Monday, December 26, 2011

Opportunity cost: student loans vs. mortgage

Over the past two weeks or so I read through Dividend Mantra's complete archives. I was introduced to him by MMM; Dividend Mantra had a guest post at MMM which is a nice introduction to dividend growth investing. The only downside is that hearing his story made me want to spend all my disposable income on dividend stocks, instead of paying down my student loans.

I talked myself down from that ledge. I'm the kind of person who gets fixated on certain things, and I've been practicing self-talk to keep my more obsessive side in check. Dividend growth investing does sound awesome. But so does paying off my student loans, and so does paying off my mortgage early.

I specifically brought up paying off my mortgage early. Now that I've read all of Dividend Mantra's posts, I looked for another Mustachian-flavored blog and happened upon Death to the Mortgage. I started reading it from the beginning. It's really inspiring, and I think one of the coolest parts is that they actually paid off their mortgage. Like, they're done, success, the mortgage is dead.

Naturally, Death to the Mortgage has gotten me excited about paying off my mortgage early. But I've already committed to vanquishing my student loans first. The question became: should I switch my goal?

My first consideration was that my mortgage is way bigger than my student loans, so it's a much longer-term goal. But past that I didn't have a good way to weigh one option versus another. So I fired up Excel and started playing with numbers. I was looking for a metric to help me decide where I should focus my early-payoff efforts. Here's the result, explanations to follow:

Loan / Target Principal remaining Monthly payment  "Payoff cost"
Mortgage  $ 407,716.50  $ 2,176.63 $   187.32
PMI  $ 42,116.50  $ 147.39 $   285.75
Sallie Mae (before)  $ 5,883.18  $ 69.88 $     84.19
Sallie Mae (after)  $ 3,883.18  $ 69.88$     55.57
Federal  $ 25,957.91  $ 192.85 $   134.60
Both student loans  $ 31,841.09  $ 262.73 $   121.19

Here I'm listing various expenses that I can eliminate by paying them off early. PMI isn't a debt but we can remove it when we have 20% home equity (that's where that "principal" number came from). I included two numbers for my Sallie Mae loan, since this weekend I sent a $2k payment to pay it down early. And I lumped both student loans together as the last line-item to offer additional perspective.

The last column is "payoff cost", which I got by dividing the principal by the monthly payment. Basically it's the average cost of decreasing your monthly expense by one dollar. For any given amount of money you want to use to reduce your expenses, you get the most bang-for-your-buck by going after the lowest "payoff cost" item first.

Notice how my Sallie Mae monthly payment is the same in both rows, but after I decreased the principal by making a big extra payment, the "payoff cost" number dropped. This illustrates that, now that I have less principal remaining on my Sallie Mae loan, it's cheaper for me to get rid of the Sallie Mae loan expense.

A downside to this "payoff cost" metric is that it doesn't consider term or total interest paid. That's fine because it's not meant to. What I'm looking at here is: how can I allocate my scarce money to best reduce my monthly expenses?

It's clear from the chart that paying off my student loans is a more effective way to reduce my monthly expenses than paying off my mortgage. What amazed me was how ineffective going after PMI is. I mean, $285 for each dollar per month of expenses saved? Expensive! Though, as a side note, a Safe Withdrawl Rate (SWR) of 3% corresponds to a "payoff cost" of $400, so there's another perspective for you.

Of course this isn't an apples-to-apples comparison. PMI isn't a debt, it's akin to throwing money away, and since by going after the mortgage I'll also be going after PMI, etc etc. But in terms of lowering my monthly expenses, targeting PMI should be at the bottom of my list.

I'm glad I did this exercise because it vindicated my focus on paying off my student loans. After my Sallie Mae loan I'll go after the federal loan, and after that I can worry about the mortgage. And some time in there I'll get started on dividend investing :)


  1. A couple of thoughts:

    1. It's probably better to look at total interest saved in some kind of near term window. This usually means knocking off the student loan. Typically this will be a loan that has a high interest rate that you haven't been paying on very long.

    2. You have to consider your tax situation. It's very likely the interest paid on your mortgage is tax-deductible. On the other hand, if you make $75k+ then there's a good chance NONE of your student interest is tax-deductible. This can make a big difference depending on your income.

