What return and cashflow improvement do i get from pre-paying 10k on 2.3% 20 year mortgage?

SPC100

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Hi,

I always considered the return from reducing my mortgage was the same as the interest rate on my mortgage i.e. 2.3%. But I never paid much attention to the cashflow benefit (if you leave the term the same).

The calculations below, indicate after paying 10k on a 20 year 2.3% Mortgage, I get 624 Euro / 6.2% back per year.

How do I explain this illusory return?

Calculations (from drjeacle calculator)

100k mortgage, 20 years, 2.3% = 520.21 per month repayment
90k mortgage, 20 years, 2.3% = 468.18 per month repayment

If I 'invest' 10k in mortgage repayments, I gain 52.03 per month (520.21-468.18), 624.36 per year.

624.36*100/10,000 = 6.2436% Return p.a.



==============================
I edited this post to add the answer here - As this turned into a long thread, and brendan was concerned people might get mislead



The answer:


My financial return is 2.3%, but the series of cashflows that give me this return are different.

e.g. I think it is easier to understand this if you pretend you are the bank, e.g. imagine you were the bank and you loaned me 10k, I could pay it back it to you in two different ways:

230 euros per year for 20 years, and then the 10k back at the end (deposit account/interest only mortgage style)
624 euros per year for 20 years, and 0 extra back at the end (typical mortgage style - try Karl Jeacle mortgage calculator 10k loan, 20 years, 2.3%).

the cashflows you would get are very different, but the interest rate is still 2.3%

You can visualise/understand the higher cashflow as getting back some of your capital each year, instead of getting it all back at the end.

If you put your 10k in a hypothetical 2.3% after tax deposit a/c for 20 years, You get the former series of cashflows, if you pay off your mortgage you get the latter series of cashflows.

Nit: For me to end up with a similar sum from both cases at the end of 20 years, I would need to re-invest the additional cashflow at 2.3%
 
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SPC100

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I used to always count it at 2.3%, but after a recent large mortgage payment, I noticed the cashflow gain was much higher.

I see how if it was an interest only loan, my gain would be only 2.3%, and the calcs confirm it:

100k mortgage, interest only, 2.3% = 191.67 per month repayment
90k mortgage, interest only, 2.3% = 172.50 per month repayment
(191.67-172.50)*12*100/10,000)=2.3%

And If I do the calcs for e.g. a 100 year mortgage, the 'gain' is calculated to be 2.6% of my 10k p.a. (over 100 years the annual capital payment is very small).

I don't think i have a good internal visualisation/representation of how my capital is included in the return. Can you explain it a bit more please?
 

RedOnion

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You're counting the entire reduced outward cashflow as return, but not factoring in the initial large negative cashflow (repayment) as far as I can see?
 

Zenith63

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Seems to me you've 'invested' €10000 which will allow you pay out €12485.13 less over the course of the mortgage, so a €2485.13 return/'profit' over 20 years. Or 1.24% per annum? Mortgage calculations are so unintuitive...
 
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RedOnion

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Ah sorry, I see it now (I think).

You're calculating the 6.2% as simple interest over 20 years.

Edit: I'm confusing myself at this stage! It's a coincidence that the simple interest return works out the same.
 
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orka

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I don't think i have a good internal visualisation/representation of how my capital is included in the return. Can you explain it a bit more please?
Your 6%-ish return would be correct if the 10K was a normal investment and you got your 10K back after the 20years. But you don't - it's gone.
It might help to imagine it as a one year 'investment'. If someone offered you a 20% return (2,000) for one year on your 10K but they kept the 10K, you can probably see it's not a great deal despite the (interest/principal) looking high. It's the same concept with the 20 years.
 

Zenith63

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People make them much more complicated than they actually are.
The calculations are logical and certainly since I've learned (through AAM) to focus on the interest it takes away much of the complexity, but for the average person their intuition is to factor capital payments in the 'cost' etc. - their intuition leads them astray or it is unintuitive...

Curious where I've gone wrong in this case coming to 1.2% though...
 

SPC100

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If you overpay a loan which charges you x% a year, you are saving x% a year. No more and no less.
Brendan
So, based on wording like this, 10,000 overpaid on a loan of 2.3%, one would expect a 230 p.a. saving.

