Should We Invest? Payback vs NPV on One Real Spend — a 75-minute classroom session
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1. For the instructor
This is a ready-to-run 75-minute session. You can teach it cold, with no prep: read this page once, print the handout in section 9, and you have everything you need. No spreadsheet, no software, and no finance or business background required — of you or of the students. The only tool anyone needs is arithmetic, and the harder numbers (the discount factors) are printed for them.
What this session is. Students meet an invented bakery that can buy a second oven to launch a new product line. One owner wants to reject it because it takes too long to “pay for itself”; a manager says that test throws away the best year and the real question is whether the money coming back, properly counted, is worth more than the money going out. Working in table groups, students compute the project’s payback period (how fast the cash returns) and its net present value (whether it creates value once you account for the wait), then defend a single invest / don’t-invest call. The point is not a trick answer; it is that a room of non-business students can run both tests and say which one should decide.
What’s in the pack. The case (section 3), a minute-by-minute run of show (section 4), the concepts you’ll teach and how (section 5), the group task (section 6), a full facilitator answer key so you can steer any table (section 7), debrief prompts (section 8), a printable student handout (section 9), a stretch variant for fast tables (section 10), and a slide outline you can present straight from (section 11).
How to run it in a mixed room. Everyone can finish the core: it needs only multiplication, addition, and one division. The discount factors are given, so no student has to raise anything to a power. Seat students in groups of 3–5 so a stronger arithmetic student can carry a weaker one, and use the stretch in section 10 for tables that race ahead. Define every term out loud the first time — the material does the same in writing.
One honest line to say at the top: this is teaching material, not a certification and not a credit-bearing course. It builds the skill and the confidence to judge an investment; it awards nothing.
A note on the clock. The run of show below is a tight 75 minutes with little slack — in a 30–40 student room budget ~85 minutes in practice (set-up, table-forming, and report-backs always run long). If you fall behind, cap report-backs at two tables and cover two of the discussion prompts. Protect the group exercise and the answer-key debrief — those are the session.
2. Session at a glance
| Audience | Mixed-ability undergrads, including non-business majors; arithmetic only, no background assumed |
| Class size | 12–40 (table groups of 3–5) |
| Total time | 75 minutes |
| Materials | Printed handout (section 9), a board or slides, pens; a basic calculator is handy but not required |
By the end students can:
- Compute a project’s payback period from a table of cash flows, and say the two things payback ignores.
- Turn a future cash flow into a present value using a given discount factor, and add those up into a project’s net present value (NPV).
- Make an invest / don’t-invest call, say which test they trusted and why, and name what the other choice would have cost.
Further reading (self-paced). This session builds on the self-serve “Decide” course Is this
project worth it? Payback, NPV, and the discount-rate trap (slug payback-vs-npv), which walks
similar arithmetic at a reader’s own pace and adds a choose-between-two-projects twist. Point
interested students there after class.
3. The case
Copperpot Bakery is an invented mid-size bakery that sells bread and pastries from three shops. All figures below are illustrative — chosen for clean arithmetic, not drawn from or claimed about any real company.
Copperpot can buy a second commercial oven for $120,000 to launch a wholesale line — baking bread overnight to sell to local cafés and restaurants. The new line would throw off cash for about five years before the oven needs replacing. Two people disagree.
- Dev, the owner, has a rule of thumb: “I don’t tie up money in anything that takes more than three years to pay for itself.” He has done the sums and the oven takes about three and a half years to pay back, so his rule says reject it.
- Mara, the new operations manager, says: “Your rule stops counting the moment we break even — it ignores that Year 5 is the biggest year of all, and it pretends a dollar in five years is worth a dollar today. Count the whole thing properly and this might be a clear yes.”
Here are the numbers everyone is arguing over. Every figure below is an in-course assumption:
| Item | Figure |
|---|---|
| Up-front cost of the oven (Year 0) | $120,000 |
| Net cash the wholesale line brings in, Year 1 | $30,000 |
| Net cash, Year 2 | $30,000 |
| Net cash, Year 3 | $35,000 |
| Net cash, Year 4 | $40,000 |
| Net cash, Year 5 | $45,000 |
| Copperpot’s cost of capital (its hurdle rate) | 10% |
Total cash coming back is $30,000 + $30,000 + $35,000 + $40,000 + $45,000 = $180,000, so the raw, undiscounted “profit” looks like $180,000 − $120,000 = $60,000. The decision students owe Copperpot: buy the oven, or not — and which test should decide? It is a real spend call: every choice costs something.
