“Time is money”.

Money has no monetary value except when it is put in the context of time. Stated alternatively: “A dollar today is worth more than a dollar tomorrow”. The value is the effect of time on invested money. This is the most basic principle of finance.

Interest is the rental cost of borrowing money. For the borrower, interest is the rent paid for borrowing money; for the lender the income earned from lending money. They are just different sides of the same coin. The concept of the time value of money is relevant in finance, accounting, law, and taxation.

Implications for Investors

There are two dimensions to value: future and present. Given a sum of money, we can determine its value at some future date if we know the interest rate at which we can invest the money. Conversely, if we know that we are to receive a sum of money in the future, we can determine its value today if we know the rate at which it is, or can be, invested. Thus, all money has “time value.”

There are two factors to consider in determining the present or future value of a sum of money: (1) the prevailing interest rate; and (2) the tax consequences of the two options. In lawsuits, it is the responsibility of counsel to raise time value issues to determine the discounted value of judgements looking to lost past profits or anticipated future earnings. Judges will not make such calculations on their own initiative.[1]

The value of money depends upon three factors:

1.    Principal amount (P);

2.    Interest rate (r); and

3.    Time (n).

 “Principal” is the amount of money originally borrowed or loaned. “Interest” is compensation for use of money [similar to rent]. Time refers to the period of borrowing, lending or investing.

All assets, tangible and intangible, can be expressed in terms of their future or present value if we can determine the rate at which the principal amount of the asset is invested or discounted over a period of time.

The appropriate rate is usually the market-determined interest or investment rate.

In economic terms, “interest” is the rental cost of borrowing money. As with all rentals, the cost of renting money may be fixed in advance, determinable at a future time, or variable according to specified conditions. Thus, interest and time are inextricably related. An interest rate is relevant if, and only if, it is specified in relation to time.

Although most of us are familiar with the calculation of simple and compound interest, we are less intuitive about the concept of the discounted value of future sums of money. This is because we are taught to think intuitively of investing for the future but not of the present value of sums of money to be received in the future. Yet, mathematically speaking, future value and present value are mirror images of each other looked at from different perspectives, such as the opposite ends of a telescope. The primary purpose of determining future and present values is to measure money in comparable terms across time periods by translating future dollars into economically equivalent current dollars, and vice versa.

Implications for Lawyers

 Lawyers deal with assets that have a “time value” in virtually all aspects of commercial practice in a variety of transactions. The following are some common areas where the principles of time value will arise:

?      Matrimonial settlements;

?      Computation of damages in litigation;

?      Valuation of charitable donations;

?      Valuation of life and remainder interests of trusts;

?      Truth in lending laws [example: interest on credit cards];

?      Usury laws under the Criminal Code;

?      Funding for children’s education;

?      Use of annuities in life insurance products;

?      Retirement planning;

?      Compounding interest on outstanding tax assessments;

?      Tax deferral and tax planning.

In addition to the above, all valuation decisions involving business and estate planning involve the time value of money. Although the context of usage may vary, the underlying principles are always the same: “Time is money”.

Financial Implications

The time value of money is intrinsic to financial and investment decisions, such as the valuation of equities and bonds. There are two underlying concepts to the time value of money: simple interest and compound interest.

Simple Interest

We start with the concept of interest and simple arithmetic.

Example 1

Suppose that Andy has $1,000, which he can invest at 10 percent simple interest per year.

If he invests the $1,000 for one year, he will earn $100 at the end of the year. If he invests for the second year, his interest will be determined on the original principal amount only ($1,000) but without any interest added, according to the same formula. He will continue to earn the same interest ($100) each year according the formula:

Interest = P x r x n

Where:

P = the principal amount invested;

r = the rate of interest for the time period; and

n = the time period.

The “n” in the formula is always equal to 1. At the end of four years, he will have earned $400, which equals 40 percent on his original principal of $1,000.

 Compound Interest

When we compound interest, the interest earned each year is calculated on the principal amount (P) and the interest earned in the preceding year.

