Engineering Finance

Solution Alternatives

A retired couple has just purchased an annuity that pays $2,000 each month. With today's prices, the annuity, along with other financial resources, provides a comfortable retirement income. The policy will pay the same amount every month until both husband and wife die. An annuity seems like a good idea because it is safe, but the couple worries about inflation. Say they live for another 20 years. The payment will still be $2,000 a month, but how much will that money buy then? We answer this question near the end of this lesson.

Inflation is the gradual increase of prices over a period of time. In the United States, prices as measured by the Consumer Price Index (CPI) have risen in every year since 1956. The link below opens a chart showing the CPI from 1967 to 2005. An index value shows the level of prices relative to the base year of 1983 where the index has the value of 100. To illustrate the affect of inflation, a person who went to work in 1967 with an annual salary of $12,000 would have to earn almost $70,000 in 2005 to have the same buying power. During that time the general level of prices has risen by a factor of 5.78.

The following links have charts and data on inflation in the United States.

Consumer Price Index
Consumer Price Index Data

The inflation rate in the United States has been relatively low since 1967 with the maximum year-to-year rate of increase somewhat below 14%. The rate in 2005 was about 3.36%. Other countries have seen higher inflation. The following gives cases of hyperinflation.

1922 Germany 5000%
1985 Bolivia >10,000%
1989 Argentina 3100%
1990 Peru 7500%
1993 Brazil 2100%
1993 Ukraine 5000%

Because a rate of 100% means that prices double in one year, the 5000% rate in Germany means that prices increased by a factor of 51 in one year. In Germany during hyperinflation, people would rush out to spend the day's wages as fast as possible, knowing that only a few hours' inflation would deprive those wages of most of its purchasing power.

The following web link has charts and data on inflation in the US.

U.S. Department of Labor ~ Consumer Price Indexes

Inflation makes it difficult to make financial decisions or even talk about relative prices at different points in time. This lesson provides quantitative tools that help with both of these problems.

Browser Page
  • Use the CPI to translate the general price levels between two points in time.
  • Given the prices of a commodity at two points in time, compute the average annual escalation rate for the commodity. Use the geometric mean for the calculation.
  • Express a cash flow with real or actual dollars. Translate between the two.
  • Given either the real or market MARR value, compute the other.
  • Do economic analyses by hand for simple projects.
  • Use the Economics add-in to do economic analyses for complex projects and for comparisons.
3.2.3 Inflation
Causes and Effects

Click the icon to view an introduction to the causes and effects of inflation.

Inflation Introduction
Expressing Cash Flows

Inflation makes it difficult to compare prices at different times. The cost of gasoline, tuition, medical expenses and other things a person or corporation might buy, typically increases with time in terms of dollars. Everyone knows, however, that a dollar today does not have the same value as a dollar in times past. Saying that the cost of something is greater than at some previous time may be true, but it is meaningless unless the effect of inflation is considered. This is partially accomplished by expressing costs in real dollars.

The money that we earn or spend in everyday commerce is measured in actual dollars. These dollars change with time with respect to the amounts that can be purchased with the same number of dollars because of inflation. When we express a price in terms of the dollars of a specified base year, the price is expressed in real dollars with respect to the base year. We translate between real and actual dollars using the general rate of inflation, usually measured by the CPI. The translation is not perfect because prices change because of other factors besides inflation, but the comparisons are more meaningful when they are done in real rather than actual dollars. The QuickTime lecture tries to explain this.

Real and Actual Dollars

The formulas below show how to translate between real and actual dollars for individual values and cash flows. The formulas assume that the base year for the real dollars is the present. Thus, we say that the real values are expressed in year-0 dollars. We use f as the general inflation rate. Note that the formulas resemble the present worth and future worth equivalence factors. When used here we are not moving money around, but changing the valuation of money.

It should be emphasized that only actual dollars are used in economic transactions. We carry actual dollars in our pockets, receive them as salary, and use them to pay bills. All the prices we see at stores and in advertisements are expressed in actual dollars. A real dollar is not real in the sense that it exists. It is a numerical measure that attempts to remove the inflationary effects from an estimate of a cost or revenue.


Our economic evaluations in earlier lessons have centered upon the MARR, or minimum acceptable rate of return. When inflation is present, cash flows can be expressed in real or actual dollars. There are two different MARR values that are appropriate to compute the present worth of the two kinds of cash flows. The real MARR is used for a cash flow expressed in real dollars. The market MARR is used for cash flows expressed in actual dollars. One might call the latter the actual MARR, but the term market is appropriate since we observe market interest rates in everyday commerce.