BUT, in fact, the outgoings actually reduce by 624.36 p.a.

I was surprised by the ~3 times difference in additional cashflow vs the "calculated saving".
 

RedOnion

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I was surprised by the ~3 times difference in additional cashflow vs the "calculated saving".
The sum of all the differences between 230 and 624 is the initial 10,000 which you have left out of calculation.

If you give me 100 euro today, and I give you back 101 euro next year, you haven't made 101% return, you've made 1%.
 

SPC100

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The sum of all the differences between 230 and 624 is the initial 10,000 which you have left out of calculation.
it's not that simple...(624-230)*20 = 7880, or maybe I misunderstood you.
 
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Brendan Burgess

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I will say it again.

It's very simple.

If you overpay a loan which charges you x% a year, you are saving x% a year. No more and no less.

If you come up with y, you are doing it wrong.

Brendan
 

SPC100

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Brendan, while I understand the benefits of having rules/shortcuts, I like to understand the how, and be able to prove it to myself.

So, based on wording like this, 10,000 overpaid on a loan of 2.3%, one would expect a 230 p.a. saving.

BUT, in fact, the outgoings actually reduce by 624.36 p.a.
So, Why is the cash flow increase much higher than the calculated saving? I think I have internalised it now!

Three ways to think about this, that helped make it clearer:

1. If I pay down all 100k of the mortgage, I would no longer have to pay the annual mortgage payment of 6,240p.a. But my return can clearly not be 6.24% p.a. as the loan was by definition at 2.3%! i.e. My loan balance would go to 0, My future cashflow would increase by 6240, I would get a 2.3% financial return on my 100k.

2. Do a mortgage monthly calculation for the lump sum you are going to pay down using the term of your mortgage. e.g. 10,000, 20 years, 2.3% = 52.02 per month. i.e. If I pay down 10k, I will save 52.02 euro per month in future cashflow, or 52 euro per month is enough to pay a 10k 2.3% mortgage over twenty years. But the return is still 2.3% on your 10k.

3. Each mortgage payment is made up of some part to reduce the loan balance, and some part to pay off this months interest.

So, When I pay off the 10k, the loan balance instantly reduces by ten thousand (I immediately have the benefit of the lower balance), and I can only calculate my financial return as not paying interest on this 10k in the future. but my future payments will be lower as there is a) less capital to repay. b) lower interest amount due to lower balance on the loan.


The financial return is the same as your mortgage rate.
The cashflow improvement, is the same as what the lump sum would cost you to mortgage on the same terms as your mortgage.

I think is very interesting to keep the annual cashflow improvement in mind though when budgeting, and to be aware that it can be a lot larger than than lump sum multiplied by interest rate.

Thanks for the discussion folks, it helped me to figure it out.
 

Sarenco

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If you overpay a loan which charges you x% a year, you are saving x% a year. No more and no less.
Strictly speaking that's only true of an interest-only mortgage.

With an amortising mortgage, making a principal repayment ahead of schedule has a compounding effect because more of your subsequent (scheduled) payments go towards paying down principal (thereby further reducing the interest payments).
 

JoeRoberts

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To be pernickity, OP would also need to factor in the opportunity cost of not investing the extra repayments in another guaranteed savings product.
 

SPC100

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Otherways to look at at my return on my 10k.

If I invest 10k in a bank at 2.3% for 20 years. Ignoring tax, after twenty years I should have 10000*1.023^20 = 15758.

How do I show the same ~16k total return from my mortgage prepayment?

If I 'invest' 10k in a mortgage, I get a cashflow saving of 624 each year. 623*20 years = 12,480. But that is not accounting for any interest on each cashflow saving. If i can invest the 624 each year at 2.3%, my spreadsheet shows me making cashflow savings over the same 20 years of about 15,622, which is close enough to the hypothetical investment.
 

SPC100

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Yes. I am now convinced the return on my 10k prepayment is 2.3%.

But the annual cashflow improvement is not 230 euro (as one might assume from dealing with deposit accounts), but 624 euros.
 
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