The phrase “time value of money” must surely be one of the most used terms that people don’t really understand. Almost invariably, people who don’t know a discount rate from Adam use the term to explain or question any financial complexity. The irony—and most business school students and graduates know this—is that time value of money isn’t all that complicated. Or at least it isn’t at the conceptual level.
The time value of money concept, which applies to loans, means that you need to include interest costs in any analysis of loans. In other words, to compare “loan A” to “loan B,” you need to account for the interest costs of each. Note that this isn’t the same thing as saying you need to compare the interest rates, however. The interest rate of a loan is important. It’s the first of the three variables used to calculate the interest charges of a loan. But you need more than just the interest rate to know what, for example, “loan A” costs. You also need to know the loan balance against which the interest rate is applied. (This is the second variable.) And you need to know for how many periods—years, months, or whatever— this calculation is made. (This is the third variable.)
Interestingly, truth-in-lending laws make it easy for consumers to make time value of money comparisons of different borrowing options. By comparing the annual percentage rate, or APR, of one loan with another, one can generally tell which borrowing option is cheapest. The APR wraps all of the costs of borrowing—all the time value of money—into a single, interest-rate-like number. By choosing the lowest APR, a consumer generally gets the cheapest loan. Unfortunately, it isn’t as easy for business borrowers to get APR information. (Truth-in-lending laws, for example, apply to consumers but not to business borrowers.) Nevertheless, it’s still generally most useful to make time value of money comparisons of different borrowing options by applying the APR concept.
The time value of money concept also applies to investments, with a slight twist: When applied to investments, you need to factor in the interest or investment earnings generated by an investment. In other words, to compare “investment A” to “investment B,” you need to account for the interest or investment returns of each. Note again that isn’t the same thing as saying you need to compare the interest rates or investment rates of returns, however. The interest rate or rate of return on an investment is important. As with borrowing comparisons, it’s only the first of the three basic variables used to calculate the investment profits from an investment. You also need to know the investment balance against which the interest rate or rate of return is applied. (This is the second variable.) And you need to know for how many periods—years, months, or whatever—this calculation is made. (This is the third variable.)
As a general rule, when people perform time value of money comparisons on investments, they compare either the present values of the two investments or the rates of return of the two investments. The rate comparison method is easier to understand because it works very much like the APRs that lenders provide consumers. To compare “investment A” with “investment B” on the basis of interest rates or investment rates of return, you compare two percentages; whichever is larger is better, so the logic goes.
Comparing investments on the basis of their rates of return, however, creates a handful of problems, as you may already know. First, simple rate comparisons ignore the fact that the investment balance is important. For example, earning a 25% return on a billion dollars is far more profitable than earning a 100% return on a million dollars. Second, simple rate comparisons ignore the rate at which intermediate cash flows are reinvested. If you have 1 million dollars to invest for 10 years and are choosing between one investment which pays 25% for one year and another investment which pays 15% for 10 years, for example, you can’t know which is better unless you know the rate at which your money can be reinvested in year two. Third, return-based investment measures sometimes suffer from a sort of mathematical phenomenon in which the return formula can’t be solved with a single, unique interest rate or investment rate of return value.
Because of the aforementioned problems with applying the time value of money to investment calculations, business analysts commonly compare investments based on their present values. Two investments’ cash flows can be evaluated on an “apples-to-apples” basis by comparing their present values: whichever investment provides the greater present value is better.
You can also compare the present value of an investment’s cash flows to its initial cash cost, making what’s known as a net present value calculation. A net present value is actually a simple cost benefit comparison. You compare the cost of an investment, meaning its cash price, with its benefits, calculated as the present value of its future cash flows. If the net present value is positive, it means the benefits exceed the cost. If the net present value is negative, it means the cost exceeds the benefit.
A challenging feature of present value and net present value calculations concerns the choice of a discount rate, or interest rate, used to convert future cash flows to their current-day, present value. For example, people argue in favor of using the cost of the capital used to fund an investment. If an investment is made using borrowed money that costs 8%, for example, someone taking this approach might use 8% as the discount rate. Another commonly argued approach is to use the rate of return offered by similarly risky investments. If you can make an investment that forces you to bear the same risk and pays a 12% return, some people argue that you should use a 12% discount. In practice, it’s worth mentioning, that one often sees discount rates set almost as a matter of management policy or as an arbitrary decision made by a key participant in the financial analysis process. In a case like this, top management might say, perhaps explicitly, that investments must produce at least a 15% return and that would mean that present value calculations should be made with a 15% discount rate.
Dealing with Inflation
One important issue you want to consider in making time value of money calculations is the effect of inflation. Over time, of course, inflation erodes the value of the currency units used to make time value of money calculations. This erosion makes it difficult to compare currency values of different time periods. For example, 1 million dollars today isn’t the same thing as 1 million dollars 20 years from now.
You can, fortunately, rather easily estimate the effect of inflation in your time value of money calculations. To do so, you simply need to use the real rate of return rather than the nominal rate of return in your calculations. You calculate the real rate of return by subtracting the inflation rate from the nominal rate of return.
As an example of how all this works, suppose that you want to estimate the future value of a long-term investment in a stock index fund. Over long periods of time, the stock market returns about 10% and inflation runs about 3.5%, so the real return equals 6.5%. If you used 6.5% in your time value of money calculations—rather than the nominal rate of return of 10%—the future value amounts you’d calculate wouldn’t include inflation. In effect, by subtracting the inflation rate from the nominal return, you subtract the effects of the inflation from the compounded, future value amounts you calculate.