Net Present Value and Other Investment Criteria

Chapter 8: Net Present Value and Other Investment Criteria

Key Concepts and Skills

  • After studying this chapter, you should be able to:
      - Summarize the payback rule and some of its shortcomings.
      - Discuss accounting rates of returns and some of the problems with them.
      - Explain the internal rate of return criterion and its associated strengths and weaknesses.
      - Evaluate proposed investments by using the net present value criterion.
      - Apply the modified internal rate of return.
      - Calculate the profitability index and understand its relation to net present value.

Chapter Outline

  1. 8.1: Net Present Value

  2. 8.2: The Payback Rule

  3. 8.3 The Internal Rate of Return

  4. 8.4 The Profitability Index

8.1: Net Present Value (NPV)

  • Definition: Net Present Value measures how much value is created from undertaking an investment.
      - Steps to compute NPV:
        1. Estimate the expected future cash flows.
        2. Estimate the required return for projects of this risk level.
        3. Find the present value of the cash flows and subtract the initial investment to arrive at the NPV.

  • Formula for NPV:
      - NPV=extSumofthePV’sofallcashflowsNPV = ext{Sum of the PV’s of all cash flows}
      NPV=extCF0+racextCF1(1+R)1+racextCF2(1+R)2+…+racextCFn(1+R)nNPV = ext{CF}_0 + rac{ ext{CF}_1}{(1+R)^1} + rac{ ext{CF}_2}{(1+R)^2} + … + rac{ ext{CF}_n}{(1+R)^n}

  • Decision Rule:
      - If NPV is positive (NPV > 0), accept the project.
        - This means the project is expected to add value to the firm and increase the wealth of the owners.

8.2: Example Project Data

  • Initial Investment (Year 0):
      - Cash Flow (CF) = -$165,000

  • Future Cash Flows:
      - Year 1:
        - CF = $63,120
        - Net Income (NI) = $13,620
      - Year 2:
        - CF = $70,800
        - NI = $3,300
      - Year 3:
        - CF = $91,080
        - NI = $29,100

  • Average Book Value = $72,000

  • Required return for assets of this risk = 12%.

8.3: Computing NPV

  • Using the specified cash flows:
      - NPV Formula:
        - NPV=−rac165,0001.120+rac63,1201.121+rac70,8001.122+rac91,0801.123NPV = - rac{165,000}{1.12^0} + rac{63,120}{1.12^1} + rac{70,800}{1.12^2} + rac{91,080}{1.12^3}
        - Calculation:
        - NPV=−165,000+56,441.33+56,357.14+64,828.94NPV = -165,000 + 56,441.33 + 56,357.14 + 64,828.94
        - NPV=12,627.41NPV = 12,627.41

  • Using TI BA II+ Calculator:
      - Input cash flows:
        - CF0 = -165000
        - CF1 = 63120
        - CF2 = 70800
        - CF3 = 91080
      - Compute NPV = CPT $12,627.41

  • Rationale for NPV Method:
      - NPV Formula:
        - NPV=PVextinflows−extCostNPV = PV ext{ inflows} - ext{Cost}
      - NPV = 0 indicates project’s inflows are exactly sufficient to repay the invested capital and provide the required rate of return.
      - Rule: Accept project if NPV > 0.

8.4: Payback Period

  • Definition: How long does it take to recover the initial cost of a project?

  • Computation Steps:
      - Estimate the cash flows.
      - Subtract future cash flows from the initial cost until the total cash flow equals the initial investment.

  • Decision Rule: Accept if the payback period is less than the preset limit.

  • Sample Payback Calculation:
      - Yearly CF:
        - Year 0: CF = -$165,000 (Cumulative = -$165,000)
        - Year 1: CF = $63,120 (Cumulative = -$101,880)
        - Year 2: CF = $70,800 (Cumulative = -$31,080)
        - Year 3: CF = $91,080 (Cumulative = $60,000)

  • Payback Period Calculation: Payback = 2.34 years (recovering investment).

8.5: Internal Rate of Return (IRR)

  • Definition: The most important alternative to NPV; widely used in practice.
      - It is intuitively appealing and based entirely on estimated cash flows.