4. Run of show
- 8 min — Hook. Put Dev and Mara’s disagreement on the board: “The oven pays back in about 3.5 years. Dev’s rule is ‘three years max,’ so he says no. Is he right?” Take three quick votes or opinions before anyone sees a calculation.
- 12 min — Teach payback. Walk the cumulative-cash table on the board (section 5), landing on payback ≈ 3.6 years. Then name out loud the two things payback threw away: the cash after it stops counting, and the wait. This sets up why one test is not enough.
- 10 min — Teach discounting and NPV, worked together. As a whole room, discount one cash flow using the printed factor (e.g. Year 5’s $45,000), then build the NPV table one row at a time so every table has seen the move once before doing it alone. Land on NPV ≈ +$13,600.
- 22 min — Group exercise. Tables use the handout to compute the payback period, compute the NPV from the given discount factors, and write one sentence making the invest / don’t-invest call and naming what the other choice would cost (section 6).
- 13 min — Report-outs and debate. Each table states its call in one sentence; tally invest vs don’t-invest on the board and let tables challenge each other (section 8 prompts).
- 10 min — Debrief and takeaway. Reveal the defensible call and what each option costs (section 7), then the one-sentence takeaway.
Total: 75 minutes.
5. Teaching points
Teach only what the call needs. Define each term the first time you say it.
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Investment decision. Spend money now (the $120,000 oven) to earn money later (five years of cash). The question is always the same: is the money coming back worth more than the money going out? Two tests try to answer it, and they can disagree.
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Payback period. How long until the cash coming back adds up to what you put in. Add the cash year by year until the running total reaches $120,000:
End of year Cash that year Running total 1 $30,000 $30,000 2 $30,000 $60,000 3 $35,000 $95,000 4 $40,000 $135,000 After Year 3 the running total is $95,000, so $25,000 is still owed; Year 4 brings $40,000, and $25,000 ÷ $40,000 ≈ 0.6 of the year. Payback ≈ 3.6 years (about 3 years 7 months). That is what fails Dev’s “three-year” rule.
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What payback ignores (its two blind spots). (1) It stops counting the moment you break even, so it never sees Year 5’s $45,000 — the single biggest year. (2) It treats a dollar in Year 5 as worth the same as a dollar today. Payback is a speed test (how fast do I get my money back), not a value test.
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Time value of money. A dollar you receive later is worth less than a dollar today, because today’s dollar could already be earning Copperpot’s 10% cost of capital. To compare future cash with today’s outlay, you discount it: shrink it for the wait.
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Discount factor and present value. A discount factor is the shrink number for a given year — for Copperpot at 10% the factors are printed on the handout (Year 1 = 0.909, up to Year 5 = 0.621). A present value (PV) is a future cash flow multiplied by its factor. Example: Year 5’s $45,000 × 0.621 = $27,945 in today’s money — a good bit less than its face value. That shrinkage is exactly what payback ignored.
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Net present value (NPV). Add up every year’s present value, then subtract the up-front cost. If NPV is positive, the project is worth more than the money tied up in it — invest.
Year Cash Factor (10%) Present value 1 $30,000 0.909 $27,270 2 $30,000 0.826 $24,780 3 $35,000 0.751 $26,285 4 $40,000 0.683 $27,320 5 $45,000 0.621 $27,945 Sum of PVs $133,600 NPV = $133,600 − $120,000 = +$13,600. Positive — the oven creates value.
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When the two tests disagree, NPV decides. Payback (a speed test) flunks the oven on Dev’s arbitrary three-year line; NPV (a value test) passes it because it counts Year 5 and prices the wait. Payback is a fine liquidity check, but the invest/don’t-invest call is a value call, so the defensible answer follows the NPV.
6. Group exercise
The task. You are Copperpot’s finance team. Dev says reject the oven (it misses his three-year payback rule); Mara says the full picture makes it a yes. Settle it. Compute both tests, make the call, and be ready to say what the losing choice would cost.
Use the handout (section 9). It has the cash flows, the up-front cost, and the discount factors already printed — you only multiply, add, and (once) divide.
Steps (about 22 minutes):
- (5 min) Compute the payback period. Add the cash year by year until the running total reaches $120,000, then work out the fraction of the last year. Write it down. Does it pass or fail Dev’s three-year rule?
