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.