Example 2

Suppose that India invests $1,000 for four years compounded at 10 percent per year. Then, at the end year 1, she will have earned $100 (same as simple interest), which is then added to the principal amount at the beginning of year 2. Hence, P in year 2 now equals $1,100. Then, she earns 10 percent on the enhanced principal of $1,100 and will receive $110. And so on. At the end of four years, she will have earned $464, which is 46 percent on her original investment of $1,000.

The compounding effect increases her rate of return by 6 percent over four years.

 Example 3

Suppose that Milo invests $10,000 for four years compounded at 10 percent per year. Then, at the end of year 1, he will have earned $1000 (same as simple interest), which is then added to the principal amount at the beginning of year 2. Then, he earns 10 percent on the enhanced principal of $11,000 and will receive $1100 in year 2. And so on. At the end of four years Milo would have earned $4,640 (rounded), which is 46 percent on his original investment of $10,000.

Note, despite their different absolute earnings, the ratio of India’s and Milo’s earnings remains the same at 1.46. In other words, regardless of the principal amount, the ratio for 10 percent for 4 years remains the same. Someone has pre-calculated the numbers in the body of Future Value Tables for different Rates (r) and Times (n), so that each ratio represents the shortcut for a specified combination of Rate and Time.

We arrive at the same result by applying a formula to determine future compounded values:

FV = P(1+r)n

Where

FV = future value

P = the principal amount invested;

r = the rate of interest for the time period; and

n = the time period.

However, the formula in this case is exponential in that the variable (n) is now the power, rather than the base. Applying this exponential function, we obtain:

FV = 1,000(1+.1)4

FV = $1,460

The Rule of 72

The Rule of 72 allows us to calculate the approximate length of time or interest rate that it will take to double an investment using compound interest. For example, assuming a compound interest rate of 8 percent, it will take approximately nine years (72/8) to double an investment. We can estimate the rate of interest required to double money in a specified number of years. For example, given an interest rate of 6 percent, it will take twelve years (72/6) to double an investment.

Retirement Planning

How much money will an individual require on retirement? Assume that Sacha invests $30,000 at 8 percent (average long term rate of return on equities) in a tax free account when he is 25 years old.

Without ever investing another dollar, Sacha will accumulate $960,000 by the time he is 70.

Berkshire Hathaway Inc.’s performance illustrates the power of compounding. For the period 1965-2019, Berkshire’s compounded annual gain equalled 20.3% compared to the S&P 500 (dividends included) gain of 10.0%. The overall gain was 2,744,062% (See: Berkshire’s 2019 Report to Shareholders).

Compounding Long-term Debt

 We see the dramatic impact of compounding in a recently reported incident in the sleepy hamlet of Mittenwalde in Eastern Germany. According to Reuters, the town historian (Vera Schmidt) uncovered a centuries-old debt slip dating back to 1562 in the archives where it had been filed. Mittenwalde apparently lent Berlin 400 Guilders on 28 May 1562 which was to be repaid with 6 percent interest per year. According to Radio Berlin Brandenburg, adjusting the debt for compound interest and inflation, the total debt now lies in the trillions. Apparently, the Mayor of Mittenwalde and his predecessors have asked Berlin for the return of their money and have made such a request every fifty-five years since 1820, but always to no avail. Mittenwalde, which had a population in 2012 of 8,800 people, would benefit enormously from repayment. Berlin, however, is not playing along. Why?

We should not underestimate the power of compounding interest in planning for retirement, paying off debt, and investing for the long run. Albert Einstein (Time’s “Person of the Century”) is reported to have said that compound interest is “the greatest invention in human history,” “the most powerful force in the universe,” and the eighth wonder of the world.” We ignore it at our peril.

[1] Lehrman v. Gulf Oil Corp. , 500 F. 2d 659, 672 (5th Cir. 1974, cert. denied, 420 U.S. 929 (1975).

Professor Vern Krishna, CM, QC, FRS, FCPA, Of Counsel: Tax Chambers LLP (Toronto)

[email protected]

www.vernkrishna.com