Present Worth Analysis for Single Projects

What is Present Worth (PW) Analysis?

Present Worth (PW) analysis is one of the most common methods in engineering economics for evaluating projects. It works by converting all cash inflows (revenues, benefits) and outflows (costs, investments) associated with a project into a single equivalent value at the present time (time 0).

You will frequently see this method referred to as Net Present Value (NPV) analysis. For our purposes in evaluating a single project, the terms PW and NPV are interchangeable. The "Net" in NPV simply emphasizes that we are summing the present values of both positive and negative cash flows.

The entire analysis hinges on one critical parameter: the discount rate. For project evaluation, this rate is your company's Minimum Acceptable Rate of Return (MARR). As we discussed in Module 2, the MARR is the minimum return a company is willing to accept from an investment, considering its risk and the opportunity cost of capital.

To get a formal definition of NPV and its formula, please review the following short text.

The NPV formula can be written concisely as:
$PW(i)=NPV(i)={\sum }_{t=0}^{n}C{F}_t(1+i{)}^{-t}$
Where:

• $C{F}_t$ is the net cash flow at the end of period $t$
• $C{F}_0$ is the initial investment (usually a negative value)
• $i$ is the discount rate (we will use the MARR)
• $n$ is the number of periods in the project's life

The Decision Rule: Making the "Go/No-Go" Choice

Once you calculate the PW of a project using the MARR as the discount rate, the decision is straightforward.

This rule is the heart of PW analysis. Let's explore what it means.

Here is the logic behind the rule:

• If PW ≥ 0: The project is expected to generate a rate of return that is at least equal to the MARR. The positive PW represents the "surplus" value the project creates, in today's dollars, after accounting for the required return. The project is financially attractive.
• If PW < 0: The project is expected to generate a rate of return less than the MARR. It fails to meet the minimum threshold for an acceptable investment and should be rejected. Investing in it would effectively destroy value compared to other opportunities that could earn the MARR.

Essentially, you are asking: "If I invest in this project, will the return I get, when measured in today's dollars, be better than the minimum return I'm willing to accept (MARR)?" A positive PW is a "yes".

Applying Present Worth Analysis: A Step-by-Step Example

Let's walk through an example that's highly relevant to your background: evaluating a software development project. We'll follow a clear, structured process.

Step 1: Establish Project Parameters

• Project: Develop a new software product.
• Initial Investment ($C{F}_0$): $150,000 (for development, licenses, initial setup). This is a cash outflow at time 0.
• Project Life ($n$): 3 years.
• MARR ($i$): 10% per year.
• Cash Flows:
  • Year 1 Inflow: $80,000
  • Year 2 Inflow: $120,000
  • Year 3 Inflow: $150,000

Step 2: Draw the Cash Flow Diagram

A diagram helps visualize the project:

      ^ +$80k     ^ +$120k    ^ +$150k
      |           |           |
------|-----------|-----------|------> Time (Years)
      0           1           2           3
      |
      v -$150k

Step 3: Calculate the Present Worth (PW)

We need to discount each future cash flow back to time 0 and sum them up, including the initial investment.

$PW(10\%)=C{F}_0+C{F}_1(P/F,10\%,1)+C{F}_2(P/F,10\%,2)+C{F}_3(P/F,10\%,3)$

The factor $(P/F,i,n)$ is $1/(1+i{)}^n$. Let's calculate the present value of each inflow:

• PV of Year 1 Inflow: $\$80,000/(1+0.10{)}^1=\$80,000(0.9091)=\$72,727$
• PV of Year 2 Inflow: $\$120,000/(1+0.10{)}^2=\$120,000(0.8264)=\$99,173$
• PV of Year 3 Inflow: $\$150,000/(1+0.10{)}^3=\$150,000(0.7513)=\$112,697$

Now, sum these present values and subtract the initial investment (or add the negative $C{F}_0$):

$PW(10\%)=-\$150,000+\$72,727+\$99,173+\$112,697$
$PW(10\%)=\$134,597$

This calculation is demonstrated in the resource below, though they have a small rounding error in their intermediate steps. The principle remains the same.

Step 4: Apply the Decision Rule

Our calculated Present Worth is $134,597.

• Is PW ≥ 0? Yes.
• Decision: The project is economically justified and should be accepted.

The result tells us that the project is expected to earn the 10% MARR plus an additional surplus equivalent to $134,597 in today's money.

Conclusion

In this lesson, you've taken the crucial step from calculation to decision-making. You now have a primary tool for assessing the financial viability of any single investment project.

• Key Takeaways:
  • Present Worth (PW) or Net Present Value (NPV) analysis converts all project cash flows to an equivalent single sum at time 0.
  • The discount rate used is the Minimum Acceptable Rate of Return (MARR), which serves as the benchmark for financial performance.
  • The decision rule is simple and powerful: If PW(i=MARR) ≥ 0, the project is financially acceptable. Otherwise, it is not.
  • A positive PW means the project is expected to earn more than the MARR, creating surplus value for the company.

Preview of the Next Lesson

Evaluating a single project in isolation is useful, but often you need to choose between several good options. For example, should you build a new system using Django, license a third-party platform, or use a low-code solution? In our next lesson, we will compare mutually exclusive alternatives using the present worth method, building directly on the foundation you've established today.