- (9 min) Compute the NPV. Multiply each year’s cash by its printed discount factor to get five present values, add them, and subtract the $120,000 cost. Show your arithmetic.
- (5 min) Make the call: invest or don’t invest. Write one sentence saying which test you trusted, why, and what the other choice would cost Copperpot.
- (3 min) Pick a spokesperson to say your one sentence in the report-out.
Low floor: every table can at least finish the payback number and one or two present values. Optional ceiling in section 10.
7. Facilitator answer key
The defensible call: invest — buy the oven. At Copperpot’s 10% cost of capital the project’s NPV is +$13,600 ($133,600 of discounted cash in, minus the $120,000 outlay), and a positive NPV means the project is worth more than the money tied up in it. That is the test that should decide, because the question — does this spend create value? — is a value question, and NPV is the value test. Dev’s objection is real but misplaced: the payback period genuinely is about 3.6 years, which does break his “three-year” rule, but payback is only a speed test. It stops counting the instant the money is recovered, so it never sees Year 5’s $45,000, the single biggest year of the whole project, and it treats that far-off cash as if it arrived today. Once you count Year 5 and shrink each year for the wait, the project clears the bar.
What each option would cost:
- Invest (recommended): Copperpot ties up $120,000 and, on these assumptions, gains about $13,600 of value in today’s money plus a new wholesale line. The honest cost: the cash flows are estimates, and the margin is not huge — if the true cost of capital were much higher, or the later years came in soft, the value could evaporate (see the stretch).
- Don’t invest (Dev’s call): rejecting on the three-year rule forfeits that +$13,600 of value and the wholesale business behind it. The cost is a value-creating project turned away because the test used ignored the best year and the time value of money — the exact mistake this session is about.
Common wrong turns. (1) “Payback is 3.6 years, over the limit, so reject” — steer them to ask what payback left out; point at the untouched Year 5. (2) “Total cash is $180,000 versus $120,000 cost, so it’s an easy $60,000 win” — that skips discounting entirely; make them apply the factors and watch $60,000 shrink to $13,600. (3) A table frozen because the two tests disagree: tell them disagreement is the whole lesson — name which test answers “is it worth it?” (NPV) versus “how fast do I get my cash back?” (payback), and decide on the first.
8. Discussion & debrief
Run these after the report-outs:
- Payback said about 3.6 years and NPV said +$13,600. In one sentence, why do the two tests point different ways here?
- The raw profit looked like $60,000 but the NPV is only $13,600. Where did the other ~$46,000 go?
- Dev’s rule is “pays back within three years.” What is that rule good for, and what does it blind him to?
- Which single year of cash does payback completely ignore, and why does that matter so much in this case?
- What would have to be true for don’t invest to become the right call, even with a positive NPV at 10%?
- If Copperpot could only afford to be wrong once, would you rather over-trust payback or over-trust NPV? Defend it.
One-sentence takeaway: Payback tells you how fast your money comes back; NPV tells you whether the whole deal is worth it — so when they disagree on an invest call, count the whole stream and follow the NPV.
9. Student handout
(Printable. One per table.)
Copperpot Bakery — the situation. Copperpot can buy a second oven for $120,000 to launch a wholesale bread line. Dev, the owner, wants to reject it: “I don’t fund anything that takes more than three years to pay for itself.” Mara, the manager, says count the whole thing properly first. All figures are illustrative.
The numbers
| Item | Figure |
|---|---|
| Up-front cost (Year 0) | $120,000 |
| Net cash — Year 1 | $30,000 |
| Net cash — Year 2 | $30,000 |
| Net cash — Year 3 | $35,000 |
| Net cash — Year 4 | $40,000 |
| Net cash — Year 5 | $45,000 |
| Cost of capital (discount rate) | 10% |
Discount factors at 10% (already worked out for you — just multiply):
| Year | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Factor | 0.909 | 0.826 | 0.751 | 0.683 | 0.621 |
Your work
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Payback period. Fill the running total, then find the fraction of the last year.
End of year Cash Running total 1 $30,000 __________ 2 $30,000 __________ 3 $35,000 __________ 4 $40,000 __________ Money still owed after Year 3 = __________ ; Year 4 cash = $40,000 ; fraction = (owed ÷ 40,000) = __________ → Payback ≈ ______ years. Pass or fail Dev’s three-year rule? __________
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NPV. Present value = cash × factor.
