Chapter 8: Net Present Value and Other Investment Criteria Notes

Chapter Overview

• Investment evaluation criteria are essential for sound decision-making in business finance.

Key Concepts and Skills

• Payback Rule:

  • Summarizes shortcomings of the payback period.
  • Discusses advantages and disadvantages related to liquidity.

• Accounting Rates of Return (AAR):

  • Explains issues associated with AAR calculations.
  • Decision rule: Accept if AAR exceeds a target return.

• Internal Rate of Return (IRR):

  • Defines and explains IRR as the discount rate that makes NPV zero.
  • Lists strengths and weaknesses, especially in cash flow analysis.

• Net Present Value (NPV):

  • Evaluates investments based on NPV principles.
  • Direct measure of value added to the firm.

• Modified Internal Rate of Return (MIRR):

  • Addresses limitations of traditional IRR.

• Profitability Index (PI):

  • Calculation methods and their significance.

NPV Decision Rule

• If $NPV > 0$, accept the project:
  • Indicates the project is expected to add value.
  • Enhances shareholder wealth.

Calculating Net Present Value (NPV)

1. Estimate future cash flows:
   • Identify inflows and outflows over the investment period.
2. Determine required return for similar risk projects, denoted as R.
3. Calculate present value of future cash flows:
   • Use the formula:
     $NPV = \frac{CF<em>0}{(1 + R)^0} + \frac{CF</em>1}{(1 + R)^1} + \frac{CF<em>2}{(1 + R)^2} + … + \frac{CF</em>n}{(1 + R)^n} - I$
   • Where $CF_t$ is the cash flow for year t, and $I$ is the initial investment.

Example Calculation

• Using provided cash flow data:
  • Year 0: $CF_0 = -165,000$
  • Year 1: $CF_1 = 63,120$
  • Year 2: $CF_2 = 70,800$
  • Year 3: $CF_3 = 91,080$
  • Required return ($R$) = 12%
• NPV Calculation:
  • $NPV = -165,000 + \frac{63,120}{(1.12)^1} + \frac{70,800}{(1.12)^2} + \frac{91,080}{(1.12)^3}$
  • Result: $NPV ext{ } = 12,627.41$

Payback Period

• Definition: Time required to recover initial investment.
• Computation:
  • Cumulative cash flow until initial investment is recovered.
• Decision Rule: Accept if payback period is less than a preset limit.

Limitations of Payback Method

• Ignorance of time value of money.
• Difficulty in establishing the cutoff period.
• Exclusion of cash flows post-payback.

Average Accounting Return (AAR)

• Calculation:
  • $AAR = \frac{ ext{Average Net Income}}{ ext{Average Book Value}}$
• Decision Rule: Accept if AAR exceeds a designated rate.

Internal Rate of Return (IRR)

• Definition: Rate at which NPV equals zero, as defined by:
  • $NPV = -I + \frac{CF<em>1}{(1 + IRR)^1} + \frac{CF</em>2}{(1 + IRR)^2} + … + \frac{CF_n}{(1 + IRR)^n}$
• Decision Rule: Accept projects where IRR exceeds required return.

Advantages and Disadvantages of IRR

Advantages:

• Intuitive appeal of measuring project profitability.
• Considers all cash flows & time value of money.

Disadvantages:

• Multiple IRR outputs for non-conventional cash flows.
• Not reliable for mutually exclusive projects.

Modified Internal Rate of Return (MIRR)

• Purpose: Fix issues with IRR by using external rates. Includes:
  • Discounting future outflows.
  • Compounding inflows to project end.

Profitability Index (PI)

• Metric: Ratio of present value of cash inflows to initial investment:
  • $PI = \frac{PV( ext{inflows})}{ ext{Initial Investment}}$
• Accept if $PI > 1$.

Real-World Application

• Use a combination of NPV and IRR for investment decisions.
• Recognize limitations of each method.
• Payback should be secondary to NPV and IRR evaluations.

General Conclusion

• Each investment measure provides unique insights; understanding their advantages and limitations is crucial for informed decision-making. Calculate all metrics for comprehensive evaluation.