## Why not look at total dollar loan costs when considering paying down/off a loan?

Non-investing personal finance issues including insurance, credit, real estate, taxes, employment and legal issues such as trusts and wills
harikaried
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### Why not look at total dollar loan costs when considering paying down/off a loan?

When someone asks about paying extra towards a mortgage in the context of either 1) extra savings that could be invested or 2) selling taxable gains, the mathematical considerations tend to focus on interest rates and expected rates of return. I would think that some people can better relate to actual dollar amounts instead of percentages as paychecks are dollar amounts. So why the focus on rates?

For example, a \$100k 4% 30-year fixed mortgage has a payment of ~\$500/mo resulting in ~\$72k total interest paid over 30 years.
[A] Putting a \$10k windfall towards the mortgage 1 year later results in ~\$19k less total interest paid.
[B] If instead the \$10k windfall came at year 7, only ~\$13k interest would be saved.

Alternatively, if one could pay an extra \$500/mo, the total interest paid over ~11 years would be \$23k saving \$49k in interest.
[C] Similarly a \$10k windfall after 1 year in addition to the extra payments now only saves an additional \$5k in interest.
[D] And if that \$10k windfall came at year 7 with the additional payments, it saves just \$1k as the loan is already almost paid off.

If instead of a windfall, one had \$10k of taxable investments that could be sold with \$1k of capital gains tax, all of the above comparisons could effectively combine the interest costs with the capital gains tax costs. So instead of saving \$19k in interest with the "windfall" in situation [A], one would be saving \$18k instead. Similarly it might not make sense to realize the gains in situation [D] as the "windfall" would result in about the same amount of taxes being paid as interest being saved.

Is something missing by looking at dollar costs instead of rates?

Gill
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### Re: Why not look at total dollar loan costs when considering paying down/off a loan?

Yes, you are overlooking opportunity cost.
Gill

Pajamas
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### Re: Why not look at total dollar loan costs when considering paying down/off a loan?

There is nothing wrong with looking at dollars instead of percentages when comparing investments. They are just different ways of looking at the same thing. It makes no difference to say that sales tax is 5% vs. \$0.05 on a \$1 item or that a \$1 investment pays \$0.05 or 5%.

With investments, you also need to consider time. When you make an extra \$10,000 principal payment at the beginning of the loan you are reducing the interest by a larger amount than at the end of the loan, which you would expect as the time the \$10,000 is "invested" is very different. I don't see what you are trying to point out there.

Principal payments on a loan to reduce interest paid provide a guaranteed, predictable "return" compared to most investments. The obvious exception is almost-risk free investments with fixed returns such as a CD but I tend to think of that as more of a savings vehicle than a true investment because the real return is usually not much more than inflation, if it even keeps pace with inflation.

grabiner
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### Re: Why not look at total dollar loan costs when considering paying down/off a loan?

The problem with comparing dollar amounts is the time value of money. If you pay an extra \$1000 this year to save \$1100 ten years from now, you haven't come out ahead, since you can invest \$1000 for ten years and earn more than \$1100.

Opportunity cost is another way of looking at this difference. If you don't pay that \$1000 now, you could invest it instead. The risk-free ten-year investment is a zero-coupon Treasury bond, which yield 2.55%; a \$1000 investment would be worth \$1286 at maturity. Thus \$1000 now is worth \$1288 in ten years if you can invest it tax-free (for example, in an IRA).

It is reasonable to compare dollars if they are paid in the same year. If you have a 3% mortgage in a 25% tax bracket, then paying an extra \$10,000 on that mortgage will save you \$300 in interest next year, which is \$225 after tax. If you instead put that \$10,000 into your Roth IRA and invest in the ten-year bond, you will earn \$255 in interest. If you put \$13,333 in your 401(k) instead, you will earn \$340 in interest, and you can keep \$285 of that (and \$10,000 of principal) after withdrawing the money at a 25% tax rate. And if you continue to hold this ten-year bond, you will earn more in interest on the bond than you pay on the mortgage every year.
David Grabiner

harikaried
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### Re: Why not look at total dollar loan costs when considering paying down/off a loan?

Gill wrote:Yes, you are overlooking opportunity cost.
Doesn't one run into the same issue when using rates? Some people say you can pay down a 4% mortgage to effectively save 4%, but there's the opportunity cost of what else could have been done with that money. Additionally, that 4% saved is not entirely clear as it has different benefits if that extra payment removes just 1 future payment or 100s of payments. In either case of rates or dollars, one should also take into account tax effects (of deduction changes, effective bond savings rate, etc.).

dm200
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### Re: Why not look at total dollar loan costs when considering paying down/off a loan?

I am involved in several aspects of consumer credit, loans, etc.

