Time Value of Money (Lecture 5)
Time Value of Money & Investment Appraisal
1. Time Value of Money – The BIG Idea
→ £1 TODAY > £1 in one year
→ Because today’s £1 can be invested & earn interest
→ People prefer cash NOW
2. Compounding vs Discounting
Compounding → Money grows forward
Discounting → Bring future money back to TODAY
Present Value of a single future cash flow:
PV = CF / (1 + r)^t
CF = future cash flow r = discount rate t = years
3. Net Present Value (NPV) – The BEST Method
NPV = Sum of all discounted cash flows – Initial Investment
= –Initial + CF₁/(1+r) + CF₂/(1+r)² + CF₃/(1+r)³ + …
Decision Rules:
• NPV > 0 → ACCEPT (adds wealth)
• NPV = 0 → Indifferent
• NPV < 0 → REJECT
Why NPV is king:
→ Uses ALL cash flows
→ Respects time value of money
→ Directly measures £££ increase in wealth
4. Discount Rate (r) = ?
→ Required return / cost of capital / hurdle rate
→ Opportunity cost of money
→ Higher r → lower PVs → harder to get positive NPV
5. Payback Period (Simple but Weak!)
Time Value of Money & Investment Appraisal
1. Time Value of Money – The BIG Idea
→ £1 TODAY > £1 in one year
→ Because today’s £1 can be invested & earn interest
→ People prefer cash NOW
2. Compounding vs Discounting
Compounding → Money grows forward
Discounting → Bring future money back to TODAY
Present Value of a single future cash flow:
PV = CF / (1 + r)^t
CF = future cash flow r = discount rate t = years
3. Net Present Value (NPV) – The BEST Method
NPV = Sum of all discounted cash flows – Initial Investment
= –Initial + CF₁/(1+r) + CF₂/(1+r)² + CF₃/(1+r)³ + …
Decision Rules:
• NPV > 0 → ACCEPT (adds wealth)
• NPV = 0 → Indifferent
• NPV < 0 → REJECT
Why NPV is king:
→ Uses ALL cash flows
→ Respects time value of money
→ Directly measures £££ increase in wealth
4. Discount Rate (r) = ?
→ Required return / cost of capital / hurdle rate
→ Opportunity cost of money
→ Higher r → lower PVs → harder to get positive NPV
5. Payback Period (Simple but Weak!)
