From Steve Baker: "Funds that charge front-end loads often have lower annual expense charges than no-load funds. How long would someone have to hold a front-loaded fund for the difference to be worthwhile, all other factors being equal?"

First off, why not get a fund with no load AND a low expense ratio? That’s what I’d recommend.

Other than that, it’s simple math (which I will shortly complicate), and the same really as asking: "How long would someone have to live in a house to make it worthwhile to take a mortgage with higher upfront ‘points’ but a lower annual interest rate?"

Let’s assume we’re talking about a low-load fund with a 3% sales fee but half a percent lower annual expenses. Or a mortgage that charges 3 points upfront — 3% — but that bears a 0.5% lower interest charge than the no-points mortgage you’re comparing it with.

The answer your child should be applauded for giving you is: 6 years. That’s the breakeven. (If your child is destined to become a lawyer, or do well on her SATs, she should answer "more than 6 years," to match the wording of the question.)

You pay $3,000 extra on a $100,000 investment (or mortgage), but you save $500 a year, or $3,000 after six years.

(If your child is destined to become a tax lawyer, she might point out that mortgage points are not always immediately deductible where mortgage interest almost always is, which skews the comparison. Looking at it on an after-tax basis, which is the only way that makes sense, you’d have to do more math if the points were not immediately deductible as well.)

But what if your child isn’t 11, as we seem to be assuming here, but 24 and just out of Wharton?

Far from being applauded for a dumb answer like "more than 6 years" — yes, we know 3 divided by .5 is 6, but that’s not why we spent $50,000 sending you to Wharton — he should be sent to the toolshed, or out behind the woodpile, or wherever it is dumb MBAs in colonial days used to be sent for a thrashing.

Because the true answer rests on the discount rate you assign to the time value of money. If none, then a 3% load is indeed neutralized in 6 years by a fund with .5% lower expense ratio.

But of course money DOES have a time value. A dollar today IS worth more than the promise of a dollar a year from now. A bird in the hand IS worth two in the bush. (Three, if it’s a distant bush or the kind whose thorns rend your garment when you go bird-hunting in it.)

So, leaving aside the fact that you might not want to be locked into this fund that long in order to start reaping the benefits of a lower expense ratio, which is another reason to be skeptical of loads, there is also the fact that the .5% you save in Year 6 is not really worth nearly as much as it would be today, assuming you can make your money grow somehow over six years. And that’s also true, to a lesser extent, of the .5% you save in Year 5, in Year 4, in Year 3, in Year 2 and, yes, even in Year 1 (since the load is paid up front, but the benefit of the lower expense ratio is spread out over the year).

There’s a lot to be said about what discount rate to choose in doing a calculation. It’s not a number you’ll find printed in the Wall Street Journal each day (and it’s not to be confused with the famous Discount Rate charged banks by the Federal Reserve). Maybe one day, when there’s a truly personal Internet version of the Journal, there will be a listing for your own, personal discount rate, based on all sorts of confidential personal financial data anyone, and certainly the Journal, will by then be able to pull up on you. But not now. You have to pick one for yourself.

If you currently are paying 18% on a credit card balance, an appropriate discount rate for you to choose for many decisions might actually be that high — 18% — because that’s what you could earn, tax-free and risk-free, on a little extra money. To you, $118 in a year is worth $100 today. You could pay Visa either $100 now or $118 a year from now. Either way works out the same: you’d be $100 less in debt.

Anyhow, back to the issue at hand:

With a 10% discount rate (which is still high), .5% in 6 years is the same as about .27% today. (To check me, multiply .5 by 90% six times. Or do it with $50 instead. Each year, if it loses 10% of its value, it’s worth only 90% as much as the year before — $27 after 6 years.)

So using these assumptions, my financial calculator tells me it would take almost 10 years for the 3% load to be "neutralized" by a .5% lower expense rate. (This requires more multiplications than you would want to do by hand, or even with a regular calculator, because it’s different for each of the six years.)

If you used a 5% discount rate, a little under 8 years. If you were crazy enough to think the two hypothetical funds you were comparing could earn 15% a year, and thus used 15% as your discount rate — 17 years. If you actually do owe $17,000 on your credit cards and pay 18% on the balance, and were thinking of borrowing yet $10,000 more at that rate to make this investment, then it would never make sense to buy the load fund. You would never catch up from your savings on the annual expenses.

But like I say, none of this is necessary. Buy a no-load fund with a low expense ratio and nobody has to go to Wharton, which saves another $50,000.

Cheesecake Lovers: Hang On!


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