Learning Objectives
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# Learning Objectives - Calculate Net Present Value and apply decision rule - Understand Internal Rate of Return and its limitations - Evaluate projects using multiple criteria ## 1. Net Present Value (NPV) $$ NPV = \sum_{t=0}^n \frac{CF_t}{(1+r)^t} $$ **Decision Rule:** Accept if NPV > 0.
Learning Objectives
- Calculate Net Present Value and apply decision rule
- Understand Internal Rate of Return and its limitations
- Evaluate projects using multiple criteria
1. Net Present Value (NPV)
Decision Rule: Accept if NPV > 0. Reject if NPV < 0. Indifferent if NPV = 0.
2. Internal Rate of Return (IRR)
IRR is r that makes NPV = 0.
Decision Rule: Accept if IRR > cost of capital.
Issues: Multiple IRRs (non-conventional cash flows), mutually exclusive projects (scale problem).
3. Payback Period
Time to recover initial investment. Simple (ignores TVM) and discounted.
4. Profitability Index
Decision Rule: Accept if PI > 1.
| Concept | Formula | Decision Rule |
|---|---|---|
| NPV | sum(CF/(1+r)^t) | Accept if > 0 |
| IRR | r where NPV=0 | Accept if > cost of capital |
| Payback | Cumulative CF = 0 | Accept if < cutoff |
| PI | PV(Future CF)/I | Accept if > 1 |
Q1: Investment 60k, CF2=$60k, r=10%. NPV?NPV = -100 + 60/1.1 + 60/1.21 = -100 + 54.55 + 49.59 = $4.14k. Accept (NPV > 0). Q2: Same project as Q1, find approximate IRR.At r=10% NPV=4.14. At r=12% NPV=-100+60/1.12+60/1.2544 = -100+53.57+47.83 = 2.46. IRR ~ 13-14%. Q3: Why is NPV preferred over IRR?NPV handles non-conventional cash flows, accounts for scale, assumes reinvestment at cost of capital (more realistic). Q4: When might IRR and NPV conflict?Mutually exclusive projects of different scale or timing. NPV gives correct ranking. Join Discord PreviousTime Value of MoneyNextRisk, Return & CAPM