ROI, NPV & Payback Period for Case Interviews (2026)

ROI measures percentage return (Net Profit / Investment Cost x 100), NPV discounts future cash flows to today's dollars, and payback period calculates years to recover the investment. Use ROI for quick same-timeline comparisons, NPV when cash flows span 5+ years or vary by period, and payback when the client prioritizes speed of capital recovery. If the interviewer mentions a discount rate, that signals NPV.

The Four Formulas: When to Use Each

ROI is the fastest to calculate and works for comparing investments with similar time horizons. Its limitation: ignoring the time value of money makes 50% ROI over 2 years look identical to 50% over 10 years.

NPV is the most theoretically correct metric, accounting for when cash flows arrive. Use the perpetuity shortcut (Annual Cash Flow / Discount Rate) for constant streams or the annuity factor for equal payments over a fixed period.

• ROI: (Net Profit / Investment Cost) x 100 — quick screening, same-timeline comparisons
• NPV: Sum of [CF_t / (1+r)^t] - Investment — uneven cash flows, 5+ year horizons, M&A valuations
• Payback: Investment / Annual Cash Flow — capital-constrained clients, risk-averse scenarios
• IRR: Rate where NPV = 0 — PE cases with hurdle rates (typically target 20-25%)

Decision Matrix: Which Metric for Which Scenario

If the interviewer does not specify which metric to use, start with payback period (fastest to calculate), add ROI for the return perspective, then offer NPV if the time horizon is long or cash flows are uneven. This shows versatility without overcomplicating the problem.

When the interviewer provides a discount rate or mentions cost of capital, that is an explicit signal to use NPV. PE and M&A contexts with hurdle rates call for IRR.

Worked Example: Technology Platform Decision

Prompt: A B2B software company must choose between two investments. Option A: upgrade existing platform for $8M, earning $3M/year for 5 years. Option B: build a new AI platform for $20M, earning $2M (Y1), $4M (Y2), $7M (Y3), $10M (Y4), $12M (Y5). Cost of capital: 12%. Negligible incremental costs.

Option A: Payback = $8M / $3M = 2.67 years. ROI = ($15M - $8M) / $8M = 87.5%. NPV = ($3M x 3.605 annuity factor) - $8M = +$2.8M.

Option B: Payback = 3.7 years (cumulative at Y3: $13M; remaining $7M / $10M Y4 = 0.7 years). ROI = ($35M - $20M) / $20M = 75%. NPV at 12%:

Synthesis: "If capital-constrained or risk-averse, Option A: faster payback (2.7 vs. 3.7 years), higher ROI (87.5% vs. 75%), lower upfront cost ($8M vs. $20M). If the client can absorb higher investment and trusts the Y4-5 projections, Option B creates $400K more value. I would stress-test Option B's NPV by reducing Y4-5 projections 20%."

Mental Math Shortcuts

Speed separates strong candidates from average ones. Memorizing a few key values lets you calculate NPV in 15 seconds instead of building a full table. The Rule of 72 (72 / rate = years to double) provides quick IRR sanity checks: at 10% growth, an investment doubles in ~7.2 years.

For equal annual cash flows, use annuity factors instead of discounting each year individually. For perpetuities, NPV = Cash Flow / Discount Rate. Example: $5M/year at 10% = $50M NPV; if it costs $40M, the investment creates $10M in value.

Annuity factors (memorize these):

Quick discount factors at 10% (approximate):

Common Mistakes in Investment Cases

Five errors that cost candidates points in investment analysis cases. Each is avoidable with awareness.

• Confusing revenue with cash flow: Use net cash flow (revenue minus all costs), not gross revenue
• Forgetting initial investment in NPV: Include the outflow at t=0 as a negative; omitting it turns a negative-NPV project positive
• Using ROI across different timeframes: 40% ROI over 2 years (20% annualized) differs vastly from 40% over 8 years (5%); annualize or switch to NPV
• Ignoring opportunity cost: Flag that $20M in Project A means $20M unavailable for alternatives
• Over-precision: Round to nearest $100K or $1M; interviewers test approach, not decimal arithmetic

Test Your Understanding

Test yourself

1 / 3

Question 1 of 3

A company invests $2M in a project that generates $500K per year. What is the payback period?

• A2 years
• B3 years
• C4 years
• D5 years

Related Guides

• Case Interview Math Practice — timed drills covering all quantitative skills
• Mental Math for Case Interviews — speed techniques for calculations under pressure
• Consulting Math Formulas — the complete formula reference sheet
• Case Interview Math Mental Shortcuts — estimation methods that save minutes
• Profitability Framework — where ROI analysis feeds into profitability recommendations
• PE Due Diligence Framework — investment analysis in private equity contexts

Sources (checked March 20, 2026)

• Hacking the Case Interview, 26 case interview formulas: hackingthecaseinterview.com/pages/case-interview-formulas
• IGotAnOffer, case interview math guide: igotanoffer.com/blogs/mckinsey-case-interview-blog/case-interview-maths
• Management Consulted, case interview formulas: managementconsulted.com/case-interview-formulas
• Corporate Finance Institute, internal rate of return: corporatefinanceinstitute.com/resources/valuation/internal-rate-return-irr
• Nucleus Research, ROI, TCO, NPV and payback guide: nucleusresearch.com/everything-to-know-about-roi-tco-npv-and-payback
• Wall Street Prep, IRR formula and calculator: wallstreetprep.com/knowledge/irr-internal-rate-of-return