Should I refinance? Help from any math wizards!

In My Humble Opinion
1

Here’s the situation. Our current mortgage is at 7.5%. The original loan amount was for $77,000 and now it’s at $66,000. The loan is a 15-year loan with a final payment date of October 2015.

But, when I went to check our acct. online, they had a thing that would let us refinance the remaining $66,000 for 5.875% for ten years. That meant the last payment date is November 2012. They would add on the additional $3,500 in closing costs to the loan, so we would be refinancing $70,000 at 5.875%. They estimate a savings of $24,000.

I’m somewhat confused because of one simple fact that I keep coming back to: why would they do this when it means they would lose $24,000? They lose three years of payments from us.

On the surface, this would appear to be a good deal. We make extra principal payments on the house every month and we would continue to do so even if we refinanced. When our truck is paid off next January, we plan on diverting that money toward the house payment. Would we save the same $24,000 if we simply put an additional $3500 against the principal?

BTW, I don’t know if the laws are the same in all states, but we can pay our house off early and not still have to pay the extra interest. In other words, if someone handed me $66,000 today, I could pay the house off and not owe another dime in interest.

2

Possibly because they know there rates are out of line with today’s market and you could easily refinance w/ another company and save a lot of $. They would rather have you at a lower rate then lose you.

3

They also get an extra $3500.00 up front, which is nice for them. You should consider shopping around for a possible no-points refinancing. There are any number of on-line sources you could check.

4

This is the correct answer. I am not a math wizard, but I have worked in the mortgage industry. Everyone is refinancing now, because rates are so low. Your lender is afraid of losing your business. It looks like a really good deal, but I agree with Finagle - it’s not impossible that you could get an equally good deal with someone else and not be charged the closing costs. Although, now that I think about it, that’s pretty unlikely. 15 year loans generally have higher interest rates than 30 year loans, and 5.875% would be pretty fabulous for a 30 year. So call around, but don’t automatically discount it because it seems too good to be true.

5

Wow, thanks for the responses everyone! You’ve convinced me to first look for a no closing cost refinance option with a comparable interest rate and not finding that, refinance with my existing lender.

6

It is so easy to be confused and misled with term loans. The idea of absolute savings in dollars is misleading because the interest you pay is the cost of using their money. Yes, you can save by paying it off sooner but that just means you did not get to use the money. If I return my rental car sooner I also save money but it does not mean I got a better deal from the rental company. Of course, if I do not need the car it is good to save money by returning it. The same with borrowed money.

The single most important thing you want to know is the equivalent interest rate you are paying after you consider all fees and expenses.

When you have too many variables it is difficult to compare so let us consider only the interest rate and equalise everything else.

Today you owe $66,000 at 7.5%. To equalise the comparison let’s say you would pay it back in 10 yrs, = 120 mo. which you can do if you want. Your monthly payment would be $783.43

You have been offered the option of changing this for a loan of $69,500 at 5.875%. In 120 mo the monthly payment is $767.24 so you save 16.19/mo but you owe greater principal for a while. The effective interest rate you pay is 7.03%, just a bit lower that the 7.5% you are paying. This means that is you are certain you will stay in the house and not refinance again, then you are better off switching to the new offer you have.

BUT

If you compare both options using a spreadsheet you can see that it is only after 52 months (4.3 yrs) that you break even. If you sell or refinance before that you have lost money. What are the chances you will stick with this mortgage to the end? Are the savings worth the risk? You have to evaluate those factors

Now, calculate the net present value of the $16.19/mo you save over ten years. Si it worth the trouble of refinancing? Is it worth the risk that you may sell or refinance again and lose money?

That is the way to analyse this problem and the way a company financing an investment would do it. Rules of thumb are worthless and a good way of misleading poor suckers into believeing they got a good deal when generally it is the bank who always hgets the good deal.

BTW, as I explained in another thread on the same topic, points and fees in practice amount to a prepayment penalty.

If you would like the Excel spreadsheet with the numbers just let me know

7

In the case we are considering ($66K, 10 yrs, 7.5% vs 5.875% $3500 fee)
the net gain at the end of 120 months is $2807. The NPV of that is about $1450.

In other words. If you have the absolute certainty that you will keep the new mortgage to the end then whatever effort refinancing requires yields you a value of $1450.

Give me the odds that you may sell or refinance after 1, 2, 3, 4, etc years and I will tell you whether the bet of refinancing yields a positive or negative chance.

