# NPV, IRR and payback for a product bet > How to calculate NPV and IRR for a product bet, what payback adds, and where each one misleads. - Course: [Finance for Product People: From Unit Economics to Business Cases](https://productovi.com/courses/finance-for-product.md) - Module: Is this bet worth making? - Lesson 22/32, ~27 min - Source: https://productovi.com/courses/finance-for-product/npv-irr-payback ## Two bets, one team **Alex Tutor:** On Klasna's product team it's time to choose between projects, and Leo has two. You'll calculate NPV, IRR and payback to pick one. **Leo:** Two ideas for next year, and the team can build one. A progress app for parents, 600,000 UAH to build, or a mock-exam mode for maths, 1,200,000. The app pays back in under two years. Easy. **Hanna:** Let's see all the cash first, year by year. Extra contribution minus extra running costs: cash flows, not profit. The app helps for two years until others copy it. > **Cash flows of three product bets** > > | Bet | Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | > |---|---|---|---|---|---| > | Parent progress app | −600,000 | 400,000 | 300,000 | 0 | 0 | > | Maths mock-exam mode | −1,200,000 | 300,000 | 600,000 | 800,000 | 800,000 | > | Lesson reminders | −200,000 | 180,000 | 120,000 | | | > > UAH. Year 0 is the build, paid now; later years are cash at year end. **Sofia:** The app: 400,000 back in year 1, then 200,000 of year 2's 300,000. That's 1 + 200/300 = 1.67 years. **Alex Tutor:** That is the **payback period**: how long until the cumulative cash is back to zero. It says how long the money is at risk. Now do the mock-exam mode. > **Exercise:** What is the **payback period** of the mock-exam mode (−1,200,000 now; then 300,000, 600,000, 800,000, 800,000 a year)? Assume cash comes in evenly within a year. ## How to calculate NPV: all the cash, in today's money **Alex Tutor:** Payback stops counting at the payback point. The app's years 3 and 4 bring nothing; the mock exams bring 1,600,000 more. Payback sees neither. **Alex Tutor:** **NPV** sees everything: discount each year's cash flow at 25% and add them up, the investment included. Mock exams: −1,200,000 + 240,000 + 384,000 + 409,600 + 327,680 = **+161,280 UAH**. $$ NPV = \sum_{t=0}^{n} \frac{CF_t}{(1 + r)^t} = CF_0 + \frac{CF_1}{1.25} + \frac{CF_2}{1.25^2} + \dots $$ *CFₜ: cash flow in year t (CF₀ is the investment, negative); r: discount rate, 25% at Klasna. Discount cash flows, never profit.* **Hanna:** Before anyone discounts anything: which numbers go into the formula? > **Exercise:** The mock-exam mode costs 1,200,000 UAH to build, paid now, and its accounts would spread that cost over four years. Which yearly numbers belong in its NPV? **Hanna:** Positive NPV means the bet earns more than our 25% and adds that much value on top, in today's money. **Alex Tutor:** Now the app. > **Exercise:** What is the **NPV** of the parent progress app at 25% (−600,000 now; 400,000 in year 1; 300,000 in year 2)? ## How to calculate IRR: the rate where NPV hits zero **Sofia:** Is there one percentage for a bet, like a return? **Alex Tutor:** Yes: **IRR**, the discount rate at which NPV is exactly zero. You find it by trying rates, or with a spreadsheet's IRR function. Mock exams: 31.26%. The app: 11.51%. Against our 25%, mock exams clear the bar and the app doesn't. **Alex Tutor:** See what IRR means by moving the rate yourself. > **Exercise:** The parent progress app costs 600,000 UAH now and brings 400,000 at the end of year 1 and 300,000 at the end of year 2. What would its **NPV** be at a discount rate of **10%** instead of Klasna's 25%? Round to two decimals. **Hanna:** Then the third idea, automatic lesson reminders: 200,000 now, 180,000 and 120,000 back. Its IRR is 34.58%. **Leo:** Higher than mock exams! So reminders win? **Alex Tutor:** If the team can build only one, compare NPVs: reminders add 20,800, mock exams 161,280. A high rate on a small sum is still a small sum. IRR alone can't rank bets of different size or timing. > **Exercise:** **True or false:** if the team can build only one bet, Klasna should pick the lesson reminders, because their IRR (34.58%) is higher than the mock-exam mode's (31.26%). ## Discounted payback period **Sofia:** Could payback at least use today's money? **Alex Tutor:** Yes: **discounted payback** adds up discounted cash flows instead. For mock exams the running total is −960,000, −576,000, −166,400, then +161,280: about 3.51 years instead of 2.38. **Hanna:** More honest about waiting, but it still ignores whatever comes after. **Alex Tutor:** Try discounted payback on the app as well. > **Exercise:** **True or false:** counted in today's money at 25%, the parent progress app (−600,000 now; 400,000 in year 1; 300,000 in year 2; nothing after) never pays back. **Alex Tutor:** So use each for what it's good at: NPV to decide, IRR as a summary, payback as a check on how long the cash is out. The full comparison: [NPV vs IRR vs payback](/blog/npv-vs-irr-vs-payback). > **Exercise:** Which statements about the **mock-exam mode** are correct at Klasna's 25% rate? ## Three measures, three blind spots **Leo:** So which number goes on the slide? **Alex Tutor:** NPV first, with the rate you used. Then IRR and payback beside it, so people see the return and the wait. And name each one's blind spot. **Hanna:** And all three are only as good as the cash flows. I'd ask the team where 800,000 a year from mock exams comes from. **Sofia:** More families in maths, or families staying longer before the exams? > **Exercise:** Match each measure to its blind spot. ## Your turn: which bet? **Leo:** Decision time. Which one do we build next year? **Sofia:** The mock exams, but the app's quick payback will come up. **Hanna:** Then answer it before anyone asks. **Alex Tutor:** A few sentences for Leo: the choice, the NPVs behind it, and why payback and IRR point elsewhere. > **Exercise:** The team can build one bet next year. Write Leo a short recommendation (3–5 sentences): which bet, its NPV at 25%, and why the parent app's quick payback and the reminders' higher IRR don't change the answer. > **Key ideas** > > - **Payback period**: years until cumulative cash returns to zero. The parent app 1.67, mock exams 2.38. It ignores everything after payback and the time value of money. > - **NPV**: every cash flow discounted to today and added up, the investment included. At 25%: mock exams +161,280, app −88,000, reminders +20,800. Discount cash flows, never profit. > - **IRR**: the rate at which NPV is zero (mock exams 31.26%, app 11.51%, reminders 34.58%). A good summary, but blind to size: never rank mutually exclusive bets by IRR alone. > - **Discounted payback** counts the wait (mock exams 3.51 years) but still stops at the payback point. > - Decide with NPV, show IRR and payback beside it, and check the cash-flow assumptions the decision rests on. **Alex Tutor:** Next: where the 25% comes from, and why a riskier bet should face a higher bar. - Previous lesson: [Time value of money: why a hryvnia next year is worth less](https://productovi.com/courses/finance-for-product/time-value-of-money.md) - Next lesson: [Hurdle rate and cost of capital](https://productovi.com/courses/finance-for-product/hurdle-rate.md) --- Productovi Learning. Free, no sign-up needed to read.