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Case Math & Quant Fluency · Lesson 6

Returns and value: NPV, ROI, EBITDA, and payback

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Intuition

When a company decides whether to build a factory, buy a rival, or launch a product, it's really asking one question: will the money we get back be worth more than the money we put in? The complication is timing — cash arrives over years, and a dollar next decade is worth less than a dollar now. The vocabulary of returns (NPV, ROI, payback, EBITDA) exists to make that comparison fair.

Think of it like lending money to a friend. You don't just want it back — you want enough extra to make the wait, and the risk, worthwhile. That "extra" is the return.

Framework

  • Time value of money: future cash is worth less than present cash; we discount it back to today.
  • NPV (Net Present Value): sum of all future cash flows discounted to today, minus the upfront cost. Positive NPV = value-creating; do it.
  • ROI / ROIC: return as a percentage of money invested. ROIC checks whether returns beat the cost of capital.
  • Payback period: how long to recover the initial outlay. Fast, intuitive, but ignores discounting.
  • EBITDA: earnings before interest, tax, depreciation, amortization — a proxy for operating cash flow, used for comparison and valuation multiples.

Worked Example

A retailer weighs a $2M store renovation expected to add $600K of profit a year for five years. Simple payback = $2M / $600K ≈ 3.3 years — fine for a five-year horizon. On NPV, you'd discount each year's $600K back to today; even at a 10% discount rate the five years of cash sum to well above $2M, so NPV is positive — go ahead. If instead the benefit were only $300K/year, payback stretches past six years and the NPV likely turns negative — kill it.

Pitfalls

  • Comparing cash flows from different years without discounting them.
  • Treating EBITDA as "profit" — it ignores real costs like interest, tax, and the capital that wears out.
  • Choosing a project on payback alone, ignoring whether the later cash is large enough to justify it.