From PV to a yes/no answer — NPV, IRR, payback, PI, and the moment of truth on Lecture 1's build-vs-buy puzzle.
| § | Topic | Minutes |
|---|---|---|
| I. | Net Present Value (NPV) & the discount-rate question | 20 |
| II. | Internal Rate of Return (IRR) & MARR | 20 |
| III. | Payback period & Profitability Index (PI) | 15 |
| IV. | Comparing mutually-exclusive alternatives | 15 |
| — | Discussion: a real decision from your team | 10 |
| V. | Verdict on Lecture 1's Elasticsearch vs SaaS | 20 |
| HW 5, Week 1 recap, questions | 10 |
The sum of every cash flow, each discounted to present value at the firm's cost of capital i.
Accept the project iff NPV > 0. The positive NPV is the project's surplus over the firm's required return.
Uses all cash flows · respects time value · directly measures value created · scales additively across a portfolio.
Of all the rules we will discuss today, NPV is the only one finance professors will defend without a "but." Every other rule earns a footnote.
| Year | Cash flow | DF @ 10% | PV |
|---|---|---|---|
| 0 | −$200,000 | 1.0000 | −$200,000 |
| 1 | +$60,000 | 0.9091 | +$54,545 |
| 2 | +$80,000 | 0.8264 | +$66,116 |
| 3 | +$80,000 | 0.7513 | +$60,105 |
| 4 | +$80,000 | 0.6830 | +$54,641 |
| NPV | — | — | +$35,407 |
NPV > 0 → the project creates value over the firm's cost of capital. Accept.
The IRR is the discount rate at which the project is exactly break-even. It is the project's implied return.
Accept iff IRR > MARR (the firm's Minimum Attractive Rate of Return).
Multiple IRRs possible with sign changes · misleads when comparing differently-sized projects · ignores reinvestment-rate assumption.
For the previous example, the IRR is ≈ 17.5% — well above the 10% MARR. Decision: accept (consistent with NPV).
MARR is the lowest return the firm requires for an investment of similar risk. It is set by leadership, not by the engineer.
| Setting | Typical MARR | Rationale |
|---|---|---|
| Cash-rich enterprise | 8 – 12% | Cost of capital + small risk premium |
| Venture-backed startup | 25 – 40% | Equity investors demand high return |
| Government / non-profit | 3 – 5% | Treasury-rate floor |
| AI / experimental product | 20 – 30% | Outcome uncertainty bumps the floor |
When the engineer is presented with a discount rate, that is the firm's MARR. Never quietly substitute your own.
The number of periods until the cumulative cash flow turns positive. Decision rule: accept iff payback < some firm-set ceiling (often 2–3 years).
Easy to compute · easy to communicate · prioritises liquidity · reasonable proxy for risk in unstable environments.
Ignores cash flows after payback · ignores time value of money (use discounted payback instead) · biases toward short-horizon projects.
Treat payback as a secondary screen, never the sole decision rule. A high-NPV project with a 4-year payback is still a high-NPV project.
PI > 1 ⇔ NPV > 0. The strength of PI is in capital rationing — when you can pick only a subset of projects under a fixed budget, rank by PI rather than NPV.
Example portfolio: Five projects, each profitable. Budget caps total investment. Rank by PI to maximise total NPV inside the budget.
A "PI of 1.30" means $1.30 of present-value benefit per $1 of capital deployed.
When two projects are mutually exclusive (e.g., two ways of solving the same problem) and have different sizes or lives, NPV and IRR can disagree:
| Project | Investment | NPV @ 10% | IRR |
|---|---|---|---|
| A (small) | $10,000 | $3,500 | 30% |
| B (large) | $80,000 | $15,000 | 16% |
A has the higher IRR; B has the higher NPV. Pick B. NPV measures absolute value creation; IRR measures rate, not scale.
A 30% return on $10K is less wealth than a 16% return on $80K. The firm is in business to maximise wealth, not return rate.
To compare two mutually-exclusive projects using IRR, compute the IRR of the incremental cash flow (B − A). If incremental IRR > MARR, the larger project is preferred.
In our example: increment is invest $70K more to gain $11,500 more NPV → incremental IRR ≈ 13.7%. Since 13.7% > 10% MARR, choose B. Consistent with the NPV verdict.
Whenever NPV and IRR seem to disagree, incremental IRR analysis reconciles them. NPV is still simpler — but some boards prefer the rate language.
In pairs (4 minutes), each describe one real decision (e.g., a tooling switch, a hire, a contract). Estimate the cash flows. Compute a rough NPV.
We will surface the best two stories for the whole room.
From the Lecture-1 poll. You voted on instinct. Now we vote on numbers.
| Alternative | Year 0 cost | Annual op | Life |
|---|---|---|---|
| A. Build in-house (Elasticsearch) | $120,000 | $30,000 | 5 years |
| B. Subscribe to SaaS search | $20,000 | $80,000 | 5 years |
Same functionality, same horizon. Discount rate: 10%. Which alternative is economically preferred?
The simple totals say A wins ($270K vs $420K). PV will sharpen that picture.
| Alt. | Build / Sub. | Year 0 | Yrs 1-5 stream | PV total |
|---|---|---|---|---|
| A | Elasticsearch | $120K | $30K/yr · P/A@10%,5 = 3.7908 | $233,723 |
| B | SaaS | $20K | $80K/yr · P/A@10%,5 = 3.7908 | $323,261 |
Verdict: at a 10% discount rate, building in-house has a PV of total cost $89,538 lower. Pick A.
Same conclusion as the simple total — but now with discipline. The math protects us when the gap is narrower.
| Assumption | Change | New verdict |
|---|---|---|
| Discount rate | Up to 25% | A still wins, by $43K |
| SaaS price falls 30% | Annual $80K → $56K | B wins by $13K |
| Build cost overruns 50% | $120K → $180K | A still wins by $30K |
| Useful life shrinks to 3 years | 5 → 3 years | B wins by $25K |
The verdict depends on useful life and SaaS pricing trajectory — not on the discount rate. Now you know what to investigate before signing the deal.
This is sensitivity analysis. Lecture 6 makes it formal.
Tomorrow: break-even and sensitivity analysis. Today you computed an NPV; tomorrow you'll learn how to stress-test it, find the assumptions that matter, and present a confidence range — not a single number.
From here forward, every lecture is built on these five lines.
Dr. Zhijiang Chen
Software Engineering Economics · Summer 2026
frostburg-state-university.github.io/bju