I often encounter very flawed thinking and approaches to these issues. Here is one:

Folks with a mortgage loan and carrying credit card balances regularly paying extra principal on their mortgage, while carrying credit card balances (and paying interest). When I point this out, they tell me that over the life of the loan, the mortgage will cost more dollars in interest so they think they are making the right choice.

afan
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### Re: Why not look at total dollar loan costs when considering paying down/off a loan?

Classic net present value problem. You have to take account of the timing and discount rate for each cash flow. Not many people can do NPV in their heads. So they come up with shortcuts, ignoring the time value of money or considering only interest rates.

If you do NPV the results are in dollars, or whatever currency you choose.
We don't know how to beat the market on a risk-adjusted basis, and we don't know anyone that does know either | --Swedroe | We assume that markets are efficient, that prices are right | --Fama

grabiner
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Location: Columbia, MD

### Re: Why not look at total dollar loan costs when considering paying down/off a loan?

dm200 wrote:I am involved in several aspects of consumer credit, loans, etc.

I often encounter very flawed thinking and approaches to these issues. Here is one:

Folks with a mortgage loan and carrying credit card balances regularly paying extra principal on their mortgage, while carrying credit card balances (and paying interest). When I point this out, they tell me that over the life of the loan, the mortgage will cost more dollars in interest so they think they are making the right choice.

And the argument I make in this situation is that if you pay off the credit card, you will save in credit-card interest, and then you can use the money which was previously going to credit-card payments to pay off the mortgage, saving in mortgage interest as well. (This is a common issue in "which debt to pay off" discussions; if you pay off one loan completely, this frees up extra cash to pay off other loans, so the benefit doesn't go away when the first loan does.)
David Grabiner

qwertyjazz
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### Re: Why not look at total dollar loan costs when considering paying down/off a loan?

'"Consistency is the ..."
If you used dollars at the same time frame across all decisions, then it would be the same. The math is easier to compare, rationally in percentages across things.
But the reality - I think - is most people think in dollars regardless of time - current cash flow or future without regard to opportunity cost. So the question would not be putting the money in the stock market vs paying down mortgage. It would be about the great post Christmas sale that we are losing out on by not buying things we really do not need.
So if thinking of the money saved convinces you to pay down mortgage, do it. We are not rational creatures without heuristics.
G.E. Box "All models are wrong, but some are useful."

harikaried
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### Re: Why not look at total dollar loan costs when considering paying down/off a loan?

Pajamas wrote:With investments, you also need to consider time. When you make an extra \$10,000 principal payment at the beginning of the loan you are reducing the interest by a larger amount than at the end of the loan, which you would expect as the time the \$10,000 is "invested" is very different. I don't see what you are trying to point out there.
It was more for comparing situation [A] to situation [C] where someone might already be paying extra towards the mortgage, so does it make sense to use the windfall towards the loan or invest instead? In particular, the \$10k saves \$19k in interest for [A] while only \$5k for [C], so someone might decide to invest the windfall in the latter case expecting to earn more than \$5k in 10 years.

harikaried
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Joined: Fri Mar 09, 2012 3:47 pm

### Re: Why not look at total dollar loan costs when considering paying down/off a loan?

grabiner wrote:The problem with comparing dollar amounts is the time value of money. If you pay an extra \$1000 this year to save \$1100 ten years from now, you haven't come out ahead, since you can invest \$1000 for ten years and earn more than \$1100.
dm200 wrote: Folks with a mortgage loan and carrying credit card balances regularly paying extra principal on their mortgage, while carrying credit card balances (and paying interest). When I point this out, they tell me that over the life of the loan, the mortgage will cost more dollars in interest so they think they are making the right choice.
qwertyjazz wrote:If you used dollars at the same time frame across all decisions, then it would be the same.
I believe all of these responses are getting at the same thing of future dollars are worth different from today/current-year dollars, and afan has provided a new-to-me financial term that seems to address how to evaluate those dollars:
afan wrote:Classic net present value problem. You have to take account of the timing and discount rate for each cash flow.
I did a quick look at a couple places:
https://en.wikipedia.org/wiki/Net_present_value
http://www.investopedia.com/terms/n/npv.asp

I would think the discount rate of future years should be the treasury bond rate that grabiner used for the appropriate length of time. I believe it should be a decent approximation to just use the average duration's treasury bond rate for a constant discount rate instead of picking a discount rate for each year.

What would the net cash flow be each year? An additional principal payment from the first year should appear as part of each of the future year's cash flow "earning" ("not expensing?") the amount paid times loan interest rate?

In my search about Net present value in the context of mortgage, it seems to be something already used by mortgage servicers to evaluate loans for whether it's profitable to them. Are there other ways to evaluate loans that lenders use that borrowers should also use to make a better financial decision?