The MARR with Inflation

Again there are formulas for translating from one kind of MARR to the other. These are given below.

Estimating Future Cash Flows

Inflation introduces some complexities for estimating the cash flow for a project. We recognize three kinds of estimates. The cash flow is first estimated using the prices at the time of the estimation; we call these today's prices. The cash flow may consist of several components. For instance, it might include revenue as well as the costs of labor, capital expenses and various kinds of materials. The cash flows associated with different components may change at different rates. In the following we call the inflation rate associated with a specific component the escalation rate for that component.

We estimate the cost or revenue for a component using today's prices. These are the prices we pay today and might be found in current catalogs. For an analysis, we must project these prices into the future. We do that by escalating the estimate. The escalated values are in actual dollars.

When there are several components to the cash flow, we sum over the components to find the actual dollar cash flow in each period.

These cash flow values may in turn be expressed in real dollars by deflating the individual values by the general inflation rate.

Formulas for estimating escalation rates are in the linked document.

Escalation Rates
Economic Analysis

The economic analysis of a project requires either the actual or the real cash flow. There are two methods for finding the NPW, and they both lead to the same value. Either find the NPW of the actual-dollar cash flow with the market MARR, or find the NPW of the real-dollar cash flow with the real MARR. The QuickTime lecture below describes several steps for economic analyses with inflation. For simplicity the lecture only uses one cash flow component and one escalation rate.

Economic Analysis with Inflation

When there are several components, the relevant formulas are summarized on the page in the next link.

Economic Analysis Formulas

The following general rule summarizes the important result of this section.

When the cash flow is in actual dollars use the market MARR to find the NPW. When the cash flow is in real dollars use the real MARR to find the NPW. The NPW values computed with the two methods are the same.

In many cases it is difficult to estimate escalation rates so analysts may assume that the components of the cash flow escalate at the same rate as general inflation. When this is true, the analysis is very much simplified by the following rule.

When the escalation rates of all cash flow components are the same as the general inflation rate, the estimated cash flow is the same as the real cash flow. Use the real MARR to find the NPW.

The NAW is a uniform series expressed in real or actual dollars. The NAW is computed by multiplying the NPW by the A/P factor. If the factor uses the real MARR as the interest rate, the result is the real-dollar NAW. If the factor uses the market MARR as the interest rate, the result is the actual-dollar NAW. When comparing alternative solutions, it is better to use the real-dollar NAW. When the annual worth represents a payment in actual dollars, such as payments on a loan, it is better to use the actual-dollar NAW.

The IRR is the interest rate that makes the NPW equal to zero. If the real-dollar cash flow is used for the evaluation, the result is the real IRR. If the actual-dollar cash flow is used for the evaluation, the result is the actual or market IRR. When used for decision making, comparing the real IRR to the real MARR, leads to the same results as comparing the market IRR to the market MARR.

The Economics Add-in
The Economics add-in allows individual escalation rates for each component. It computes the NPW, both real and actual NAW and IRR values. It also computes actual and real cash flows.

The Economics add-in is easy to use and it should be handy for homework and computer based exams. For a review of the add-in basics without audio, click on the QuickTime icon.

Economics add-in with Inflation

Click the Excel icon for more extensive instructions at the ORMM site.

Economics - Inflation

To illustrate the use of the add-in consider the following example. A businessman is considering the purchase of an asset that has an initial cost of $2,000. The asset promises an annual return of $600. Its operating cost is $100 the first year, $150 the second, and increases by $50 in each subsequent year. The salvage value for the asset in 10 years is $400. These values are estimated in today's prices. The cash flow diagram is below.

To analyze the project with the Economics add-in, check the Inflation box in the Add Project dialog. Click the browser icon below to open a window with the Excel worksheet created by the dialog. The figure shows the project after we have added data. The data describes our assumptions about inflation and escalation rates. We are assuming a general inflation rate of 6%. Escalation rates for the components of the investment and cash flow items are entered as differences from the general inflation rate, or as incremental inflation rates. Here we see that the initial cost line has an incremental inflation rate of 4%. This means that the initial cost is escalating at a rate of 6% + 4% = 10%. Because the initial cost is expended at time 0, inflation has no effect on this value. The salvage value will, however, escalate at the 10% rate. Instead of being $400, as estimated in today's prices, the salvage will increase in actual dollars at a rate of 10% per year. The factor value for the row reflects both the 20% salvage estimate and the 10% price escalation.

