Time is Money: Part 2

Covid 19 is causing havoc in the economy and small businesses are suffering daily. However, businesses need to be cautious about tax disputes that are pending on assessments in the Tax Court of Canada, which is closed for business during these troubled times. Outstanding assessments can accumulate interest at an alarming rate. In Part 1, we described the forms of interest and their effect on savings. In this part, we go the next step to see their impact on future values, retirement planning and tax assessments.

We saw in Part 1 that there are two forms of interest, simple and compound. We refer to interest paid only on the amount originally invested, but not on any interest that accrues subsequently, as simple interest. Simple interest is a function of the principal sum (P) multiplied by rate (r) multiplied by time (n):

Interest = P × r × n

Example 1

If Nicola deposits $10,000 in a guaranteed investment certificate (GIC) for a period of one year at 6 percent, the GIC will be worth $10,600 at the end of the year. The interest earned is $600, or 6 percent of the principal amount for one year. If she invested at 6 percent simple interest for four years, the total sum of interest will be $2,400, and the GIC will equal $12,400.

In contrast, compound interest refers to the process whereby interest is earned not only on the amount originally invested but also on subsequently accrued interest. Compound interest starts out with exactly the same formula as simple interest but extends it to account for the reinvested interest. Thus, the interest on the second and subsequent time periods is calculated exponentially on the initial principal amount and any interest accumulated in preceding time periods.

Example 2

Suppose one invests $10,000 in a GIC at 8 percent compounded annually for two years, the GIC is worth $11,664 at the end of the second year. At the end of the first year the principal and the interest are $10,800 (the same as with simple interest). But the interest for the second year is calculated as 8 percent of $10,800, which is $864

Future Values

Future value is the sum to which an amount, or a series of periodic equal amounts, will grow at the end of a period of time, invested at a particular compound interest rate. Hence, future value (FV) is the amount to which a current Principal (P) will grow at the end of a period of time (n) invested at a compounded rate (r) of interest:

FV = P(1+r)n

Future Value tables specify the value of $1(P) at various interest rates (r) over various periods of time (n). The tables are a simple way of applying the formula. Alternatively, one can use a financial calculator.

Example 3

Jasmine invests $5,000 in a TFSA, which will earn 8 percent interest compounded for twenty years. The future value of $1 at 8 percent for 20 years is a factor of 4.66. Hence, $1 will grow to $4.66 in twenty years. Therefore, $5,000 will grow to $23,300 in that time.

Future value tables typically relate interest rates (r) and time (n) on an annual basis. Where the compounding is more frequent, we must adjust the r and n factors to accommodate more frequent compounding effects. The formula demonstrates that the longer the time horizon for investment and the more frequent the compounding intervals, the greater the future value of a present sum of money.

Example 4

Suppose that in example 3, the 8 percent annual rate is compounded semi-annually. Then we adjust r to 4 percent and n to 40 semi-annual periods to accommodate semi-annual compounding. The appropriate factor of $1 is 4.80. Hence, $1 will grow to $4.80 and $5,000 will grow to $24,000. The semi-annual compounding yields $700 more than annual compounding.

The more frequent the compounding, the higher the cost of borrowing or the rate of return. We can generalize the future value factor when a contract requires interest compounding more than once a year and still use the tables. When interest is compounded c times a year, multiply the number of years that P will be invested times c and divide the interest rate (r) by c and then see where the two lines intersect in the table.

Example 5

Suppose that Ravi deposits $2,000 in a tax-free account that pays 6 percent per year, compounded semi-annually, for five years. The bank will pay 3 percent every six months (6%/2) over 10 times periods (5*2). A future value table gives us a factor of 1.34. Hence, the $2,000 will grow to $2,680 in five years.

The lesson is simple: a lender will benefit from compounding interest as frequently as possible and the borrower will pay more for frequent compounding. Thus, in an open and competitive market, the borrower and the lender must negotiate both the interest rate and the frequency of compounding intervals.

Impact of Interest on Tax Assessments

There is no negotiation on interest rates in tax law. The Income Tax Act and Regulation 4301 prescribe the rates to be charged and they are set each quarter. There are two principal rates:

1.    The rate of interest payable by a taxpayer to the CRA on late taxes;

2.    The rate of interest payable by the CRA to a taxpayer on refunds.

The prescribed rates in Q1 2020 are as follows:

Refunds (4%)

Late Taxes (6%) 

The rate of interest paid to taxpayers is taxable as income. The rate payable on late taxes is non-deductible and must be paid with after-tax dollars. Translated, this means that a taxpayer with a 50 percent marginal tax rate will need to earn 12 percent income to pay 6 percent in late taxes. Even though the Tax Court is closed these days because of Covid 19, the interest on outstanding assessments does not stop accumulating. Not a very good deal for the taxpayer but lucrative for the tax collector.

