Wraparound Mortgages – Calculating the yield

Wraparound Mortgages – Calculating the yield

Lennox wanted to sell his apartment building and put a price of $155,000 on it. He had an existing first mortgage in the amount of $155,000 on it. The apartment building already has an existing mortgage of $75,000  that had 20 years remaining with an interest rate of 8% per annum. 

Glen an investor wants to buy the apartment building and offers to pay the following terms:

Price of Apartment Building: $150,000

Cash down                            $35,000

Wraparound                           $135,000 (this would be a 20 year payout at 10%)

Glenn then explained to Lennox how this would return a yield of over 13% over the term of the mortgage. We can show this with illustrations. In the proposed financing $150,000 wraparound. It will be set up with a 20 year amortization at 10% per annum. This would put the total annual payment at around $13,317. The required payment on the existing mortgage is $7,527 which would be substracted from Glens annual payments of $13,317 this leaves around $5790 for Lennox. This translates into a monthly payment of around $482.00 for the 20 years (unless he sells the mortgage or uses it in an exchange for another property). This payment, on the equity in the wraparound of $40,000 wouuld correlate to a monthly payment based on the 20 year payout of around 13.5%

How was the Yield on Lennox’s mortgage Calculated?

Since there was only one existing mortgae, and the wraparound was for the same term as the existing mortgage this is fairly simple caculation. So what happened was by the end of the term which is 20 years each mortgage would have been fully paid off. Glen would make one payment each month that would total about $13,317 for each year of the 20 year period. At the same time Lennox or any successor holder of that mortgage wouuld pay the existing payment of $7527 per year and collect on the difference of $5789 on an equity of $40,000. Therefore to find the actual effective yeiled on this wraparound for the total term of the mortgage (20 years), you simply need to find the constant rate on the payment toward the difference. As long as the terms of the existing mortgage and the wraparound are identical and there is no interim ballon mortgage there is relatively quick way to calculate the yield by finding the constant rate of payment on the difference. 

How to find the Constant Rate of Payment on the Difference

1. Once you have determined that there is an annual payemnt of $5789 which you have calculated by taking the total payment on the wraparound and then subtracting the payment on the existing mortgage. You then take this figure and divide this amount by the total amount owed on the difference (known as the equity in the wraparound). In our example it is $40,000 but it could be any amount. 

2. The sume off $5789 divided by $40,000 equals 0.144

3. Next we convert the answer  of 0.144 into a percentage amount by moving the decimal two placces to the right. The percentage is not 14.47. This is known as the constant rate of payment for an amorizing mortgage with monthly payments. 

4. You will need to locate Constant Annual percents Table. This is a table EXpressing the sum of 12 Equal Monthly Payments need to Amortize a Principal Amount for the Term of Years Shown. On the Y axis of the table are the pecentages slowing increase in increments as move down the page. On the X axis were the number of years of the loan increasing in increments as move from left to right across the page)You then then go the 20 year column and find the constant percents that come closest and bracket 14.47% we derived earlier. 

5. In our case we found the following percentages.

Percent Interest                                       Twenty years

13.25                                                        14.273

13.5                                                           14.488

From these figures we can deduce that since the desired percent is more than the 13.25% percent interest but slightly less than that for 13.5% percent interest, the actual effective interest yield on the difference for the full term of the wraparound mortgage is about 13.45% since our rte of 14.47% is closer to the 13.5%.

What we can conclude from this

If Lennox were to hold this mortgage for the full 20 years, his effective yield would be 13.45% per year. This would be based on his equity of $40,000 and the mortgage payments to full term. However it is important to remember that mortgages do not allways run to the full term. If Glenn for Glen decided to sell the property after a few years, the new buyer would probably want to refinance to a new terms from an institutional or other lender. This would be good news for the holder the wraparound mortgage, because if the mortage is paid off there can be a bonus to the holder. 

When the Mortgage is Paid off Early

When a mortgage is paid off early the holder of the can receive a interest rate bonus. To expalin this assume that Glen sells the property at the end of the first year and a new buyer refinances the wraparound, paying off the amount owed. Take a look at the table below

—————————————————————–Wraparound mortgage—————–The existing mortgage

Original amount                                                    $115,000.00                                      $75,000.00

Annual Payment                                                   $13,317.00                                        $7,527

Term of years                                                        20                                                      20

Interest rate                                                          10%                                                   8%

End of which year                                                 19 years                                            19 years

Amount still owed                                                 $113,100                                           $73,412

The final amount is found by finding the constant rate for the remaining term, at the interest rate for the mortgage, and dividing that rate into the annual payment. 

If Glenn paid off the wraparound it would cost him $113,100 out of which Lewis would have to pay $73,412 leaving him with a balance of $39,687 from the original $40,000 difference. At the end of the first year then, Lennox would have gottten.

—————————————————————————————————————————————–

In monthly payments                                                                                                    $5,789.00

Payoff at the end of the year                                                                                        $39,687.00

Total amount paid to Lennox                                                                                        $45,476.00

Subtract orignal Principal amount                                                                                $40,0000

                                                                                                                       —————————

Net interest for the first year                                                                                          $5476.00

Therefore the effective yield bae on an annual return for the first year based on a payoff of the existing mortgage and the wraparound at that time would be found by dividing the original principal amount which is $40,000  in the net interest for the year. The sum of $5,476 divided by $40,000 roughly equals 13.62% per annum. 

The point of this example is that with a wraparound mortgage the actual effective yield will be higher if the mortgage is paid off early than if held to maturity. This mortgage yield went from 13.45% to 13.69 on the prepayment of the first year. The yield earned at the end of the first year payoff in a mortgage which is described will be its maximum annual yield. Each year thereafter, the mortgage yield will move closer to the $13.45 per annum.