NPV and IRR formulas explained step by step. Net present value vs internal rate of return — when to use each, decision rules, and CFA Level 1 practice questions.
Sum of PV of all cash flows (including initial investment). Accept if NPV > 0. The theoretically best capital budgeting method.
Discount rate that makes NPV = 0. Accept if IRR > required return. May conflict with NPV for mutually exclusive projects.
Time to recover initial investment. Simple but ignores TVM and cash flows after payback.
NOPAT / Invested Capital. Measures how efficiently capital is deployed. Create value when ROIC > WACC.
Options embedded in capital projects: option to delay, expand, abandon, or switch. Add value beyond NPV.
Sunk cost fallacy, pet projects, failure to consider opportunity costs, optimism bias, anchoring.
NPV
Where: r = required return (WACC for firm projects)
IRR
Where: IRR = rate where NPV equals zero
Payback Period
Where: Simpler but ignores TVM
ROIC
Where: NOPAT = Net Operating Profit After Tax
NPV
Accept if NPV > 0
IRR
Accept if IRR > required return
Payback Period
Ignores TVM and post-payback CFs
WACC
After-tax weighted average cost
Cost of Equity (CAPM)
Risk-free + equity risk premium
DOL
Operating leverage sensitivity
DFL
Financial leverage sensitivity
DTL
Total leverage effect
Breakeven
Units to cover fixed costs
Use when:
Avoid when:
When NPV and IRR give conflicting rankings for mutually exclusive projects, an analyst should:
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