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Introduction to Finance

Is this project worth doing?

Bring every cash flow back to today and the NPV rule decides. Then see when the IRR agrees with it, the five ways it can mislead, and what payback rules leave out.

Part 1 · The NPV rule · Step 1 of 14

Costs now, benefits later: compare them in today's dollars

The project's cash flows
012345years−$10,000$2,000$2,000$4,000$4,000$5,000
Benefits against costs, both in today's dollars
−$5k$0$5k$10k$15ktoday's $$12,313PV(benefits)$10,000PV(costs)$2,313NPV
A firm pays for a project today and collects the benefits over the next few years. Dollars at different dates cannot simply be added, so first bring each one back to today with the rules of time travel (discounting). Then the net present value is NPV = PV(benefits) − PV(costs). The NPV rule: make the investment when NPV > 0, because then the benefits are worth more than the costs, in today's dollars. The project here costs $10,000 today and pays $2,000, $2,000, $4,000, $4,000 and $5,000 over five years.
Try it: Switch the timeline to present values, then raise the discount rate. Every later dollar shrinks, and the far-off ones shrink the most.
Discount rate, r10%
The timeline shows
NPV
$2,313
PV of benefits
$12,313
PV of costs
$10,000
NPV = $2,312.99 > 0: invest. The benefits are worth $2,312.99 more than the costs today.
PV(benefits) = 2,000 ÷ 1.100 + 2,000 ÷ 1.100² + 4,000 ÷ 1.100³ + 4,000 ÷ 1.100⁴ + 5,000 ÷ 1.100⁵ = $12,312.99
Each benefit divided by (1 + r) once for every year you wait.
NPV = $12,312.99 − $10,000.00 = $2,312.99

Final coming up and NPV versus IRR still feels slippery?

Bring your problem sets. We work through them together until every type feels routine.

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