Calculating Return from Early Principal Payment on Mortgage

[chrispy]

In an attempt to better my skills at capital allocation, as an exercise I put together an Excel sheet that attempts to calculate the rate of return from an early payment to the principal of a mortgage.  The numbers and situation do not apply to me and the example is strictly math based.  The example I was trying to calculate is:

 

$100k, fixed 30 year, 4.25%

Person is able to put down $10k (10% of mortgage) at some point during the 30 years

Calculate the return of the early $10k payment

 

The excel sheet works fine at determining how much principal, interest, and when the loan will complete early.  Due the amortization of the mortgage, the return depends on when the payment is made during the life of the loan.  The trouble I am having is determining the return of the $10k that was paid to the principal early.  I put together a few cases off to the right that try and determine the return.  I dont think any are exactly correct.

 

Could anyone provide guidance on this calc?

 

Thanks!

 

EDIT: Is it just as simple as you save the 4.25% of the $10k every year?  Should there also be a way to account for the shortened duration of the loan?

AmortizationCalculator.xlsx

[gfp]

I think you are overthinking it.  The annual return on the prepayment is the mortgage rate. 

 

In the real world, the after-tax cost of the mortgage loan (in the United States) is less than the headline rate because of the tax deductibility of the interest.  So if you were comparing 'returns' for the money you were considering making a mortgage principal prepayment with, in the real world you would want to compare after-tax returns.  The 4.25% would be less after taxes in the United States.  And you would compare that with other after-tax returns available to you.

 

[JRM]

I think the answer is a little more complicated than a risk free 4.25% return.  Because of the amortized nature of a mortgage loan a pre-paymement earlier in the loan term has a larger affect than later in the loan term both in terms of the interest reduction and loan period. 

 

The question is what is the optimal use of your capital.  I recently went through this exercise for myself, and I calculated the present value of the interest portion of the payments that were eliminated due to the pre-payment (or early payment) or my mortgage.  The interest payments eliminated will be on the back end of the mortgage term, so the further away they are the less they are worth in present value terms (although it always feels better to eliminate loan payments).  The hard part is to determine a reasonable discount rate.  My remaining loan is fairly short (6 years) so I don't feel comfortable assuming 6-8% if I invest the money in the market over that short of a time period.  I used 2% for my discount rate.  I should be able to collect at least this much in dividends/interest with the money during the next 6 years.  The discount rate represents my opportunity cost. Then divide the calculated present value by your $10k to determine the return.  This exercise is a little easier if you are looking at paying off the remainder of the loan.

 

Chances are investing the $10k in the market for 30 years will be better return than pre-paying a mortgage with a low interest rate.  Although, I'm all for getting rid of a mortgage payment.  The amortized mortgage payment is a soul sucking burden.  Freeing up that monthly cash flow is liberating.

[TorontoRaptorsFan]

I highly recommend paying your mortgage off as fast as you can.

 

There's peace of mind that you'll feel when you realize you no longer have to make a payment to the bank and next paycheque is all yours to keep.

 

 

 

[Ross812]

Mathematically your return on paying on the mortgage early is the interest rate - tax - [risk free rate - inflation] (Just use the current I bond rate)

 

So its the mortgage rate 4.25% - tax deduction (depends on income probably between 0-1% use .5%) - I-Bond 1.96% =  1.8% over an I-Bond. It is also not risk free because holding onto a mortgage means the bank is taking on inflation risk (you are hedging inflation) and there is optionality to walk away if property prices implode i.e. the bank is taking on a portion of the housing market risk.

 

I agree with paying off the mortgage gives peace of mind, but mathematically it is a poor capital allocation. 

[chrispy]

Thank you for all of the responses.

 

I agree with how it is a poor use of capital if the person is going to sell the property before the mortgage is paid off.  But if the person was to pay off the mortgage 2 years early and stay at the property, does that person receive a hefty dividend for 24 months?

 

Either way, it does not seem like the best use of capital.  Thanks for everyone's input.