CRA compounds interest on a daily basis on outstanding amounts of taxes payable [§ 161(1) and §248(11) ITA]. Hence, it is almost always to a taxpayer’s advantage to pay her taxes on a contentious assessment and then challenge its validity at a later date. It is virtually impossible for a taxpayer to obtain an alternative investment that will yield an equivalent amount of interest for the same risk. Since tax disputes can continue for 10 to 15 years (some even longer), the daily compounding effect has an enormous financial impact on the ultimate amount payable if the taxpayer ultimately loses the appeal. 

Example 6

Suppose that Greg owes $50,000 in assessed taxes. If unpaid, at a rate of 6 percent (Q1, 2020), the tax bill will climb to $91,100 in 10 years. The $41,000 of interest payable will not be deductible for tax purposes. Hence, a taxpayer with a 50 percent marginal tax rate would need to earn $82,000 just to pay the interest. If Greg pays the $50,000 assessment upfront and wins his case after 10 years, he will receive his $50,000 together with interest of $24,590, but it will be fully taxable. Hence, a 50 percent marginal rate taxpayer would retain only $12,295 net of taxes. A nice source of revenue for a spendthrift government!

Taxes and Investments

Taxes play a significant role in determining future values. Taxes payable reduce the amount of interest available for reinvestment (the “r” in the formula) and, hence, reduce the compounding effect on the principal sum. 

Example 7

Suppose that Nicola invests $10,000 in a tax-sheltered investment that earns 10 percent compounded annually for ten years. At the end of ten years, the future value of the investment will be $25,900. The accumulated gain of $15,900 represents the gross compound interest over a period of ten years. Thus, the money more than doubles in ten years.

However, the results change dramatically if Nicola invests in a taxable investment.

Example 8

If Nicola pays tax at 40 percent on her earned interest on a current basis, she will have only 6 percent to reinvest each year. The future value of $10,000 invested at 6 percent (net) will be $17,900 at the end of ten years. Thus, the ultimate value of the net after-tax investment is only $8,000, or 31 percent less than its value in the tax-sheltered investment.

Taxes erode investment returns. Here we see the simple mathematics of tax planning for investments, retirement, tax shelter programs, and the benefits of tax deferral. Since taxes decrease the amount that can be reinvested, it generally pays to defer the payment of taxes (the longer, the better) provided that the CRA is not accruing interest on the outstanding amount.

 Example 9

A $1,000 investment compounding annually at 20 percent in a tax shelter is worth $1.47 million after forty years. If the investment is taxed annually at 25 percent, the net return is 15 percent and the investment is worth approximately $267,000 in forty years.

If taxed at 40 percent, the net return is 12 percent and the investment is worth only $93,100 after forty years. Hence, tax deferral is one of the most effective means of retirement and estate planning.

Nominal and Effective Interest Rates

When we speak of interest rates, we must distinguish between “nominal” and “effective” rates. The difference between the two depends upon the method of calculation and the frequency of the compounding period. For example, when we say that a person borrows money from a bank at 10 percent annual rate of interest, that is the nominal rate. The effective rate of interest will also be 10 percent, but only if interest is calculated at year-end. As we saw above, if the compounding period is more frequent, the effective rate of interest increases. This is important with credit cards that disclose annual percentage rates (APR) but charge interest monthly. If the APR is 18 percent annually, the monthly charge rate is 1.5 percent, which makes the effective rate of interest 19.56 percent.

 Section 347 of the Criminal Code of Canada makes it a criminal offence to charge usurious interest rates, which is defined as annual interest that exceeds 60 percent. The purpose of the provision is to discourage loan sharking. In fact, the provision is rarely applied against “loan sharks”, who, instead, use other unorthodox collection methods (see The Sopranos for a dramatic account of the techniques used). The provision is more often used against legitimate commercial lenders.

In Garland v Consumers’ Gas Co, for example, the defendant gas company sold its gas to consumers under a sales agreement that contained a late penalty payment (LPP) clause that required customers to pay a charge of 5 percent on monthly unpaid bills if payment was not made within sixteen days. On an annual basis, the LPP violated Section 347 of the Criminal Code if a customer paid within thirty-seven days, but not if a customer paid after that period. Applying a “wait-and-see” approach, which determines the effective rate of interest when payment is actually made, the Supreme Court of Canada held that the LPPs violated the Criminal Code.

Interest is at the root of all money decisions because time is money.

Professor of Law, University of Ottawa, Tax Counsel, Tax Chambers LLP (Toronto)