Summary NPV & IRR Explained - Complete Mini-Guide

NPV & IRR EXPLAINED

FINN1011 Finance | Complete Mini-Guide


1. Net Present Value (NPV)
NPV measures the value created by an investment in today's pounds.



NPV Formula:


NPV = -C₀ + CF₁/(1+r)¹ + CF₂/(1+r)² + ... + CFₙ/(1+r)ⁿ


NPV = -C₀ + Σ [CFₜ / (1+r)ᵗ]



NPV Decision Rule:
• NPV > 0: ACCEPT ✓ (creates value)
• NPV < 0: REJECT ✗ (destroys value)
• NPV = 0: Indifferent (earns exactly required return)




2. Worked Example: NPV Calculation

Project Details:
• Initial Investment: £10,000
• Cash flows: £4,000 per year for 4 years
• Discount rate: 10%


Calculate NPV:
NPV = -10,000 + 4,000/(1.10)¹ + 4,000/(1.10)² + 4,000/(1.10)³ + 4,000/(1.10)⁴
NPV = -10,000 + 3,636 + 3,306 + 3,005 + 2,732
NPV = -10,000 + 12,679
NPV = £2,679


Decision: NPV > 0 → ACCEPT the project




3. Internal Rate of Return (IRR)

IRR is the discount rate that makes NPV = 0. It's the project's "rate of return."



IRR Definition:


0 = -C₀ + CF₁/(1+IRR)¹ + CF₂/(1+IRR)² + ... + CFₙ/(1+IRR)ⁿ



IRR Decision Rule:
• IRR > r (cost of capital): ACCEPT ✓
• IRR < r: REJECT ✗
• IRR = r: Indifferent




4. NPV vs IRR: Comparison

Aspect NPV IRR


Measures £ value created % return


Decision rule NPV > 0 IRR > r


Considers TVM? Yes ✓ Yes ✓


Uses all cash flows? Yes ✓ Yes ✓