Computation Section
Investment Economics


The add-in can also be used to analyze economic investments with price inflation. The inflation analysis is available with or without taxes. We repeat the example used earlier, but add the effects of inflation. We first neglect tax considerations. In this section, we show how to describe and compare projects when price inflation is present. We assume that the user has some idea of the notation and concepts associated with inflation.

A businessman is considering the purchase of an asset that has an initial cost of $2000. The asset promises an annual return of $600. It's 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.

We add inflation by assuming that the general rate of inflation is 6%. In addition we assume that all individual cash flows, including the salvage value, also inflate at 6%. Again we will accept the project if it satisfies the minimum accepted rate of return of 10%. When inflation is present, we must specify that this is the MARR in "real" terms.

The project is defined by choosing the Add_Project item from the Economics menu. Here we note that the Inflation button has been checked for the example, but the Tax button is unchecked.



Project Definition


On clicking OK, the project definition appears on the worksheet. Several new data items and result items appear on the form. In column H near the top of the form there are two entries for the MARR. The Real MARR is entered as data in H9 and the Actual (or Market) MARR is computed in cell H10. An estimate for the general inflation rate is in cell H11.

In the lower half of the display a new column, column J for the example, is added for both investment data and cash flow data segments. The new column holds an incremental inflation rate for each component of the cash flow. This entry shows the difference between the general inflation rate and the escalation rate for each component. The incremental rate is positive is the escalation rate is greater than the general inflation rate and negative if the escalation rate is less than the general inflation rate. For this example we have entered 0% indicating that all components escalate at the same rate as general inflation.


Click the image to expand

The numbers placed in the Amounts column are the values of the cash flows estimated at "today's" prices. When an escalation rate is greater than 0, the actual dollar expenditures or revenues grow as a function of the time they occur. When the cash flow is measured in terms of the dollars at the time of the cash flow, the measure is called actual dollars. A real dollar value is the actual dollar value reduced to remove the effect of general inflation. Formulas relating the three measures are below.

The rightmost column shows the equivalent value, or the present worth, of the project at time 0. At time 0, real and actual dollars are the same.


Rates of Return


At the top of the display we place new quantities that relate specifically to inflation analysis.

Real MARR: This is the minimum acceptable rate of return when returns are measured in real dollars. This quantity may be changed and the Worth column will automatically adjust.

Actual MARR: This is the minimum acceptable rate of return when returns are measured in actual dollars. This quantity is computed using the formula below. The quantity will change automatically when either the real MARR or the general inflation rate changes.

General Inflation: This is the average inflation rate for comparing real and actual dollars.

An investor desires to earn an interest rate the provides a reward for giving up money, but the investor also must earn an amount that compensates for the loss in value due to inflation. The real MARR is the minimum acceptable rate to be earned if there were no inflation, while the actual (or market) MARR includes an allowance for inflation. The relations between the two quantities are given in the equations below.


Worth Measures


At the right of the display we show several measures of the worth of the project.

Present Worth: This is the value of the project at time 0 when all cash flows are replaced by their equivalent values at time 0. The value is the same whether measured in actual or real dollars.

Real Uniform (Life): This is the uniform annual equivalent (NAW) of the present worth when it is spread over the life of the project using the real MARR.

Actual Uniform (Life): This is the uniform annual equivalent (NAW) of the present worth when it is spread over the life of the project using the actual MARR.

For most situations the real NAW is the best measure of annual costs.

Present Worth(SP): This is the present worth considering only the cash flows within some study period that may be more or less than the life. The study period may be different from the life when several replicas of the project are repeated as when comparing two projects of different lives. In some situations it may be useful to set the study period as less than the life of the project.

Real IRR: This is the internal rate of return when cash flows are measured in real dollars. It should be compared to the real MARR. The cell is shown in green to indicate that it is a computed quantity. Choose Compute Rates from the Economic menu to compute the rate. This is not a dynamic quantity and it must be re-computed whenever the data is changed.

Actual IRR: This is the internal rate of return when the cash flows are measured in actual dollars. It is computed directly from the real IRR using the general inflation rate and a formula similar to the formula shown above relating the real and actual MARR values.

For the example, all the measures show that this project makes more than the required MARR. All present and annual worth's are positive, and the IRR values are both greater than the minimum acceptable rates or return.


Cash Flows

  Selecting Show Cash Flows from the Economics menu builds the cash flow described by the project. When inflation is included in the model, columns are provided for both the actual and real cash flows. The NPW and IRR values are computed directly from the cash flows using built-in Excel functions. They should agree with the values computed by the add-in on the project display. The example shows the effects of inflation. For the example, all cash flows had the same inflation rate as general inflation. In this case the real cash flow is the same as the estimated cash flow. The payback period is computed using the Cumulative Real Values, shown in the column on the right.
  With inflation, there is a difference between real and actual cash flows. The graphical display shows actual revenues as black lines and real revenues as green lines. Actual disbursements are shown as red lines and real disbursements as maroon lines. The investment at time 0 is the same in both real and actual dollars. The real color is foremost, so only the maroon line shows.


When Inflation Rates are Different


To illustrate the effects of different inflation rates, we modify the example as below with a variety of assumptions about the price escalation rates for the components. Click the figure to see a larger version of the form created by the add-in.

Click the image to expand

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. The equations below indicate how the NPW representing the initial cost is computed.

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 be 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 $741. The positive value indicating 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. Cell L34 holds the IRR of the project using real cash flows, while L35 is the IRR computed with 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 give 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 that ambiguity. We provide so many 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 cash flow for this example is shown below.



Comparing Projects

  To compare two projects, they both must include inflation parameters. For an example, two projects are shown below. We compare them by choosing Compare Projects from the Economics menu. To compare more projects than two, choose Compare Multiple from the menu. The examples from this section are from and earlier version of the add-in.

Click the image to expand

  The comparison controls the Real MARR, in cell L4 for this example. 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.

The graph shows the incremental cash flow of Infl_B over Infl_A. The graph was constructed by the add-in.

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tree roots

Operations Management / Industrial Engineering
by Paul A. Jensen
Copyright 2004 - All rights reserved

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