    Keep working on those student loans. They'll be gone soon.

  2. Can you explain the "Payoff Cost" some more? I understand how you calculate it, but I am not seeing how it represents the cost of reducing the monthly payment by a dollar.


  3. Sure.

    Here's how I see it: by paying off a loan, I'm "buying" a reduction in my monthly expenses. The more money I owe on a loan, the more expensive it is to buy that monthly expense reduction. So if I pay off my Sallie Mae loan for $3883.18, I've bought myself a reduction in monthly expenses of $69.88, at a price of $55.57 per $1/month.

    Of course, this completely ignores the true cost of the expenses. That, basically, is the interest rate.

  4. @boringbill,

    Unfortunately you were right about #2. I started playing with TurboTax and none of my student loan interest is deductible. Huge bummer.

    I made a $2k payment that cleared recently. It feels good getting out of debt early.

  5. Wait a minute here .. why do you care about monthly expenses at all, rather than true cost? Aren't we going for long-term wealth rather than short-term cashflow? I'd suggest paying off the loan with the highest interest rate, regardless of balance!

  6. Hey MMM,

    First let me acknowledge that this post is some sloppy theorycrafting on my part. I'm working on a better theoretical justification of "payoff cost", but long story short, yes, interest rate is the primary driver of which debt should be paid off first.

    I do think there's an important tradeoff between minimizing total interest paid and minimizing monthly expenses. That's what I hope to address in a follow-up post. Admittedly it's somewhat of an edge case, but I'll let everyone pass judgement when I'm done.

  7. Mustachian acolyte- I went through a similar thought process recently. . . and the PMI won out handily! I wasn't concerned about 'snowballing' anything which is I think what your payoff cost basically tells you. Rather I just wanted to save the most money. The PMI was effectively a 3% fee on the amount of difference between 80% LTV and what I had above that. . .plus my mortgage is at 3.9% so, I'm getting a nearly 7% guaranteed return by paying it off. It might make sense to do a comparison that way.

  8. I recently discovered this "snowballing" concept and it is most of what I was trying to get across. If your interest is in saving the most money, PMI is a good target. I think our PMI is something around 1.5% but I could be totally making that up.

    For me I think the best thing is still to target my student loans, but I plan on reevaluating every so often and write it up if I decide to change course :)

  9. (Perhaps the same thinking as Slugsworth here)

    I've been thinking through the same dilemma, eliminating PMI versus eliminating some student loan debt/payments. I care more about true long-term economic cost rather than monthly payment.

    The way I look at is: I would have to pay $33,000 to eliminate PMI. Each year this $33,000 is costing me $4600 in PMI. $4600/$33000 = 13.66% which is a much higher rate than my student loan debt. This is true even though the PMI is only 0.5% in nominal terms. Plus I get the added bonus of reducing the interest accruing on my mortgage by more rapidly reducing the principal balance (as a 'side effect' of paying down to eliminate the PMI).

    As you get closer and closer to paying off the PMI it becomes more and more attractive. That last few hundreds dollar of principal you need to eliminate to pay off PMI is costing you a horrid effective interest rate -- doesn't work quite the same as student loans in my mind, since PMI is a fee which doesn't reduce in amount as you eliminate principal, while interest accruing on a loan is reduced as you eliminate principal -- even if your loan payment will stay the same.

    Putting everything in interest rate terms helped me make (what I think is) a fair comparison -- though I'd welcome other perspectives.

    1. That's a lot of PMI. I'm not surprised your calculus is different, and in your case I'd definitely support aggressive payments on the mortgage to eliminate PMI.

  10. I'm really enjoying your blog.

    Had to throw out one more consideration at which debt to repay.

    My sister and I had a conversation about her debts about a year ago. The biggest they had were mortgage and her husband's student loans. I asked why not pay off the student loan as fast as possible. Her response was that if DH was hit by a bus, his student loans are immediately forgiven, but the mortgage wouldn't be.

    I scoffed at the minuscule likelihood of that. Well, not 6 months later, he had a massive heart attack and died. These things happen.