🏢 Corporate Issuers

NPV Formula & IRR Formula — How to Calculate Net Present Value

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.

Key Concepts

Net Present Value (NPV)

Sum of PV of all cash flows (including initial investment). Accept if NPV > 0. The theoretically best capital budgeting method.

Internal Rate of Return (IRR)

Discount rate that makes NPV = 0. Accept if IRR > required return. May conflict with NPV for mutually exclusive projects.

Payback Period

Time to recover initial investment. Simple but ignores TVM and cash flows after payback.

Return on Invested Capital (ROIC)

NOPAT / Invested Capital. Measures how efficiently capital is deployed. Create value when ROIC > WACC.

Real Options

Options embedded in capital projects: option to delay, expand, abandon, or switch. Add value beyond NPV.

Capital Allocation Pitfalls

Sunk cost fallacy, pet projects, failure to consider opportunity costs, optimism bias, anchoring.

Formulas

From this module

NPV

NPV = Σ CFt/(1+r)t - Initial Investment

Where: r = required return (WACC for firm projects)

IRR

NPV = 0 = Σ CFt/(1+IRR)t

Where: IRR = rate where NPV equals zero

Payback Period

Payback = Years before full recovery + (Unrecovered amount / CF in recovery year)

Where: Simpler but ignores TVM

ROIC

ROIC = NOPAT / Invested Capital

Where: NOPAT = Net Operating Profit After Tax

Master Formula Sheet -- Corporate Issuers

NPV

NPV = Σ[CFₜ / (1+r)ᵗ] - Initial Investment

Accept if NPV > 0

IRR

Rate where NPV = 0

Accept if IRR > required return

Payback Period

Time to recover initial investment

Ignores TVM and post-payback CFs

WACC

WACC = w_d × r_d(1-t) + w_e × r_e

After-tax weighted average cost

Cost of Equity (CAPM)

r_e = Rᶠ + β(R_m - Rᶠ)

Risk-free + equity risk premium

DOL

DOL = %ΔOI / %ΔREV = (Rev - VC) / (Rev - VC - FC)

Operating leverage sensitivity

DFL

DFL = %ΔEPS / %ΔOI = OI / (OI - Interest)

Financial leverage sensitivity

DTL

DTL = DOL × DFL

Total leverage effect

Breakeven

Q = FC / (P - VC)

Units to cover fixed costs

Decision Frameworks

NPV vs IRR: which to follow?

Use when:

  • NPV: always correct ranking for mutually exclusive projects
  • IRR: useful for communication (percentage return is intuitive)

Avoid when:

  • Following IRR when it conflicts with NPV — NPV maximizes shareholder wealth
  • Using IRR with non-conventional cash flows (multiple IRRs possible)

Test Your Understanding

When NPV and IRR give conflicting rankings for mutually exclusive projects, an analyst should:

Ready to study NPV Formula & IRR Formula — How to Calculate Net Present Value?

Jump into the full module with cheat sheets, flashcards, mind maps, and practice questions.

Start Studying

No signup required. Create an account anytime to save progress.