Glossary of Time Value of Money Terms

Michael Sack Elmaleh , CPA, CVA

Video: Inflation

One fundamental reason for time value conversions is to account for changes in the purchasing power of money. When the purchasing power of the dollar goes down over time this is called inflation. When the purchasing power goes up this is called deflation. Historically inflation is far more common than deflation. If we were simply measuring the purchasing power decline in time value formulas, we would substitute the rate of inflation for the “i” term in our time value formulas.

The possibility of future inflation presents challenges in applying time value conversions. Fist as we have seen before “i’ in some applications represents an opportunity cost. This is the rate of return that we could have earned if we did not use funds for a particular purpose like funding a specific business investment opportunity. Usually, a risk-free interest rate like the rate of return on treasury bonds is used for this purpose. It reflects the minimum return for the use of our money.

Does the Risk Free Rate Encode Inflation?

The conceptual problem that arises is the possibility that this risk-free rate already encodes the expected changes in purchasing power due to inflation. And there is some reason to believe this is true. When treasury rates are low this reflects the fact that the Federal Reserve governors do not expect significant inflation in the near term. When rates are higher this reflects the Fed’s expectation of higher inflation.

Take a close look at this chart below which maps the annual rate of inflation measured by the changes in the Consumer Price Index (CPI) and the average return on the Ten-Year treasury note from 1950 through 2019. You can see that the curves track each other very closely. You will also note that the treasury rate in most years is slightly higher than the inflation rate. This would seem to imply that if we use a treasury rate as our “i” in time value formulas we would not need to separately adjust projected cash flows for the impact of inflation.

Just How Should We Encode Inflation?

Suppose we think that the risk-free treasury rate is not sufficient to account for all expected losses in purchasing power. Our challenge then is how to specifically adjust our cash flow projections to reflect this loss. The standard metrics for inflation are Department of Labor Statistics price indices, one termed a Consumer Price Index (CPI), the other a Producer Price Index (PPI). The CPI is a measure of the average change over time in the prices paid by urban consumers for a market basket of consumer goods and services. Indexes are available for the U.S. and specific geographic areas. The market basket covers expenses in food and beverages, housing, apparel, transportation, medical care, recreation, education and communication, and other goods and services.

In contrast the PPI measures a representative sample of intermediate goods and services utilized by all economic sectors in producing their final output. One way to distinguish the CPI from the PPI is to say that the CPI measures prices from the standpoint of the consumer, while the PPI measures price changes from the standpoint of the seller.

There is a strong inclination when projecting future cash flows in a time value problem to simply use one of these indices to reflect future inflation. Let’s go back to the retirement example we looked at in an earlier chapter. There a person wanted to know whether they had enough savings to retire. In that example we used the prospective retirees current living expenses as the benchmark for her future living expenses once retired. We did not adjust those expenses for the impact of inflation because we argued that any expected increases in cost of living would be more than offset by increases in rates of return on her retirement savings.

How Reliable is the CPI?

Suppose we wanted to be more conservative and adjust her living expenses for expected inflation instead. What rate of inflation should we use? Should we use the most recent rates of inflation based on the CPI, or should we use an average rate based over a certain number of years? What problems might we encounter in utilizing the CPI as an adjustment factor at all? It turns out that there are more than a few problems in using the CPI to adjust future living expenses. The CPI has its critics.

One criticism is that the CPI ignores the ability of consumers to substitute cheaper products and services for more expensive ones. A second criticism is that the CPI ignores the impact of innovations that actually reduce the costs of basic goods and services. An obvious example is the dramatic reduction in the cost of long-distance communication. Another criticism involves the CPI’s so-called urban bias. The CPI looks at a market basket for urban consumers. But price changes may be quite different for rural and suburban consumers. Spending habits may also differ for different demographic groups as well. Young city dwellers may have radically different spending habits than older city dwellers.

Beware of Long Term Averages

What’s the conclusion? At least with respect to the retirement example prudence might dictate at least some allowance for increases in cost of living that would not be compensated for by adjustments in social security payments and rates of return on pension assets. Given that inflation rates have been under 2% annually for some time an annual adjustment of between 1 and 1.5% might be appropriate.

What about our savings for college example? This is an economic sector where inflation has been anything but modest. Here is a chart showing the annual and cumulative percentage increases in tuition costs from 1990 to 2020.

You can see that over this period tuition costs have risen almost 180% or just under 6% per year. So, in projecting the amount of savings needed should we assume that costs will compound at about 6% per year?

Not so fast. If you look closely at the inflation curve you will note that the greatest amount of annual increase was in the 90’s and aughts. You can see that in recent years the rate of annual increase has tailed off significantly. In fact, the annual average growth rate for the last six years has been only 2.5%. So, if our parents are going to adjust for inflation a rate of inflation in this range would be far more realistic.

I think the key take away should be that in time valuing future cash flows a great deal of judgment is called for in applying inflation increases. Do not robotically apply the latest CPI or PPI figures. As in the case of college tuition if there is separate historical pricing data available it should be utilized instead of a composite index. If the cash flow projection covers only a few years, it may be acceptable in times of relatively modest overall inflation to not adjust future cash flows at all.

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