Everything so far moved single streams through time. Net present value is the decision rule built on top. Discount all of a project's cash flows, outflows and inflows alike, to today at the opportunity cost of capital, and add them up.
NPV = Σ CFₜ/(1+r)ᵗ summed from t = 0, with CF₀ usually negative because it's the investment.
How do you read NPV, and why is it the master rule?
Its interpretation is exact. NPV is the amount by which doing this beats your next-best alternative of equivalent risk, in today's money. An NPV of +₹40 crore means that if you undertake the project, you're ₹40 crore richer today than if you'd put the same capital to work at r. NPV = 0 doesn't mean "pointless." It means the project earns r and you paid a fair price. NPV < 0 means the alternative wins.
That gives you the rule. Accept if NPV > 0, and among mutually exclusive options take the highest NPV.
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Why is NPV the master rule? Because it has four properties, and nothing else has all four:
- It answers the actual question. "Does this create value over my alternative?" It answers in currency, the unit you can spend. A percentage like IRR tells you the rate of value creation but not the amount, and you can't pay salaries with a rate.
- Value additivity. NPV(A + B) = NPV(A) + NPV(B). Firm value is the sum of project NPVs. A conglomerate is the sum of its parts, which is the basis of sum-of-the-parts valuation. Adding a zero-NPV project changes nothing. No other criterion adds up like this. You can't sum IRRs or average paybacks.
- It handles any cash-flow pattern. Sign changes, gaps, irregular amounts: NPV never breaks, never goes multiple, never fails to exist. On the internal rate of return page you'll watch IRR do all three.
- Its reinvestment logic is sound. NPV implicitly assumes interim cash flows are reinvested at r, the opportunity cost, which is what money really earns elsewhere. IRR assumes reinvestment at the IRR itself, as you'll see next.
And this is the bridge to everything you came here for. A stock is a claim on a cash-flow stream. Its intrinsic value is the present value of that stream, and buying at price P is a project with CF₀ = −P. So "is this stock attractive?" is the same question as "is the NPV positive at my required return?" Here's Phase 3 in one line. The cost-of-capital work builds r, the forecast builds the CFₜ, terminal value handles the far future, and NPV is the master rule that assembles them. Question 5 of the five-questions spine, what is the price implying, and is that beatable?, is an NPV question.
Net present value example, and which rate to use
Try a worked micro-example to set the pattern. The numbers are synthetic. A project costs ₹250 crore today and returns ₹90, ₹110, ₹130 crore over three years, and r = 11%.
NPV = −250 + 90/1.11 + 110/1.11² + 130/1.11³ = −250 + 81.08 + 89.28 + 95.05 = +₹15.41 crore, so accept. It beats the 11% alternative by ₹15.4 crore in today's money.
On choosing r. You'll build the discount rate properly soon, but the principles bind now. Match risk, because a lottery-like cash flow discounted at a G-sec rate is fiction. Match currency: ₹ cash flows at ₹ rates, $ at $. And match inflation basis, which the real-versus-nominal section covers. The rate is a property of the cash flow being discounted, never of the entity doing the discounting.