NPV vs. Alternative
Investment Criteria
Business Investments
• Office building
• Manufacturing
machinery
• CRM system
• New product line
• Merger
• Advertising
• R&D
Common element:
Capital committed
over time in exchange
for future benefits
Investment Criteria
• We need a decision criterion that will
properly weigh the benefits of the investment
against the cost of committing the capital
The NPV Criterion
T
Ct
NPV  
t
t 0 (1  R )
• Criterion: Invest if NPV > 0
• NPV values project net benefits using
shareholders’ required rate of return
Implications of Positive NPV
T
T
Ct
Ct
NPV  
0
I
t
t
t 0 (1  R )
t 1 (1  R )
• In an efficient market, stock price rises by
amount of NPV per share
• Value of project benefits exceeds value of
costs
• Market value exceeds book value
Alternative #1: Payback Period
• Payback period = # of periods until
cumulative project inflows = initial
outlay
• Criterion: don’t invest if payback period
exceeds some specified cutoff (e.g., 3
years)
Aspects of Payback
Reasons for use:
• Bias toward liquidity
• Guard against
overly optimistic
forecasts
Problems:
• Effectively
discounts cash
flows before
payback threshold
at 0%, cash flows
after that at  %
Verdict:
Alternative #2:
Average Accounting Return (AAR)
average net income
AAR 
average book value
• Calculate an average rate of return on capital
invested over project life
• Criterion: invest if AAR > some specified
standard (cost of capital?)
Aspects of AAR
Reasons for use:
• Apparent
consistency with
accounting
statements
Problems:
• Income and cash
flow are different
(depreciation can be
misleading)
• Doesn’t consider
time
Verdict:
Alternative # 3:
Internal Rate of Return (IRR)
T
T
Ct
Ct
0
I

t
t
t  0 (1  IRR )
t 1 (1  IRR )
• Find the discount rate that sets NPV = 0
• Criterion: invest if IRR exceeds cost of
capital
Aspects of IRR
Reasons for use:
• Simple, intuitive
• Properly considers time
value of money
Problems:
• Multiple IRRs
• Incorrect ranking for
mutually exclusive
projects
Verdict:
• Mixed
• OK for yes/no
• Don’t use to rank
Alternative #4: Profitability Index (PI)
T
Ct

t
t 1 (1  r )
PI 
I
• Compute a benefit-cost ratio
• Criterion: Invest if PI > 1
Aspects of PI
Reasons for use:
• Intuitive (“bang per
buck”)
• Properly considers
time value of money
Problems:
• Doesn’t rank
projects properly
Verdict:
• Mixed
• OK for yes/no
• Don’t use
to rank
Calculating NPV
Discount
Incremental
After-tax Cash Flows
at the Cost of Capital
Incremental
Stand-Alone Principle:
Project Balance Sheet
D
A
E
Estimate project total
market value as if it
were a stand-alone firm
Include all project cash
flow effects
Total market value: no
financing cash flows
Determining Incremental Cash Flow
Ignore sunk costs:
NPV analysis is
always forwardlooking
Determining Incremental Cash Flow
Include opportunity costs
• Adopting a project often
means not doing something
else
• Using idle capacity for
one product means not
using it for some other
product
• Replacing a machine
means using the new
machine and not using
the old one
Determining Incremental Cash Flow
• Include all side
effects
• Erosion
• e.g. Bud vs. Bud Lite
• Synergies
• e.g. “franchise” movies
Project Time Line
t=0
Project
Initiation
Initial outlay
+ disposal of
replaced assets
+ ITC (if any)
t=T
Period of Project Operations
Project
Termination
Project Cash Flow
= Project Operating CF
-  net wkg capital
- cap ex
Disposal of
assets +
wkg cap
recovery
Project After-Tax Operating Cash Flow
Operating Cash Flow (OCF)
= (Sales – Cash Op.Cost – Dep)(1-T) + Dep
= (Sales – Cash Op.Cost)(1-T) – Dep(1-T) + Dep
= (Sales – Cash Op.Cost)(1-T) +TDep
Tax Shield Approach
OCF = (Sales – Cash Op.Cost)(1-T) + TDep
Tdep is the depreciation tax shield (i.e., taxes
saved by the ability to deduct depreciation)
Depreciation Methods
• Straight-line
• Deduct equal fractions of original cost over the life
of the project
• MACRS
• Modified Accelerated Cost Recovery System
• Deduct specified fractions of original cost over
allowable “life” for property class
MACRS Depreciation
Class
3-year
5-year
7-year
Examples
Research equip.
Autos, computers
Most industrial
equipment
Year
3-yr
5-yr
7-yr
1
33.33%
20.00%
14.3%
2
44.44
32.00
24.5
3
14.8
19.20
17.5
4
7.4
11.5
12.5
5
11.5
8.9
6
5.8
8.9
7
8.9
8
4.5
Tax Consequences of Asset Disposal
Original cost
Selling price A
Taxable income
Depreciated book value
Tax-deductible loss
Selling price B