Chapter 9: Net Present Value and Other Investment Criteria

Objectives of Chapter 9

  • After studying the activities in this chapter, you should be able to:

    • Part 1

    1. Discuss the payback rule and some of its shortcomings.

    2. Discuss the discounted payback rule and some of its shortcomings.

    3. Explain accounting rates of return and some of the problems with them.

    4. Show the reasons why the net present value criterion is the best way to evaluate proposed investments.

    • Part 2

    1. Present the internal rate of return criterion and its strengths and weaknesses.

    2. Calculate the modified internal rate of return.

    3. Illustrate the profitability index and its relation to net present value.

Key Concepts and Skills

  • Understanding capital budgeting tools to evaluate investments:

    • Payback

    • Discounted Payback

    • Average Accounting Return (ARR)

    • Net Present Value (NPV)

    • Internal Rate of Return (IRR)

    • Modified Internal Rate of Return (MIRR)

    • Profitability Index (PI)

  • Discounted Cash Flow Methods: NPV, IRR, MIRR, and PI are classified under this.

Project Evaluation

  • Types of Projects:

    • Independent Projects: Acceptance or rejection does not affect other projects.

    • Mutually Exclusive Projects: Acceptance of one project excludes others.

    • Types of Projects:

    • Expansion Projects: New investments.

    • Replacement Projects: Also called cost-saving projects.

Questions for Capital Budgeting Decision Criteria

  • Does the decision rule adjust for the time value of money?

  • Does the decision rule adjust for risk?

  • Does the decision rule indicate whether value is being created for the firm?

Payback Rule

  • Definition: The length of time it takes to recover the initial investment.

  • Calculation Method:

    1. Estimate cash flows.

    2. Subtract future cash flows from the initial cost until recovered.

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

Example of Payback Calculation

  • Initial Cost: $165,000

  • Cash Flows:

    • Year 0: ($165,000)

    • Year 1: $63,120

    • Year 2: $70,800

    • Year 3: $91,080

  • Yearly Computation:

    • Year 1: Initial recovery = -165,000 + 63,120 = -101,880 still to recover

    • Year 2: -101,880 + 70,800 = -31,080 still to recover

    • Year 3: -31,080 + 91,080 = 60,000; project pays back in Year 3.

  • Payback Calculation:
    extPaybackPeriod=2+rac31,08091,080extyears=2.341extyearsext{Payback Period} = 2 + rac{31,080}{91,080} ext{years} = 2.341 ext{ years}

Advantages and Disadvantages of Payback Rule

  • Advantages:

    • Easy to understand.

    • Adjusts for uncertainty of future cash flows.

    • Biased toward liquidity.

  • Disadvantages:

    • Ignores the time value of money.

    • Requires an arbitrary cutoff point.

    • Ignores cash flows beyond cutoff point.

    • Biased against long-term projects (e.g., R&D).

Discounted Payback Period

  • Definition: Similar to payback, but includes present value calculations of cash flows.

  • Decision Rule: Accept if it pays back within the specified discounted period.

Calculation of Discounted Payback Period

  • Accept if pays back on a discounted basis within specific time, e.g., 2 years.

  • Year 1:
    −165,000+rac63,1201.12=−108,643-165,000 + rac{63,120}{1.12} = -108,643

  • Year 2:
    −108,643+rac70,800(1.12)2=−52,202-108,643 + rac{70,800}{(1.12)^2} = -52,202

  • Year 3:
    −52,202+rac91,080(1.12)3=12,627;-52,202 + rac{91,080}{(1.12)^3} = 12,627; project pays back in Year 3.

  • Cumulative Cost and Cash Flows:

Payback Period Computation

extPaybackPeriod=2+rac52,20291,080=2.805extyearsext{Payback Period} = 2 + rac{52,202}{91,080} = 2.805 ext{years}

Advantages and Disadvantages of Discounted Payback Rule

  • Advantages:

    • Accounts for time value of money.

    • Easy to understand.

    • Doesn't accept negative NPV investments if future cash flows are positive.

  • Disadvantages:

    • May reject positive NPV investments.

    • Requires arbitrary cutoff point.

    • Ignores cash flows beyond the cutoff.