To clarify a bit more what I said before: Points and other fees work as prepayment penalties because you owe more principal as you go along. compare two loans:

A- $100,000, no fees, 6.32395%, 360 mo @ $620.53
B- $103,500, $3,500 fee (net $100,000), 6.0000%, 360 mo @ $620.53

Note that in both cases you get the exact same net loan (100K) and pay back the exact same monthly payment for the exact same number of months. If you keep the loan to the end there is NO difference but if you cancel any time before that you owe more with loan B. That difference is a prepayment penalty which starts as $3500 and decreases over time to zero after the term of the loan is over.

To compare two loans meaningfully you have to take this into consideration. A loan with higher nominal interest can, in fact, be better for you.

It may be that the loan that works best if you keep it to the end works worst if you don’t. Then you need to consider the odds.

8

To continue with this fascinating analysis _ . . . .

The NPV if you cancel the loan after 30 months is -1192 (you lose money), after 60 mo $324 (you break even), after 90 mo $1169 and after 120 mo $1445.

So, assume your chances of cancelling the debt at those times are equal at 25% each. then the present value of your refinancing is $437.

If your chances are different just do the weighted average

9

Aaa! My head is going to explode! :slight_smile: (Would you believe I have a BBA?)

Thanks for the additional responses, but now I’m confused. Is it not worth the effort to refinance, or is it only worth it if we’re not going to sell for at least the next four years?

The chance of selling or refinancing again is very low. We like where we’re at, and we don’t have any intent of moving anytime soon. Also, we’ve done a lot of work remodeling this house already to make it exactly the way we like it.

10

Hey, confusion is not an acceptable response! Either you fall asleep or you understand everthing!

Ok, here’s the deal: If you keep the loan for the ten years, in exchange for the trouble of refinancing you have gained right now $1445 (minus any other expenses incurred on account of the refinacing). This is the NPV which will be about double in ten years.

If it so happens that you you cancel the loan after 90 mo it is still worth doing and you have gained a NPV of $1169

If you happen to repay the loan after 60 mo $324 your value gained now is $324 which pretty much means you wasted your time now for a measly $324 so you break even.

If you repay the loan after 30 months you have just lost today NPV of $1192 and you are better off sitting tight

And, obviously, if you repay the loan the next day after you refinance, you have lost $3500 plus time wasted.

Note that I did not say “if you move”, I said if you repay the loan which means refinance, repay, sell the house, whatever.

In my experience people are quite bad at predicting their future and there is much more uncertainty than they are aware of. “How could I imagine I could get laid off?” Duh! “How could I imagine this great opportunity would come up?” “How could I imaginemy mother in law would die and we would have to move?” In general people think they will stay in one place much longer than they actually do. We have seen threads of people desperately trying to get out of commitments whether they be apartments, cars or whatever. So, the thing is to be realistic. What are the chances you’ll want to sell or refinance or repay the loan? Maybe you’ll inherit money? What are the chances you’ll have to move? etc. Look at all the possibilities in a realistic way. If you are almost certain you will not refinance in any way in the next 7 years, then go for it. The longer you keep the loan, the more sense it makes. But also think that you are locking yourself in. If you decide to refinance or repay in 3 years you have just lost a bundle.

11

I have a question about the “effective interest rate” mentioned by sailor. The advertised rate was 5.875% and the “effective” interest rate was 7.03%. That seems like quite a big difference. Would the $3,500.00 closing cost being added to the refinancing account for the increase in interest rate? I’m interested in this thread because I’ve been toying with the idea of refinancing my condo with a home equity loan and remodeling my kitchen and bathrooms.

12

Part of the issue is who is the “they” you’re dealing with. I just re-financed…my mortgage broker got a fee, then his company paid off the old loan and got me a new one at the lower rate. The additional interest at the higher rate is the bank’s loss, not the broker’s, so it’s very much in his interest to entice you to do something which pays him a fee.

13

medstar, the points and fees are gimmicks which amount to a prepayment penalty since prepayment penalties are not allowed by law but banks do not want you to prepay. Look at it this way: $100,000 loan, $2,000 in points or fees, 5% interest, = 360 monthly payments @ $1060.66. The bank says they have just lent you $100,000 when in truth they have just lent you $98,000 and are giving you a lot of fancy explanations. The truths is you just got a loan for $98,000 at 5.44%, 360 months at $1060.66 with a prepayment penalty which starts out at $2000 and diminishes over time. That’s reality, the rest is their sales pitch.

If you give me your numbers I’ll comapre your loans for you.