Project Evaluation with Real vs. Actual Dollars

Introduction

In our last lesson, you learned how to convert entire cash flow streams between actual (or nominal) dollars (A$) and real (or constant) dollars (R$). You now have the mechanical skill to create two different, but equivalent, representations of a project's finances, one that includes inflationary effects in the cash flows (A$) and one that doesn't (R$).

Today, we address the critical next step: how to use these cash flow streams to make a correct investment decision. Simply converting the dollars isn't enough; you must also use the correct interest rate for your analysis. The central goal of this lesson is to learn how to perform project evaluations using either real or actual dollars consistently. This means pairing the right type of cash flow with the right type of interest rate.

For someone in your role, scaling businesses and evaluating technology projects, this is a vital skill. An incorrect pairing can lead you to reject a profitable project or accept a losing one, all because inflation was handled improperly.

1. Market vs. Real Interest Rates: The Missing Piece

To perform a consistent analysis, we need to introduce two distinct types of interest rates.

• Market Interest Rate (i): This is the interest rate you typically see quoted in the marketplace (e.g., by a bank for a loan or a savings account). It includes a premium for expected inflation. It is also called the nominal interest rate.
• Real Interest Rate (i'): This is an interest rate that has been adjusted to remove the effects of inflation. It represents the "real" growth in your purchasing power.

These two rates, along with the inflation rate ($f$), are linked by a fundamental relationship known as the Fisher Equation.

As the resource shows, the precise relationship is:
$(1+i)=(1+i^{\prime })(1+f)$

From this, we can solve for either the market rate or the real rate:

• To find the market rate (i): $i=(1+i^{\prime })(1+f)-1$, which simplifies to $i=i^{\prime }+f+i^{\prime }f$
• To find the real rate (i'): $i^{\prime }=\frac{(1+i)}{(1+f)}-1$

For small values of $i^{\prime }$ and $f$, a common approximation is $i\approx i^{\prime }+f$. While convenient, we will use the exact formula for our calculations to ensure accuracy.

2. The Two Consistent Approaches to Project Evaluation

Now we can combine our knowledge of cash flows and interest rates. The cardinal rule of analysis under inflation is: You must be consistent. You either do everything in the "real" world or everything in the "actual" world. Mixing them will lead to incorrect conclusions.

There are two correct methods for evaluating a project:

1. The Real Method: All project cash flows are stated in real (constant) dollars, and they are discounted using the real interest rate (i').
2. The Actual Method: All project cash flows are stated in actual (nominal) dollars, and they are discounted using the market interest rate (i).

Any other combination is incorrect. For example, using a market MARR (which includes an inflation component) to discount real cash flows (which don't) effectively penalizes the project twice for inflation, making it appear less valuable than it is.

The following resource clearly outlines these correct and incorrect approaches and provides a worked example showing that both correct methods produce the identical result.

3. A Practical Application: Evaluating a Tech Upgrade

Let's solidify this by walking through the example from the reading, framing it for your context.

Imagine you're considering upgrading your company's servers. The new, energy-efficient servers are estimated to produce savings of $20,000 per year in today's prices. This is a real cash flow stream because it's based on today's (Year 0) cost of energy. The project life is 8 years.

Your company's nominal MARR is 7% ($i=0.07$), and you expect general inflation to average 5% per year ($f=0.05$). What is the Present Worth (PW) of these savings?

Method 1: The Real Method (Real Cash Flows, Real MARR)

1. Cash Flows: We already have the cash flows in real terms: an annuity of R$20,000 for 8 years.
2. Interest Rate: We need the real MARR ($i^{\prime }$).
   $i^{\prime }=\frac{(1+0.07)}{(1+0.05)}-1=0.01905\text{ or }1.905\%$
3. Calculate PW: Find the present value of the annuity using the real MARR.
   $PW=20,000(P/A,1.905\%,8)=20,000\left[\frac{(1+0.01905{)}^8-1}{0.01905(1+0.01905{)}^8}\right]\approx \$147,113$

Method 2: The Actual Method (Actual Cash Flows, Nominal MARR)

1. Interest Rate: We use the given nominal MARR, $i=7\%$.
2. Cash Flows: We must first convert the R$20,000 annuity into a series of actual dollar cash flows by inflating each one.
   • Year 1: A$ = 20,000(1.05)¹ = $21,000
   • Year 2: A$ = 20,000(1.05)² = $22,050
   • ...
   • Year 8: A$ = 20,000(1.05)⁸ = $29,549
3. Calculate PW: This is a geometric gradient series, where the cash flows grow at a rate $g=f=5\%$. We discount this series of actual cash flows using the nominal MARR ($i=7\%$). The formula for the present worth of a geometric gradient series is $PW=A_1\frac{1-(1+g{)}^n(1+i{)}^{-n}}{i-g}$.
   $PW=21,000\left[\frac{1-(1+0.05{)}^8(1+0.07{)}^{-8}}{0.07-0.05}\right]\approx \$147,113$

Both methods yield the same Present Worth. In this case, the Real Method was computationally simpler because we could use the standard annuity factor. The Actual Method required converting each cash flow or using a more complex gradient formula. This is a practical tip: if your cash flows are given as a simple real annuity, using the Real Method is often faster.

The image below shows another example, this time for calculating an IRR, but the principle is identical: the analysis must be done consistently in one domain (actual or constant/real) to be correct.

Conclusion

You have now learned the complete process for handling inflation in project evaluation. It's a two-step process: first, get your cash flows and your interest rate into the same "world" (either actual or real), and second, perform your analysis.

• Key Takeaways:
  • Project evaluations must be consistent: use real cash flows with a real interest rate OR actual cash flows with a market interest rate.
  • The market rate ($i$), real rate ($i^{\prime }$), and inflation rate ($f$) are linked by the formula $(1+i)=(1+i^{\prime })(1+f)$.
  • Mixing analysis types (e.g., using a market rate with real cash flows) leads to biased and incorrect investment decisions.
  • Both consistent methods will always yield the same PW, IRR, or other economic metric. You can choose the method that is computationally easier for the problem at hand.

Preview of the Next Lesson

So far, our analyses have assumed that our cash flow forecasts will come true as planned. However, the future is uncertain. As a manager, you often have the flexibility to change strategy as new information becomes available. In our next lesson, we will begin exploring this by introducing Real Options. You will learn to define and identify common types of strategic options in technology projects, such as the option to defer an investment, expand a successful project, or abandon a failing one. This will add a powerful new layer to your evaluation toolkit.