The cost of borrowing

The opportunity cost of borrowing

I'm a saver at heart. A dollar saved is another dollar I can mismanage investing. Yet, given the massive amount of credit card debt and home refinance debt of this country, there's a lot of non-savers out there. I have to believe that those with a spend-now attitude, the so called "gold collar" workers, simply don't know how costly it is to spend beyond your means. Yet sadly, I think even if they did, they wouldn't care.

I think one of the problems is non-symmetry of a dollar owed versus a dollar gained. Consider the following two scenarios.

1) Happy: If I told you I would give you an extra $1000 a month, how happy would you be?

2) Sad: In contrast, if I told you I'm going to increase your bills/housing cost by an extra $1000 a month, how unhappy would you be?

I'm betting you'd be a lot unhappier than happier. Yet if you borrow money (aka use a credit card and don't pay it off) you get your happy day now but suffer the (much) sadder days later. And there's more sad days than happy days. Doesn't seem like such a good deal does it?

But since this a column on investing, let's do the math.

Things are a bit different depending on whether you have the money or not. For the sake of simplicity let's assume you can either buy a $18000 econo car or spend another $10000 for a new $28000 nicer car. Clearly you'll be at least $10K poorer if you buy the nicer car. The question boils down to, how much does spending the extra $10,000 cost you down the line.

Case A: you have to borrow the extra $10K. (How you get the first $18K doesn't matter since in both cases it is treated the same).

[Nicer car] you have borrow the $10K and get a 8% loan for 5 years. This loan is short enough that we'll ignore the compounding of the interest. The total interest you'll pay is 10K * 8%/year * 5 years * 1/2 = $2K in interest. (The 1/2 comes in because after you're steadily paying down the principal and over the loan lifetime [5 years], on average you only have 1/2 the original principal building up interest. In reality, the 1/2 term would be slighly higher, say 0.55 or 0.60 since 8% * 5 yrs = 40% isn't completely negligible compare to the original loan). In general, for short term low interest loans, the interest you pay is Principal * Interest rate * Loan Duration * 1/2.

[Econo car] Instead, if you bought the econo-car and had invested the money you used for the loan payments, you would have gotten investment gains. Let's say you could earn a paltry 6% on your money. Over 5 years, again ignoring compounding the investment return you would get is $10K * 6%/year * 5 years * 1/2 = $1500. (Again the 1/2 is because initially you have no money invested and it linearly builds up, so on average over the 5 years you have 1/2 the money invested earning returns).

So with our numbers, that buying the more expensive car means you'll be $13,500 poorer after 5 years. If you don't like the loan rate and investment return I used, the formula is

Principal * (Loan Interest + Investment Return) * Loan Duration * 1/2.

In short it's a double whammy when you borrow, because instead of having the money grow, you're not only unable to invest, you're losing some of it to pay off the loan interest. And you never get this money back.

To beat this over your head, let's say instead you're borrowing with a credit card, which charges 18%. Then, borrowing this $10K (assuming you pay it off after 5 years, which is iffy) would cost you another $1K in lost money or a total of $4500. In reality, by ignoring compounding the numbers come out friendlier. So let's say that you'll really be down an extra $6K in addition to the $10K. Namely, not only are you $10K poorer, you have additionally agreed to dispose of out an extra $100 a month, every month, just to buy the nicer car. How much nicer was that car again?

Case B: you have the money.

Here, it's simpler. If you buy the cheaper car, you can invest that money and earn your 6% (or 8% or 10%) over 5 years, so after 5 years you are $14K to $16K richer. Here, I'm assuming compounding since the money is all there from the beginning.

So in this case the cost is
Principal * (Investment Return) * Loan Duration .

The last whammy

The other whammy is that if you spend more for a car or TV or dinner or most anything "fun", at the end of 5 years, that item usually isn't worth any more than if you just saved the money.
So in most cases, you really are out the $10K + the non-neglible cost of borrowing.

A few more notes

When does the of the interest rate matter? E.g. for a 2 year 6% loan, compounding is neglible but for a 30 year 7% mortgage, most of what you pay is the

Another case which a pesky reader asked about is what if you borrow when you don't have to and invest the money in something with more return than the loan interest rate. Again assuming a lightweight loan that you continually pay down, then your return on paper (aka you are making money, here) is:
Principal * (Investment return - interest rate) * Duration * 1/2.

But if you factor in taxes, things don't look so nice. You always pay taxes on investment gains, but for almost all loans (except mortgages) you get no tax break. Let your overall tax rate be TaxRate, so you get to keep (1-TaxRate) of your investments assuming you sell your investments to pay back the loan.

Principal * [(Investment return * (1 - TaxRate)) - interest rate] * Duration * 1/2.

If the loan was a balloon payment in which you pay back everything at the end, then the 1/2 goes away. This formula also makes intuitive sense.