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Critique of NPV. 04/29/08 Ch. 6. Merits and Flaws of NPV. We will examine issues that are sometimes problematic for NPV Project Interactions – Mutually Exclusive Unequal Lives Replacement Decisions Capital Rationing Side Costs Synergy Embedded Options But it is still the best model….

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Critique of npv l.jpg

Critique of NPV

04/29/08

Ch. 6


Merits and flaws of npv l.jpg
Merits and Flaws of NPV

  • We will examine issues that are sometimes problematic for NPV

    • Project Interactions – Mutually Exclusive

    • Unequal Lives

    • Replacement Decisions

    • Capital Rationing

    • Side Costs

    • Synergy

    • Embedded Options

  • But it is still the best model…


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Project Interactions

  • Mutually Exclusive Projects

    • Definition: Accepting one project means rejecting another project

    • Example: When two projects require the same scare resource

      • Scare resource, plot of land

      • Projects, build restaurant or build service station

      • Assumes you can not acquire a similar scarce resource, another plot of land

      • Assumes you can not have a dual use of the land…Taco Bell Express at a Service Station

  • NPV does a nice job of picking the right project but IRR may not...diagram to explain…


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Unequal Lives

  • If two or more projects have different lives, the NPV model favors the longer lived project

  • Can you correct for this bias?

    • Extend shorter project to match life of longer project

      • Assumptions are that you can “invest” at the termination of the short-term project in a very similar project, the cost of capital has not changed and you do not have access to additional capital at start of the project

      • Compute NPV for the short project and the extension

  • Compute Equivalent Annuities

    • Equivalent Annuity = NPV x (r / [1-(1+r)-n]

    • Problem 3, Heating System for a Building


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Unequal Lives – Equivalent Annuity

  • Problem 3

    • Solar Heating, Cost $12,000 with annual costs of $500, infinite life

    • Gas Heating, Cost $5,000 with annual costs of $1,000, and will last twenty years

    • Oil Heating, Cost $3,500 with annual costs of $1,200 and will last fifteen years

  • Compute present value of costs at 10% cost of capital

    • (1) Solar $17,000 (2) Gas $13,514 (3) Oil $12,627

  • Compute Equivalent Annuities

    • (1) Solar $1,700 (2) Gas $1,587 (3) Oil $1,659

  • Pick the lowest equivalent annuity…Gas

  • Issues with this approach?


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Replacement Decision

  • Fits Mutually Exclusive as we only want one choice…either keep current system, immediately replace current system, or wait and replace later (which is keep current system)

    • Issues that are important --

    • Salvage Value

      • Let’s re-examine this and how we deal with salvage value

      • Example…replace delivery truck with new delivery truck

      • Old truck (five years old)…original cost $38,000

      • New truck (expected life is eight years) …cost of $64,000

      • Old truck depreciation life was five year life (MACRS), book value is 5.76% x $38,000 = $2,189

    • What if “blue book” is $1,200 for old truck

    • What if “blue book” is $2,189 for old truck

    • What if “blue book” is $4,800 for old truck

  • Does replacement lower future costs? Does replacement increase future revenues? Why replace now?


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Solutions to Salvage Value

  • Book Value of Truck is 38,000 x 0.0576 = $2,189

  • At sales price of $1,200

    • Loss on Disposal is $1,200 - $2,189 = $989

    • Tax Credit (40% tax rate) $989 x 0.40 = $396

    • Cash Flow at Disposal = $1,200 + $396 = $1,596

  • At sales price of $2189

    • No loss or gain

    • Cash Flow at Disposal = $2,189

  • At sales price of $4,800

    • Gain on Disposal is $4,800 - $2,189 = $2,611

    • Tax (40% tax rate) $989 x 0.40 = $1,044

    • Cash Flow at Disposal = $4,800 - $1,044 = $3,756


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Profitability Index Example

  • Problem #1 ($150 million max on spending)

    Project Initial Inv. NPV PI

    A $25 $10 0.40

    B $30 $25 0.83

    C $40 $20 0.50

    D $10 $10 1.00

    E $15 $10 0.67

    F $60 $20 0.33

    G $20 $10 0.50

    H $25 $20 0.80

    I $35 $10 0.28

    J $15 $ 5 0.33


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Ranking by NPV vs PI

Outlay $ Rank by NPV Outlay $ Rank by PI

$ 30 B $ 10 D

$ 65 C & H* $ 30 B

$ 45 D, G & E $ 25 H

$140 $ 15 E

* Can’t pick F as it puts $ 60 C and G

you over the $150 $140

Total NPV $95 $95

With a portfolio approach both give the same answer!


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Problems with PI

  • Assumes capital rationing applies to the current period only and that projects can only be done during current period…

  • Assumes all investment is up front

    • Projects with cash outflow in future periods will be overstated with PI

    • Future cash outflow will constrain future periods

  • PI may not spend all current capital – so other combinations may produce higher NPV


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Side Costs and Sunk Costs

  • Should be included as part of the incremental costs of a project but may be difficult to quantify

  • Opportunity costs

    • Project must “carry” the lost revenues of other uses

    • People – taken for new project

    • Resources – taken for new project

  • Sunk Costs

    • Do not include if truly sunk costs

  • Erosion – Substitute Products

    • Include if truly eroding other products


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Synergy, 2+2 = 5

  • When adding new projects in the whole is greater than the parts, you get synergies

  • Often used for mergers

    • Firm A Value + Firm B Value < Firm (A+B) Value

  • Where does synergy come from?

    • Reduction in duplicate costs

    • Using excess capacity

    • Complementary Products

  • Timing of synergy…immediate or much later?


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Embedded Options

  • Not a problem with NPV…

    • But, difficulty to quantify and properly add into the expected future cash flow

    • There is an element of probability here…the probability that this project will lead to additional projects

  • Option to delay…projects always compete with themselves over time…again, just need to find the NPV today versus the NPV tomorrow


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Embedded Options

  • Expansion

    • Once a project has been completed additional projects become available

      • How do you incorporate this into the original NPV decision of the initial project?

      • What happens if you do not take on the additional projects?

  • Abandonment

    • Is this an option for every project?

    • How do you incorporate abandonment value in the future cash flow of a project?


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NPV remains the Best

  • The problem with NPV is not in theory but in practice

    • Problems with finding the right WACC for the project

    • Problems with finding the right future cash flows for the project

    • Usually the only comfortable number in cash flow is the initial outflow

  • Other models all have these same cash flow estimation problems…plus other issues


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Weekly Homework for Thursday

  • Problem 4 – Replacement, unequal lives

  • Problem 5 – Unequal lives

  • Problem 7 – Salvage Value

  • Problem 15 – Capital Rationing

  • Problem 16 – Opportunity costs

  • Problem 18 – Lease option

  • Problem 21 – Opportunity cost


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