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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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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…

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…

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

- Extend shorter project to match life of longer project
- Compute Equivalent Annuities
- Equivalent Annuity = NPV x (r / [1-(1+r)-n]
- Problem 3, Heating System for a Building

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?

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?

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

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

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!

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

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

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?

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

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?

- Once a project has been completed additional projects become available
- Abandonment
- Is this an option for every project?
- How do you incorporate abandonment value in the future cash flow of a project?

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

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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