## Beware of phony math when borrowing to invest

A while ago in one of my videos, I made the point that borrowing to invest only makes sense if you expect to earn a higher after-tax return than the interest rate on the loan. Being a conservative fellow, I also argued that most investors are better off learning how to save than taking on debt to finance their retirement portfolios.

Well, this did not sit well with financial advisers, who think borrowing to invest is the best thing since rising-crust pizza. After all, borrowing gives them more assets to manage and puts more fees in their pocket. One adviser, whom I'll call Jordan, even provided some calculations to "prove" that borrowing to invest is beneficial even if the investor earns a lower after-tax return than the interest rate on the loan.

Is this really possible? To find out, we'll examine Jordan's claim in detail (I've edited and condensed his e-mail for clarity). For simplicity, I'll assume that interest charges and investment income both compound tax free.

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John,

I just watched your video on "borrowing to invest in an RRSP". You say that if the loan interest is X per cent you need to make the same interest in your investments just to break even. This statement is simply not true.

Consider if you took out a \$25,000 loan @ 8 per cent, and paid it off over 10 years.

Total interest paid: \$11,398.28

Total liability (loan plus interest): \$36,398

Therefore \$25,000 invested @ 8 per cent = \$36,398, right? WRONG! In fact, \$25,000 invested @ 8 per cent for 10 years = \$53,973. So you're ahead by \$17,575.

For \$25,000 to grow to \$36,398 over 10 years your investments would need to grow just 3.83 per cent! Thus, to break even on an 8-per-cent loan your investments would need to yield just 3.83-per-cent annually.

You may wonder why I felt the need to write this e-mail. My intent is to try to give you an insight so you can make more helpful videos moving forward.

Jordan

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Jordan:

Thank you for offering to help me make better videos. However, your math is flawed, not mine.

You state that \$25,000 invested at 8 per cent over 10 years would compound to \$53,973. I agree.

Further, you state that if you borrow \$25,000 at 8 per cent and pay off the loan over 10 years, you'd pay \$11,398.28 in interest and \$25,000 in principal, for a total of \$36,398. I agree with that as well. This works out to 120 monthly payments of \$303.32 – out of your own pocket.

To recap: Over 10 years you spend \$36,398 of your own money – \$303.32 a month – to retire the loan. You now have \$53,973. So, as you say, you are ahead by \$17,575.

Great! But here's the key question: Where did this \$17,575 come from? You seem to think it was made possible by borrowing, but you're wrong. The \$17,575 was entirely because of your own contributions of \$303.32 a month.

The proof? Consider a second scenario where, instead of taking out a loan, you started with nothing and invested the same \$303.32 a month at 8 per cent. There is no loan to retire, so instead of paying off debt all your money is earning compound interest at 8 per cent.

Guess what? After 10 years, your money would grow to \$55,491.19. (The only reason my number is slightly higher than your \$53,973 figure is that I used monthly compounding, whereas you assumed annual compounding.)

In both cases the growth is all because of your own contributions. The fact that you borrow at 8 per cent, and earn interest at 8 per cent, is a wash. They cancel each other out.

Now, I want to show you why borrowing at one rate and earning a lower rate is a money-losing strategy.

In your example, you state that you need to earn just 3.83 per cent for \$25,000 to grow to \$36,398 over 10 years. True. But does that mean if you borrow at 8 per cent and earn 3.83 per cent you come out even? Not at all. You would earn a negative return of 4.17 per cent (8 minus 3.83) on every borrowed dollar. So the sooner you pay off that loan, the better.

The only reason you "break even", as you claim, is that over 10 years you put in \$36,398 – \$303.32 a month – of your own capital to reduce this money-losing debt to zero. As this harmful debt is reduced, the \$25,000 compounding at 3.83 per cent makes a larger and larger relative contribution to your net worth. In other words, by making monthly payments against your loan you are slowly digging yourself out of a hole and eventually you will recoup all of your losses and "break even" as you say.

But I would point out that investing \$36,398 of your own money and ending up with the same \$36,398 10 years later amounts to a nominal return of zero. After inflation, your real return would be very much negative.

Even without taking inflation into account, borrowing at 8 per cent and earning 3.83 per cent is a terrible idea. If you still aren't convinced, consider what would happen if you didn't borrow at all. Instead of taking out a loan, you decided to invest your \$303.32 a month at 3.83 per cent. After 10 years you'd have \$44,265 – about \$8,000 more than if you'd borrowed.

Clearly, not borrowing is superior in this case. Why? Because if you borrow at a higher rate than you earn, you lose money.

Now, this is not to say I am against borrowing to invest in all cases. Companies borrow all the time, but only if they are confident they can earn a higher after-tax return by investing the money. Similarly, experienced investors can use leverage prudently, but again, only if they believe they can earn a higher after-tax return than the after-tax interest rate on the loan. There are also certain circumstances where taking out a short-term RRSP loan makes sense.

However, I don't believe that borrowing to invest is appropriate for all investors, because the interest rate on the loan creates a serious hurdle to overcome, particularly when combined with other fees.

I realize that borrowing to invest benefits lenders, fund companies and advisers. They all make money when clients borrow. But you owe it your clients to give them an accurate assessment of the potential risks and rewards, free of spurious calculations that purport to justify the practice.

Investment Reporter and Columnist

John Heinzl has been writing about business and investing since 1990. A native of Hamilton, he earned a master's degree from the University of Western Ontario's Graduate School of Journalism and completed the Canadian Securities Course with honours. More