Critique of NPV


1
Critique of NPV

• 04/29/08
• Ch. 6

2
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

3
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
  landTaco Bell Express at a Service Station
• NPV does a nice job of picking the right project
  but IRR may not...diagram to explain

4
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-(1r)-n
• Problem 3 Heating System for a Building

5
Unequal Lives Equivalent Annuity

• Problem 3
• Solar Heating Cost 12000 with annual costs of
  500 infinite life
• Gas Heating Cost 5000 with annual costs of
  1000 and will last twenty years
• Oil Heating Cost 3500 with annual costs of
  1200 and will last fifteen years
• Compute present value of costs at 10 cost of
  capital
• (1) Solar 17000 (2) Gas 13514 (3) Oil 12627
• Compute Equivalent Annuities
• (1) Solar 1700 (2) Gas 1587 (3) Oil 1659
• Pick the lowest equivalent annuityGas
• Issues with this approach

6
Replacement Decision

• Fits Mutually Exclusive as we only want one
  choiceeither keep current system immediately
  replace current system or wait and replace later
  (which is keep current system)
• Issues that are important --
• Salvage Value
• Lets re-examine this and how we deal with
  salvage value
• Examplereplace delivery truck with new delivery
  truck
• Old truck (five years old)original cost 38000
• New truck (expected life is eight years) cost of
  64000
• Old truck depreciation life was five year life
  (MACRS) book value is 5.76 x 38000 2189
• What if blue book is 1200 for old truck
• What if blue book is 2189 for old truck
• What if blue book is 4800 for old truck
• Does replacement lower future costs Does
  replacement increase future revenues Why replace
  now

7
Solutions to Salvage Value

• Book Value of Truck is 38000 x 0.0576 2189
• At sales price of 1200
• Loss on Disposal is 1200 - 2189 989
• Tax Credit (40 tax rate) 989 x 0.40 396
• Cash Flow at Disposal 1200 396 1596
• At sales price of 2189
• No loss or gain
• Cash Flow at Disposal 2189
• At sales price of 4800
• Gain on Disposal is 4800 - 2189 2611
• Tax (40 tax rate) 989 x 0.40 1044
• Cash Flow at Disposal 4800 - 1044 3756

8
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

9
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
• Cant 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!

10
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

11
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

12
Synergy 22 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
• Where does synergy come from
• Reduction in duplicate costs
• Using excess capacity
• Complementary Products
• Timing of synergyimmediate or much later

13
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 herethe
  probability that this project will lead to
  additional projects
• Option to delayprojects always compete with
  themselves over timeagain just need to find the
  NPV today versus the NPV tomorrow

14
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

15
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 problemsplus other issues

16
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