyer's downpayment.

     

  3. Finally, you calculate the yield on the actual money the seller is lending as follows:

    • Press the PV key to enter the result of the calculation above.

      In our problem, Press the PV key to enter the result of the calculation above.

     

    • Now, calculate the payment surplus that the seller gets to keep each month by pressing the RCL key, and the number of the storage register used to store the wrap-around payment (probably 1).

      In our problem, now calculate the payment surplus that the seller gets to keep each month by pressing the RCL key, and the number of the storage register used to store the wrap-around payment (probably 1). The display shows -849.76.

     

    • Next, press the minus key and enter the payment from the seller's old mortgage.

      In our problem, next press the minus key and enter the payment from the seller's old mortgage, by pressing 563.66 and the key to indicate that the 563.66 is a payment.

     

    • Now, press the equals key to complete the subtraction.

      In our problem, now press the equals key to complete the subtraction. The display shows
      -286.10.

     

    • Enter the result into the Payment register by pressing the PMT key.

      In our problem, enter the result into the Payment register by pressing the PMT key.

     

    • The yield to the seller on the wrap-around mortgage is now computed by pressing the I/YR key.

      In our problem, the yield to the seller on the wrap-around mortgage is now computed by pressing the I/YR key give a result of 16.91.


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