Is this project worth it? Payback, NPV, and the discount-rate trap
1. Before you start
When you spend money now to earn money later, two questions decide whether it is worth it. Payback period asks: how long until the cash coming back adds up to what I put in? Net present value (NPV) asks a harder question: once I account for the fact that a dollar next year is worth less than a dollar today, is the whole stream of future cash worth more than what I spend? A tiny example: pay $100 today, get $60 next year and $60 the year after. Payback is two years. But those future dollars, shrunk for the wait, might be worth only $104 today — so the NPV is a slim +$4, not the +$20 the raw numbers suggest.
Three honest statements before you start:
- This is a Decide course. You read a situation, learn the ideas, and make a call. You do not write or run any code.
- The companies below, Meridian Freight and Brightleaf Dairy, are composite — invented firms built from ordinary figures so the arithmetic is clean. No number is a claim about any real company.
- This is not a certification. It proves, to you, that you can judge an investment and defend it.
You need arithmetic and the patience to divide by a growing number a few times. That is the whole mechanic of discounting.
2. The Situation
Meridian Freight, a regional parcel carrier, can buy an automated sorter for $500,000 that would cut labour and speed throughput, throwing off cash savings for about five years. The operations director loves it: “it pays for itself in under three years.” The finance lead is wary: “under whose assumptions? At the right discount rate this might not clear the bar at all.” You have to make the call, and defend it, in front of both.
The trap is that the same project can look like an easy yes on one test and a near-miss on another — and the number that decides which is true is one nobody has pinned down: the discount rate.
3. What you’ll be able to do
After this course you will be able to:
- Compute a project’s payback period and say exactly what it ignores.
- Discount a future cash flow to its present value, and compute a project’s NPV.
- Judge an investment by NPV and explain why it can disagree with payback.
- Show how the discount rate you choose can flip a “yes” into a “no,” and defend the rate you used.
4. Prerequisites & time box
Prerequisites: arithmetic, and comfort reading a small table of numbers. Helpful but not required: the idea that money has a cost over time. No spreadsheet needed, though one makes the sums faster.
Time box: about 19 minutes of reading (measured), plus real thinking time on the call — this one rewards working the numbers yourself. That is under the 25-minute cap for a concept course.
Difficulty: 6 / 8 — a manager-level decision: several factors move at once and the naive reading points the wrong way, so you have to reason past it.
5. The case & where the numbers come from
Meridian Freight is a composite logistics company: its investment and cash-flow figures are in-course assumptions chosen for clean arithmetic, not drawn from or claimed about any real firm. The methods — payback period, discounting, present value, net present value, cost of capital — are standard finance and cited in section 11. Every dollar below is an assumption; every present value and NPV is computed from these figures inside the course, so you can reproduce each one.
The sorter investment:
| Item | Figure |
|---|---|
| Up-front cost (Year 0) | $500,000 |
| Net cash saving, Year 1 | $150,000 |
| Net cash saving, Year 2 | $180,000 |
| Net cash saving, Year 3 | $180,000 |
| Net cash saving, Year 4 | $150,000 |
| Net cash saving, Year 5 | $120,000 |
| Meridian’s cost of capital (hurdle rate) | 12% |
Total cash coming back is $150,000 + $180,000 + $180,000 + $150,000 + $120,000 = $780,000, so the raw, undiscounted “profit” looks like $780,000 − $500,000 = $280,000. Hold that number; it is the one that misleads.
6. The Concepts
Payback period
Payback period is how long until cumulative cash inflows repay the up-front cost. Add up the savings year by year:
| End of year | Cash that year | Cumulative |
|---|---|---|
| 1 | $150,000 | $150,000 |
| 2 | $180,000 | $330,000 |
| 3 | $180,000 | $510,000 |
The $500,000 is repaid partway through Year 3: after Year 2 you have recovered $330,000, leaving $170,000, and Year 3 brings $180,000 — so $170,000 ÷ $180,000 ≈ 0.94 of the year. Payback ≈ 2.9 years (about 2 years 11 months). That clears the operations director’s “under three years” rule.
But notice what payback threw away: it stopped counting at Year 3 and never looked at Years 4 and 5 ($150,000 + $120,000 = $270,000 of cash it ignored), and it treated a dollar in Year 3 as worth the same as a dollar today. Payback is a liquidity test (how fast do I get my money back), not a value test. For value, you need NPV.
The time value of money
A dollar you receive in a year is worth less than a dollar today, because today’s dollar could be put to work — covering Meridian’s own cost of capital of 12%. To compare future cash to today’s outlay, you discount it by dividing by (1 + r) once for each year of waiting. The discount factor for year n at rate r is 1 ÷ (1 + r)^n. At r = 12%:
| Year | Discount factor 1 ÷ (1.12)^n |
|---|---|
| 1 | 0.8929 |
| 2 | 0.7972 |
| 3 | 0.7118 |
| 4 | 0.6355 |
| 5 | 0.5674 |
Work one out so you trust the rest: the Year-2 factor is 1 ÷ (1.12)² = 1 ÷ 1.2544 = 0.7972, exactly the table’s second row. Each later row just divides by another 1.12.
A present value is a future cash flow times its discount factor. Meridian’s $120,000 in Year 5 is worth $120,000 × 0.5674 = $68,093 today — a little over half its face value. That shrinkage is exactly what payback ignored.