  • IRR Definition and Decision Rule:
      - Definition: IRR is the discount rate that makes NPV = 0.
      - Decision Rule: Accept the project if IRR > required return.

  • Computing IRR Without Calculator:
      - Requires trial-and-error approach.

  • Using TI BA II+ Calculator:
      - Enter cash flows as for NPV. Press IRR, compute.
      - IRR = 16.13% (greater than 12% required return).

  • Excel IRR Calculation:
      - Use the formula:
        - =IRR(B3:B6)=IRR(B3:B6)
      - Result: IRR = 16.13%.

8.6: NPV versus IRR

  • Comparative Analysis:
      - NPV: Solve for NPV given r.
      - IRR: Solve for IRR given NPV = 0.

  • Main Differences:
      - Nonconventional cash flow scenarios can lead to different conclusions.
      - IRR may produce multiple results, whereas NPV provides a clear indication of value increase.

8.7: Nonconventional Cash Flows

  • Example:
      - An investment costs $90,000 and generates:
        - Year 1: Cash Flow = $132,000
        - Year 2: Cash Flow = $100,000
        - Year 3: Cash Flow = -$150,000
      - Required return = 15%.

  • Decision Analysis:
      - NPV Calculation: Accept if NPV > 0.
      - For this example:
        - NPV = $1,769.54 > 0
        - IRR = 10.11% (indicating reject).
        - Recognize the conflicting results due to nonconventional cash flows.

8.8: Independent versus Mutually Exclusive Projects

  • Independent Projects:
      - Cash flows of one project are unaffected by the acceptance of the other.

  • Mutually Exclusive Projects:
      - The acceptance of one project precludes accepting the other.

8.9: Reinvestment Rate Assumption

  • IRR assumes reinvestment at IRR:
       - Fails to provide realistic scenario.

  • NPV assumes reinvestment at WACC:
      - More realistic and practical approach.

8.10: Example of Mutually Exclusive Projects

  • Data:
      - Project A:
        - IRR = 19.43%
        - NPV = $64.05
      - Project B:
        - IRR = 22.17%
        - NPV = $60.74
      - Required return is 10%.

  • Selection Criteria:
      - Depending on rates, choose the one with higher NPV or faster payback based on discount rate relation.

8.11: Conflicts between NPV and IRR

  • Efficiency in Decision Making:
      - Always use NPV when there's conflict since it directly measures increase in firm value.

  • Unreliable scenarios for IRR include:
      - Nonconventional cash flows and mutually exclusive projects.

8.12: Profitability Index (PI)

  • Definition:
      - Measures the benefit per unit cost, based on the time value of money.
      - A PI of 1.1 indicates generating an additional $0.10 per each dollar invested.

  • Decision Rule: Accept projects if PI > 1.0.

  • Formula for Profitability Index:
      - PI=racPV(extCashInflows)extAbsoluteValueofInitialInvestmentPI = rac{PV( ext{Cash Inflows})}{ ext{Absolute Value of Initial Investment}}

8.13: Summary of NPV, IRR, Payback, and Profitability Index

  • NPV Summary:
      - NPV = Difference between market value (PV of inflows) and cost; accept if NPV > 0.

  • IRR Summary:
      - IRR = Discount rate making NPV = 0; accept if IRR > required return.

  • Payback Summary:
      - Payback period measures length until the initial investment is recovered; accept if payback period < target.

  • Profitability Index Summary:
      - PI measures the relationship between benefits and costs; accept if PI > 1.

8.14: Quick Quiz

  • Scenario: An investment costs $100,000 with inflows of $25,000/year for 5 years. Required return = 9%. Required payback = 4 years.

  • Quick Tasks:
      - Determine payback period.
      - Compute NPV.
      - Compute IRR.
      - Decision: Accept or reject, based on the primary decision method.

  • Key Notes: Identify when IRR rule is unreliable.

8.15: Quick Quiz Solution Summary

  • Summary Results:
      - Payback = 4 years.
      - NPV = -$2,758.72.
      - IRR = 7.93%.

  • The project should be rejected based on NPV method; conflicts arise in decision-making criteria questions for initial investments.