Blend and Extend Loans

amortization.com Ltd.
Burlington, Ontario
CANADA

905-639-0374
905-407-7988

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Blend and Extend Loans

Blending Two Loans

From a mathematical point of view, loans and mortgages are really the same thing, the only difference being the “type of compounding” used (“compounding” affects the value of the interest factor). Using the example below it matters not what the compounding is because it is easy to select it from a menu in the MORTGAGE2 PRO calculator.

When two loans are blended or consolidated into one loan, interesting questions arise!
The example shown is a loan of $200,000 at 3% and a second loan of $50,000 at 6%. This example could be considered a first and second mortgage even though the amortization period for a second mortgages is usually shorter. The same example could also be viewed as a mortgage with 5 years remaining in the term and wanting to borrow an additional $50,000 at 6% in order to perform home renovations. Monthly compounding was selected because that type of compounding is applicable for personal loans and collateral mortgages in Canada and all variations of loans and mortgages in the USA. The logic and calculations are identical had semi-annual compounding been selected which would address the bulk of Canadian mortgages.

What is the blended interest rate for the new blended loan? The answer depends upon your point of view. From the borrowers point of view, adding the two separate monthly payments together and paying down the total of the two principals over the next 5years is the obvious route. From a lenders point of view, the lender would like to receive the same yield (return on investment as per deemed reinvestment) as the sum of the yields for the two separate loans. Will the new blended rate satisfy both the lender and the borrowers concerns?

The first and obvious answer one would jump at, is the arithmetic average rate of 4.5% ( (3+6)/2=4.5% ). Probably the next answer would be the weighted average of 3.60%
(200/250 x .03 + 50/250x.06 = 3.60%)

The actual blended interest rate that would satisfy the lender and the borrowers concerns is arrived at as follows.

Negative amortization schedules for the two separate loans demonstrate what the monthly cash flows would accumulate to over 60 months. Add the two accumulations from the balance column together ($232,323.36 + $67,442.52) and you arrive at the lenders future value. It is assumed that the lender reinvests, at the same interest rate, the monthly payments as he receives them (aka deemed reinvestment). Using a present value of $250,000 and a period of 5 years the effective interest rate (the actual interest rate per period) is calculated as 3.697536% which corresponds to an annual interest rate of 3.64% at two decimal places( because of “monthly compounding”).

In this example, if the lender offered you the weighted average of 3.60% you would save yourself an extra few dollars in interest costs (approx $269) over the next five years, compared to having two separate loans at their respective rates of 3% and 6%.

Blend and Extend

The blend and extend calculation is performed the same way. Assume the amortization period is 30 years for the blended loan so that the monthly payments are more reasonable. The monthly payment for the blend and extend loan is $1,172.31 versus the blended monthly payment of $4,563.21 which was initially based upon the 5 years remaining in the amortization period. As before add the two FV balances ($491,368.42 + 301,128.56 = $792,496.98) and using $250,0000 as the PV and 30 years as the number of periods, calculate the Interest Rate per Period to be 3.920666%. Using the up/down arrows on the CALCULATOR until an AIR of 3.852% corresponds to an EIR of 3.9207400% and you see that the new blended payment is $1,172.31 per month. As a check or verification, one could set the payments to zero in the SPREADSHEET and see that the FV (this time calculated over 360 payments) agrees fairly well with the one time PV/FV calculation even though the EIRS are not exact. (within approx $17)

If a lender uses the weighted average method for a blend and extend loan you are ahead of the game by a little over a quarter of a percentage point and you would save an extra $12,849 ($172,030.21 - $159,180.82) over the 30 years.in this particular example. There are loans officers that use the weighted average method because they either don’t have time to perform the proper calculation or they don’t know how its done. Regardless of the reason the borrower saves significant interest costs over the 30 years. The lender may justify this as the cost of keeping you in the herd (retaining your mortgage business).

Note it is very difficult if not impossible to get present value future value numbers to agree to the penny in these FV/PV calculations because the exponent function in the mathematical equation is very sensitive to the number of decimal places used for describing the annual interest rate, that is why the total of the two monthly payments do not agree.