Average Accounting Return (AAR)

  • Definition: Average net income divided by average book value.
    AAR=racextAverageNetIncomeextAverageBookValueAAR = rac{ ext{Average Net Income}}{ ext{Average Book Value}}

  • Must have a target cutoff rate; decision rule: Accept if AAR is above a specified rate.

  • Example: If average net income = 15,340 and average book value = 72,000, then:
    AAR = rac{15,340}{72,000} = 0.213 = 21.3 ext{%}

Advantages and Disadvantages of AAR

  • Advantages:

    • Easy to calculate (often available data).

  • Disadvantages:

    • Ignores time value of money.

    • Uses arbitrary benchmarks.

    • Based on accounting measures rather than actual cash flows.

Net Present Value (NPV)

  • Definition: The difference between the present value of cash inflows and the cost of the investment.

  • Calculation Steps:

    1. Estimate expected future cash flows.

    2. Estimate the required return for the projects corresponding risk level.

    3. Find the present value of cash flows and subtract initial investment.

  • Decision Rule: Accept project if NPV > 0.

NPV Calculation Example

NPV=−165,000+rac63,1201.12+rac70,800(1.12)2+rac91,080(1.12)3=12,627.41NPV = -165,000 + rac{63,120}{1.12} + rac{70,800}{(1.12)^2} + rac{91,080}{(1.12)^3} = 12,627.41

  • Result: Positive NPV means project adds value to the firm.

Decision Criteria Test for NPV

  • Does NPV account for time value of money? Yes

  • Does NPV account for risk? Yes

  • Does NPV provide an increase in value? Yes

  • Should NPV be a primary decision rule? Yes

Internal Rate of Return (IRR)

  • Definition: The discount rate that makes NPV = 0.

  • Decision Rule: Accept if IRR > required return (also known as hurdle rate).

  • Calculation:

    • Use cash flows to find IRR via financial calculator.

    • Example: Cash flows yield an IRR of 16.13% vs. a required return of 12%. Accept the project because IRR > required return.

Advantages of IRR

  • Intuitively appealing; simple to communicate.

  • If IRR is high enough, not need to estimate required return.

Drawbacks of IRR

  • May lead to misleading conclusions for mutually exclusive projects or non-conventional cash flows.

  • Need to exercise caution with high IRR values as they may indicate unrealistic cash flow projections.

Modified Internal Rate of Return (MIRR)

  • Purpose: Addresses limitations of IRR by providing a clearer picture of profitability.

  • Methods to Calculate MIRR:

    1. Discounting approach: Discounts negative cash flows back to the present.

    2. Reinvestment approach: Compounds all cash flows to project end.

    3. Combination approach: Discounts negative cash flows while compounding positives.

  • Advantages: Guarantees one solution, avoids multiple IRR problem.

Profitability Index (PI)

  • Definition: Ratio of present value of future cash flows to initial investment.
    PI=racextPVoffuturecashflowsextInitialInvestmentPI = rac{ ext{PV of future cash flows}}{ ext{Initial Investment}}

  • Interpretation: A PI of 1.1 indicates a gain of $0.10 for every dollar invested.

Advantages and Disadvantages of PI

  • Advantages:

    • Closely related to NPV, usually yields identical decisions.

    • Easy to communicate and understand.

    • Useful with limited available capital.

  • Disadvantages:

    • May lead to incorrect decisions when comparing mutually exclusive investments.

Summary of Investment Criteria

  • NPV: Take project if NPV > 0; preferred criterion due to its accuracy.

  • IRR: Accept if IRR exceeds required return; unreliable for non-conventional cash flows.

  • MIRR: Provides clarity on investment profitability, guarantees single answer.

  • PI: Use if PI > 1; cannot rank mutually exclusive projects.

  • Payback & Discounted Payback: Ignore time value; used for quick decisions.

  • Average Accounting Return: Based on accounting metrics, not recommended for serious decision-making.

Ethical Considerations in Capital Budgeting

  • Ethical dilemmas posed by decisions leading to potential cheating or environmental harm.

  • Responsibility to balance profit with ethical considerations beyond mere financial measures.

Conclusion

  • Understanding and applying diverse investment criteria essential for effective capital budgeting, guiding firms towards optimal investment decisions while considering both financial and ethical implications.