Inflation, Taxes, and Lousy Journalism

The Toronto Star recently featured an article that compared two financial strategies, namely paying off one’s mortgage versus maximizing RRSP contributions. The article provided a fairly generic analysis of the issue; however, towards the end, author Paul Brent presented a highly flawed and misleading quantitative example. The purpose of this short response is to explain the errors in Brent’s article and provide general tips on financial analysis.

The author’s scenario (see note 1) introduces us to a hypothetical 35-year-old Toronto resident who received a $10,000 windfall. He currently has a 5.5% rate mortgage with a $330,000 principal and a twenty-five year amortization period. The resident has a 35% marginal tax rate. The author compares the cash flow implications of a one-time excess mortgage payment to a one-time RRSP contribution (both in the amount of $10,000) (see note 2 & note 3).

Brent estimates that making a one-time mortgage payment will “save $25,000 over the lifetime of the mortgage” and will reduce the amortization period by 1.5 years. Based on the data provided, I estimate that lifetime mortgage payments would be reduced from $617K to $578K; this produces $39K in savings (actually quite a bit higher than Brent’s estimate). More problematically, Brent’s article is missing half the story.

One of the most fundamental principles of investment analysis is that long-term cash flows must be reduced (“discounted”). A dollar in the future is worth less than a dollar today for several reasons. First, due to inflation, the purchasing power of a dollar in the future is less than a dollar today. Second, since humans are generally risk-adverse, they must be compensated for the inherent risks in deferring use of their money. Therefore, due to factors including reduced purchasing power and human psychology, future amounts of money are inherently less valuable than current amounts.

To compare monetary values from different time periods, analysts look at the present value of future cash flows. The present value of a cash flow is the dollar amount from the future, translated into an equivalent amount today. For example, assuming 5% inflation compounded annually, $100 received ten years from now has a present value of approximately $61 ($100 / (1.05^5)).

The fundamental flaw in Brent’s article is that he fails to account for the corrosive power of inflation. While it is literally true that a one-time $10,000 mortgage payment will save a homeowner roughly $39K, most of these savings would occur more than a decade into the future. The benefits of lower mortgage payments in the future would be greatly reduced due to inflation. Assuming a 3% discount rate, the present value of the author’s proposed one-time $10,000 mortgage payment is just $19K. In other words, inflation erodes half of the estimated benefits of making an early mortgage payment. Failing to take inflation into account is sloppy and irresponsible because it greatly overstates the present value of savings.

Brent’s article is equally faulty when discussing the cash flow implications of a $10,000 RRSP contribution. He estimates that, given an 8% growth rate, the contribution would provide the taxpayer with an additional $50,000 of cash flow.

While it is literally true that the investment would grow by approximately that amount ($48K to be precise), Brent once again fails to account for inflation. Discounted at 3% (see note 4), the $48K increase in the investment is only worth $29K today. Inflation thus erodes roughly 40% of the growth.

Brent makes another critical error. He only considers the before-tax rate of return on the investment. The Canadian government taxes various kinds of investment income in different ways; failing to account for taxes could cause individuals to make poor investment decisions. All funds withdrawn from an RRSP are included in the taxpayer’s income (with a few exceptions, which are beyond the scope of this response). Assuming that the hypothetical taxpayer maintains a 35% marginal tax rate, his investment, adjusted to present value, is suddenly worth only $19K after tax.

Finally, the author does not suggest why an 8% RRSP growth rate is appropriate. Many bonds offer around a 4% return while Canada’s main stock market, the TSX, has grown at a compounded annual rate of about 12% over the past five years. The implicit assumption of a 50/50 split between debt and equity investments should have been explained clearly. Alternately, the author could have explained that a stronger preference for equity investments would make an RRSP contribution relatively more attractive than paying off the mortgage.

Brent’s article is faulty because he doesn’t account for two of the most fundamental problems investors deal with: inflation and taxes. By omitting two factors that significantly reduce investors’ true purchasing power, Brent is overstating the value of the benefits that taxpayers receive from following his advice. Promising taxpayers huge sums of savings that will never materialize due to inflation and taxes is misleading and dishonest.

I’d like to stress that I’m not offering any specific conclusions regarding the mortgage versus RRSP debate (because all of the numbers presented here are dependent on numerous case-specific assumptions). Also, non-financial factors should also be considered (i.e., a taxpayer who is debt-averse would be more likely to pay off his mortgage). Still, despite the inherent uncertainty in financial analysis, there are no excuses for the sloppy journalism present in the Toronto Star article.

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Several technical notes:

Note 1: Frank Wiginton, who developed the hypothetical scenario, deserves at least as much criticism as Brent.

Note 2: I'm still not sure how the author calculated a $25K savings. I'm fairly sure my calculation of $39K is correct.

Note 3: All of my calculations were done in Excel spreadsheets; I have not found a way to upload them here. If you wish to examine my spreadsheets or calculations, send me an e-mail.

Note 4: I am using a very conservative 3% discount rate. This reflects the Bank of Canada’s targeted inflation rate of 2% plus an additional 1% risk premium. Had I used a larger risk premium, the present value of Brent’s mortgage savings would have been reduced even further.