Net present value
NPV is the sum of every future cash flow’s present value, minus the up-front cost. If NPV is positive, the project earns more than the cost of the money tied up in it — accept. At Meridian’s 12% hurdle rate:
| Year | Cash | Discount factor | Present value |
|---|---|---|---|
| 1 | $150,000 | 0.8929 | $133,929 |
| 2 | $180,000 | 0.7972 | $143,495 |
| 3 | $180,000 | 0.7118 | $128,120 |
| 4 | $150,000 | 0.6355 | $95,326 |
| 5 | $120,000 | 0.5674 | $68,093 |
| Sum of PVs | $568,963 |
NPV = $568,963 − $500,000 = +$68,963. So at a 12% cost of capital the sorter is worth it — but by far less than the $280,000 the raw numbers suggested. Most of that headline “profit” was the time value of money quietly eaten by the five-year wait.
(An interactive calculator sits here — enter the up-front cost, up to five yearly cash flows, and a discount rate, and it returns each present value, the NPV, and the payback period. Drag the rate and watch the NPV cross from positive to negative.)
The discount-rate trap
The whole answer hangs on that 12%. The sorter is a riskier bet than Meridian’s routine spending, so suppose finance argues its real hurdle rate is 20%. Rediscount the same cash flows:
| Year | Cash | Discount factor 1 ÷ (1.20)^n | Present value |
|---|---|---|---|
| 1 | $150,000 | 0.8333 | $125,000 |
| 2 | $180,000 | 0.6944 | $125,000 |
| 3 | $180,000 | 0.5787 | $104,167 |
| 4 | $150,000 | 0.4823 | $72,338 |
| 5 | $120,000 | 0.4019 | $48,225 |
| Sum of PVs | $474,729 |
NPV at 20% = $474,729 − $500,000 = −$25,271. The same project with the same cash flows is a clear yes at 12% and a clear no at 20%. Somewhere between them the NPV crosses zero — that crossover rate (the project’s internal rate of return) is about 17.6%. Payback never saw any of this: it reported “2.9 years” regardless of the rate. The lesson is blunt: an NPV is only as honest as the discount rate behind it, so the rate is not a detail to wave through — it is the argument. Whoever picks the rate picks the answer, so make them defend it.
7. Your Call
You have seen how payback, NPV, and the discount rate decide Meridian’s single yes/no. Now a different decision lands on your desk.
Brightleaf Dairy has budget for one equipment upgrade and two proposals on the table — a different company in a different sector from Meridian’s freight operation, and a different shape of decision: not “yes or no” but “which one.” Each costs $300,000; Brightleaf’s cost of capital is 10%. The cash savings differ in timing:
| Year | Project A (cash) | Project B (cash) |
|---|---|---|
| 1 | $180,000 | $60,000 |
| 2 | $150,000 | $120,000 |
| 3 | $60,000 | $180,000 |
| 4 | $30,000 | $180,000 |
| Total | $420,000 | $540,000 |
Project A’s cash arrives early; Project B’s builds over time. Brightleaf can fund only one.
How this differs from the taught case (the transfer): this is a different company and sector (a dairy, not Meridian’s logistics), the figures are different so the arithmetic must be redone, it is a different kind of decision (choose between two projects — a ranking — rather than accept or reject a single one), and it adds a constraint the taught case did not have (one budget, the two projects are mutually exclusive). The core concept is the same: payback and NPV, and where they disagree.
8. Self-check
Before you write the memo, make sure you can say each of these in one line:
- What does payback measure, and what are its two blind spots?
- How do you turn a Year-4 cash flow into a value you can compare with today’s outlay?
- Why can the same project be a yes at one discount rate and a no at another — and who should defend the rate?
If any is fuzzy, reread section 6 — payback, discounting, NPV, and the discount-rate trap are the whole course.
9. Stretch
Push the decision further on your own:
- Back at Meridian: the sorter’s internal rate of return is about 17.6%. In plain words, what does that number tell a board that a single NPV at 12% does not? (The genuinely harder one — think about what happens to the “accept” decision as the true cost of capital drifts up toward it.)
- Suppose Brightleaf could split its budget and half-fund each project at half the cash flows. Does ranking by NPV still give the right answer, and what new question does a shared budget raise?
- Rediscount Brightleaf’s Project B at 20% and at 5%. At which rate does A come closest to catching B, and why does that direction make sense?
10. Ship it — your decision memo
Write a one-page memo to Brightleaf’s leadership. State the call (fund Project B — higher NPV, about +$112,000 vs +$53,000 — even though Project A pays back sooner). Show the reasoning in two or three lines (both cost $300,000; discounted at 10%, B’s later-but-larger cash is worth more today; payback measures speed, not value). Name what you rejected (choosing A on its faster payback) and why. Name the one thing that would change your mind (a real liquidity constraint that makes getting cash back fast worth more than total value, or a higher justified discount rate that narrows B’s lead). Keep it to a single page leadership grasps in two minutes. This memo is your own argued claim — not a credential.
11. Sources
Meridian Freight and Brightleaf Dairy, and every dollar figure attached to them, are composite and illustrative — constructed for clean teaching arithmetic, not drawn from or claimed about any real company. The methods used to evaluate them are standard finance; references below.
| Concept / claim | Source (publisher) | URL | Accessed |
|---|---|---|---|
| Payback period definition | Wikipedia — Payback period | https://en.wikipedia.org/wiki/Payback_period | 2026-07-19 |
| Time value of money / discounting | Wikipedia — Time value of money | https://en.wikipedia.org/wiki/Time_value_of_money | 2026-07-19 |
| Net present value = sum of discounted flows − outlay | Wikipedia — Net present value | https://en.wikipedia.org/wiki/Net_present_value | 2026-07-19 |
| Discounted cash flow method | Wikipedia — Discounted cash flow | https://en.wikipedia.org/wiki/Discounted_cash_flow | 2026-07-19 |
| Cost of capital as the hurdle/discount rate | Wikipedia — Weighted average cost of capital | https://en.wikipedia.org/wiki/Weighted_average_cost_of_capital | 2026-07-19 |
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