Lecture 3B - Investment Appraisal (cont)
Investment Appraisal Overview
Course from Lincoln International Business School, Dr. Chau Le David
Focus on investment appraisal techniques to evaluate projects.
Investment Appraisal Techniques Studied
Techniques Covered:
Payback periods (including discounted payback)
Accounting rate of returns
Net present value (NPV)
Current Topic: Internal Rate of Return (IRR) which considers discounted cash flows.
Internal Rate of Return (IRR)
Definition: IRR is the cost of capital at which the NPV of an investment is zero.
To find IRR, solve the NPV equation for r (rate of return).
NPV Equation:
NPV = -I(small 0)+ C1/(1 + r) + C2/(1 + r)^2 + C3/(1 + r)^3 + ⋯ + Cn/(1 + r)^n
NPV Example (in £)
Cash Flow Projection:
Year 0: Outlay = -100,000, Cash Flow = -100,000
Year 1: Net Cash Flow = 40,000, DCF @9% = 0.91743, Present Value = 36,697.25
Year 2: Net Cash Flow = 40,000, DCF @9% = 0.84168, Present Value = 33,667.20
Year 3: Net Cash Flow = 53,000, DCF @9% = 0.77218, Present Value = 40,925.72,
Calculated NPV: £11,290.17
Plotting NPV Example
Visual Representation:
Showcases NPV against varying costs of capital.
NPV = 0 point intersects where IRR = 9%.
Calculating IRR Using Linear Interpolation
Process:
Guess R1 with positive NPV and R2 with negative NPV.
Use interpolation formula:
IRR* = R1 + (R2 − R1) × NPV1/(NPV1 − NPV2)
Example: Guess R1 = 9%, NPV1 = 11,920 and R2 = 20%, NPV2 = -8,211:
Calculated IRR: 15.36%
Decision Criteria for IRR
Accept projects where IRR > hurdle rate.
When comparing projects, prefer the one with the highest IRR.
Questions on comparability arise between differing investment sizes.
Comparison of IRR and NPV
IRR Results: Presented in percentage.
NPV Results: Represented in cash value (£).
IRR assumes a constant discount rate; NPV accommodates changing rates.
Conflicts Between IRR and NPV
Usually, no conflicts for single projects with conventional cash flows.
Conflicts arise:
Mutually Exclusive Projects: Higher IRR may not correlate with higher NPV.
Non-Conventional Cash Flows: Possible multiple IRRs.
Example of Conflicting Projects (Investment A vs. B)
IRRs: A = 24%, B = 21%
Simple intuition suggests A is better, but NPV may indicate otherwise dependent on rates.
Influence of Discount Rate on Project Preference
Low Discount Rate (<15%): Prefer Project B (higher NPV).
High Discount Rate (>15%): Prefer Project A (higher IRR).
Profitability Index (PI)
Definition: Present value of future cash flows divided by the initial investment.
Implication: PI > 1 indicates a project worth pursuing with a positive NPV.
Can be misleading in comparing mutually exclusive projects.
Applications of NPV in Practice
Considerations when applying NPV:
Relevant Cash Flows: Assess cash flows occurring as a result of the project.
Tax Effects: Determine after-tax cash flows.
Inflation Impact: Recognize how inflation reduces future cash flow values.
Investment Risk: Be aware of uncertainties affecting returns.
Incremental Cash Flows Considerations
Include: Cash generated by the project, opportunity costs, side effects.
Ignore: Sunk costs, apportioned fixed costs unless they are incremental.
Effects of Taxation on Cash Flow
Incorporate corporate tax in cash flow calculations.
Account for the timing and amount of tax payments for accurate NPV estimation.
Effects of Inflation on Cash Flow
Inflation diminishes the real value of future cash flows.
Use real rates for real cash flows and nominal rates for nominal cash flows.
Investment Appraisal and Risk
Define risk as measurable circumstances with assigned probabilities.
Understand downside risk as the potential of receiving lower than expected returns.
Practice of Capital Budgeting
Real-world application varies; historical preference for payback period.
Recent trends show increasing popularity of discounted cash flow methods.
Survey Insights on Capital Budgeting Techniques
Most Used Methods: NPV and IRR.
Differences in usage based on company size and geography.
Concept Quiz Topics
Understand NPV rule and its implications.
Commonly used capital budgeting procedures.
Circumstances when IRR and NPV yield same or conflicting decisions.