Project with Inflation

For our example, we assume that the returns for the project escalate at a rate of 7%, that is, 1% greater than general inflation. Since this is a uniform series when estimated in today's prices, the return measured in actual dollars will increase with time. The return in one year when measured in actual dollars is equal to (1.07) times the value in the previous year. The uniform series representing operating cost is growing at a 4% rate, that is 2% less than general inflation. We assume that the gradient component is constant in actual dollars, so the escalation rate is 0 and the incremental inflation rate is -6%. The factors computed by the add-in and shown in the factor column of the form adjust the cash flows for the inflationary effects. The NPW values are computed in the right-most column.

The results of the analysis are computed at the upper right of the form. With the assumed parameters, the project has the NPW of $740.94, shown in cell L30. The positive value indicates that the project returns more than the MARR. There are two kinds of Uniform Worth. The first, in cell L31, is the NAW computed using the real MARR. This value is the uniform equivalent expressed in real dollars. The second, in cell L32, is the NAW computed using the market MARR. This value is the uniform equivalent expressed in actual dollars. Cell L33 holds the NPW for the study period. For the example, the study period is the same as the life, so this value is the same as L30. Cell L34 holds the IRR of the project computed using the real cash flows, while L35 is the IRR computed using the actual cash flows. Both exceed their respective MARR values.

Although the table above shows six measures for the worth of the project, they all lead to the same decision. They all indicate that the project is acceptable. For simple investments, the measures always give the same results. For non-simple investments where there are multiple values for the IRR, use of the RIC rather that the IRR resolves the ambiguity. We provide all these measures because they are useful in different contexts. Most decision makers probably prefer the Actual IRR as a measure because they are familiar with rates of return and most rates are expressed as market rates.

The Show Cash Flow command provides both actual and real cash flows. The payback period is based on the cumulative real cash flow.


To compare two or more alternatives with the same lives, compare their NPW values as described in an earlier lesson. The only complication introduced by inflation is in the computation of the individual NPW values.

When comparing alternatives by the NAW method, only the real NAW is relevant.

When comparing alternatives with the NAW method, it is most reasonable to compare their real NAW values.

To compare mutually exclusive alternatives with the ROR method, use incremental analysis. The incremental method can be performed with either real or actual cash flows. With real cash flows the decision to accept or reject uses the real MARR. With actual cash flows, the decision to accept or reject uses the market MARR.

When comparing alternatives with the ROR method, the IRR values computed for incremental investments depend on whether the cash flows are expressed in real or actual dollars.

The add-in has a Compare Projects command that explicitly compares two or more projects when inflation is present. Click the browser icon below to open a window showing the two alternatives used for an example. They are similar to the example described earlier, but the second has greater first cost and no salvage value. The assumed escalation rates are also different.

Comparison Alternatives

Click the browser icon below to open a window showing the Dynamic comparison created by the Compare Projects command. The comparison form allows the user to adjust the real MARR used for the comparison. It is found in cell M4 for this example. This cell is linked by formula to the real MARR values of the two alternatives. We have used Infl_B as the challenger and Infl_A as the defender, because Infl_B has the greater initial investment. The extra investment yields a real return of 15.4% and it is certainly justified when the real MARR is 10%. The cash flow of the comparison shows the difference between the two alternatives.

Comparison Results

It is more difficult to compare alternatives with different lives, because the least common multiple of the lives involves one or more like-for-like replacements. The availability of similar replacements is questionable when inflation is present. In this course we will not tackle comparisons with different lives when inflation is included in the problem statement.


We started this lecture with the question:

An annuity payment is $2,000 a month. How much will the payment be worth in 20 years?

To compute the result, assume an inflation rate of 3% a year, a number that reflects recent rates. You should answer:

In real dollars the payment is worth:

In 20 years the purchasing power of the payment is reduced to almost half of its current value.




. Browser Page
Inflation Summary


Inflation Problems


Navigation Front Page Lessons Resources

Return to Top of Page

Engineering Finance
by Paul A. Jensen
Copyright 2005 - All rights reserved

Front Page Lessons Resources