Year Cash × Factor = Present value 1 $30,000 0.909 __________ 2 $30,000 0.826 __________ 3 $35,000 0.751 __________ 4 $40,000 0.683 __________ 5 $45,000 0.621 __________ Sum of PVs __________ NPV = Sum of PVs − $120,000 = __________
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Your call (circle one): INVEST / DON’T INVEST
One sentence — which test you trusted, why, and what the other choice would cost:
Your question: Buy the oven or not — and which test, payback or NPV, should decide?
10. Stretch
For tables that finish early:
- What would flip the call? The NPV is positive at 10% but only by $13,600. Redo the NPV assuming Copperpot’s real cost of capital is 15% instead (at 15% the factors are 0.870, 0.756, 0.658, 0.572, 0.497). Does the project still clear the bar? Somewhere between 10% and 15% the NPV crosses zero — that crossover rate (the project’s internal rate of return) is about 14%. In one line, what does that number tell Dev that a single NPV at 10% doesn’t?
- Fix Dev’s rule instead of breaking it. Dev likes payback because it’s fast to compute. Is there a version of a payback rule that wouldn’t have wrongly rejected this oven? (Hint: what if the cutoff were four years, or what if you discounted the cash first and then measured payback?) Name the trade-off your fix introduces.
- Back-loaded vs front-loaded. Suppose the same $180,000 of total cash arrived in the reverse order ($45,000 first, down to $30,000 last). Without full recomputation, would the payback be faster or slower, and would the NPV be higher or lower? Explain the direction.
11. Slides
Slide 1 — Dev vs Mara: buy the oven?
- Copperpot can buy a $120,000 oven for a new wholesale line.
- Dev: “pays back in ~3.5 years — over my three-year rule — so no.”
- Mara: “your rule ignores the best year. Count it all first.”
- Presenter note: Take three quick votes before any numbers go up.
Slide 2 — The numbers everyone’s arguing over
- Cost $120,000 up front; cash back $30k, $30k, $35k, $40k, $45k over five years.
- Total cash $180,000 → looks like a $60,000 “profit.” Hold that number.
- Cost of capital: 10%.
Slide 3 — Test 1: payback (how fast does the money come back?)
- Running total: 30 → 60 → 95 → 135 (thousands). Hits $120k partway through Year 4.
- Payback ≈ 3.6 years — fails Dev’s three-year rule.
- Presenter note: Ask what payback stopped counting. Answer: Year 5’s $45k, and the wait.
Slide 4 — A dollar later is worth less than a dollar today
- Discount = shrink future cash for the wait, using Copperpot’s 10% cost of capital.
- Year 5’s $45,000 × 0.621 = $27,945 in today’s money.
- Presenter note: This shrinkage is exactly what payback ignored.
Slide 5 — Test 2: NPV (is the whole deal worth it?)
- Add all five present values = $133,600; subtract the $120,000 cost.
- NPV = +$13,600. Positive → the oven creates value.
- Presenter note: Point out the $60,000 “profit” shrank to $13,600 once the wait is priced in.
Slide 6 — Your task
- Compute payback, compute NPV (factors are printed), then make the call.
- One sentence: which test you trusted, why, and what the other choice would cost.
- Presenter note: Groups of 3–5. Hand out the worksheet now.
Slide 7 — The defensible call: invest
- NPV is +$13,600 at 10% — a value test says yes.
- Payback’s “no” was a speed test that threw away the biggest year.
- Cost of Dev’s “no”: a value-creating project and a wholesale line, turned away.
Slide 8 — When the tests disagree, follow the value test
- Payback = how fast my cash returns. NPV = whether the deal is worth it.
- Takeaway: for an invest call, count the whole stream and follow the NPV — and say what your call would cost if you’re wrong.
12. Sources & license
Full provenance is in SOURCES.md in this folder.
Honest data line. Copperpot Bakery and every dollar figure here are composite and illustrative — invented and purpose-built for clean teaching arithmetic. No figure is drawn from, or claimed about, any real company.
License and disclaimer. This module is offered for free classroom use under the canonical
wording maintained in company/legal/classroom-license.md; refer to that file for the license
terms. In plain words: this material is provided as-is, with no warranty; it is not a
certification and awards no credit; and it makes no promise of any particular result. It is
teaching material to build a skill, nothing more.
Instructor teaching material, provided as-is. Not accredited, not a certification, and not affiliated with or endorsed by any university. Uses composite (invented) companies and illustrative figures.