The Optimality of the NPV Rule

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```					The Optimality of the NPV Rule
In this chapter, we will introduce
alternative investment rules such as …
 IRR: Internal Rate of Return

 The Payback Rule

 Accounting-Based Rules

… and see why NPV is preferable to all
0
The Net Present Value (NPV)
Rule
   Net Present Value (NPV) = Total PV of future
CF’s + Initial Investment CF
   Estimating NPV:
   1. Estimate future cash flows: how much? and
when?
   2. Estimate discount rate
   3. Estimate initial costs
   Acceptance Criteria: Accept if NPV > 0
   Ranking Criteria: If mutually exclusive
projects, choose the highest NPV                   1
Good Attributes of the NPV
Rule
   1. Uses cash flows
   2. Uses ALL cash flows of the project
   3. Discounts ALL cash flows properly

   In recent years, the NPV rule has
become the dominant investment rule.
Today, we will see why other rules are
inferior.
2
The Payback Period Rule
   How long does it take the project to
“pay back” its initial investment?
   Payback Period = number of years to
recover initial costs
   Minimum Acceptance Criteria:
   set by management
   Ranking Criteria:
   set by management
3
The Payback Period Rule
   Ignores the time value of money
   Ignores cash flows after the payback
period
   Biased against long-term projects
   Requires an arbitrary acceptance criteria
   A project accepted based on the payback
criteria may not have a positive NPV
   Easy to understand
   Biased toward liquidity
4
The Discounted Payback
Period Rule
   How long does it take the project to
“pay back” its initial investment taking
the time value of money into account?
   By the time you have discounted the
cash flows, you might as well calculate
the NPV.
   You are still ignoring cash flows far in
the future (as in strategic investments).
5
Average Accounting Return Rule

Average Net Income
AAR 
Average Book Value of Investent
   Ranking Criteria and Minimum Acceptance
Criteria set by management
   Ignores the time value of money
   Uses an arbitrary benchmark cutoff rate
   Most seriously: Based on book values, not cash
flows and market values
   The accounting information is readily available
   Easy to calculate                                 6
Internal Rate of Return (IRR)
   IRR: the discount that sets NPV to zero

   Minimum Acceptance Criteria:
   Accept if the IRR exceeds the required return.

   Ranking Criteria:
   Select alternative with the highest IRR

   Does not distinguish between investing and
borrowing.
   IRR may not exist or there may be multiple IRR
   Problems with mutually exclusive investments
   Easy to understand and communicate               7
The Internal Rate of Return:
Example
Consider the following project:
\$50          \$100        \$150

0           1            2            3
-\$200
The internal rate of return for this project is
19.44%
\$50        \$100        \$150
NPV  0                         
(1  IRR ) (1  IRR ) (1  IRR )3
2

8
The NPV Payoff Profile for This
Example
If we graph NPV versus discount rate, we can
see the IRR as the x-axis intercept.
Discount Rate      NPV           \$120.00
0%         \$100.00          \$100.00
4%          \$71.04           \$80.00
8%          \$47.32
\$60.00
12%          \$27.79
\$40.00
NPV

16%          \$11.65
20%          (\$1.74)
IRR = 19.44%
\$20.00
24%         (\$12.88)           \$0.00
28%         (\$22.17)
32%         (\$29.93)
-1%
(\$20.00)     9%       19%         29%    39%
36%         (\$36.43)         (\$40.00)
40%         (\$41.86)         (\$60.00)
Discount rate
9
Problems with the IRR
Approach
• Multiple IRRs are possible.
• Are We Borrowing or Lending?
• The Scale Problem.
• The Timing Problem.

10
Multiple IRRs
\$200      \$800
There are two IRRs
for this project.
0              1           2          3 Which one to use?
-\$200                              - \$800
100% = IRR2
NPV

\$100.00

\$50.00

\$0.00
-50%        0%
(\$50.00)
50%
0% = IRR1100%       150%     200%

Discount rate
(\$100.00)

(\$150.00)                                                11
The Scale Problem
Would you rather make 100% or 50% on
What if the 100% return is on a \$1
investment while the 50% return is on a
\$1,000 investment?

12
The Timing Problem
\$10,000   \$1,000    \$1,000
Project A
0        1          2        3
-\$10,000
\$1,000     \$1,000      \$12,000
Project B
0        1          2        3
-\$10,000
The preferred project in this case depends on the
discount rate, not the IRR.                              13
The Timing Problem:
Projects A and B
\$5,000.00
\$4,000.00
Project A
\$3,000.00
Project B
\$2,000.00
10.55% = “crossover rate”
NPV

\$1,000.00
\$0.00
(\$1,000.00) 0%      10%       20%     30%       40%

(\$2,000.00)
(\$3,000.00)
12.94% = IRRB   16.04% = IRRA
(\$4,000.00)
14
Discount rate
Calculating the Crossover Rate
Compute the IRR for either project “A-B” or “B-A”
Year Project A Project B Project A-B Project B-A
0 (\$10,000) (\$10,000)          \$0          \$0
1 \$10,000     \$1,000      \$9,000     (\$9,000)
2 \$1,000      \$1,000           \$0          \$0
3 \$1,000 \$12,000        (\$11,000)    \$11,000

\$3,000.00
10.55% = IRR
\$2,000.00
\$1,000.00
NPV

A-B
\$0.00
B-A
(\$1,000.00) 0%      5%       10%         15%   20%
(\$2,000.00)
(\$3,000.00)
Discount rate                        15
Mutually Exclusive vs.
Independent Projects
   Mutually Exclusive Projects: only ONE of
several potential projects can be chosen, e.g.
acquiring an accounting system.
   RANK all alternatives and select the best one.

   Independent Projects: accepting or rejecting
one project does not affect the decision of
the other projects.
   Must exceed a MINIMUM acceptance criteria.

16
Profitability Index (PI) Rule
Total PV of Future Cash Flows
PI 
Initial Investent
   Minimum Acceptance Criteria:
   Accept if PI > 1
   Ranking Criteria:
   Select alternative with highest PI
   Problems with mutually exclusive investments
   May be useful when available investment funds are
limited
   Correct decision when evaluating independent
projects; simple rule                             17
Example of Investment Rules
Compute the IRR, NPV, PI, and payback
period for the following two projects.
Assume the required return is 10%.

Year      Project A     Project B
0          -\$200           -\$150
1           \$200             \$50
2           \$800            \$100
3          -\$800            \$150     18
Example of Investment Rules
Project A   Project B
CF0            -\$200.00    -\$150.00
PV0 of CF1-3    \$241.92     \$240.80

NPV =         \$41.92         \$90.80
IRR =      0%, 100%         36.19%
PI =          1.2096         1.6053

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Example of Investment Rules
Payback Period:
Project A           Project
B
Time      CF Cum. CF           CF Cum. CF
0       -200       -200      -150    -150
1        200          0        50    -100
2        800        800       100       0
3       -800          0       150     150
Payback period for project B = 2 years.
Payback period for project A = 1 or 3 years?
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Relationship Between NPV and
IRR
Discount rate   NPV for A   NPV for B
-10%         -87.52     234.77
0%           0.00     150.00
20%          59.26      47.92
40%          59.48      -8.60
60%          42.19     -43.07
80%          20.85     -65.64
100%           0.00     -81.25
120%         -18.93     -92.52
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NPV Profiles
\$400
NPV

\$300
IRR 1(A)    IRR (B)        IRR 2(A)
\$200

\$100

\$0
-15%    0%   15%   30%    45%   70%   100% 130% 160% 190%
(\$100)

(\$200)
Project A
Discount rates
Cross-over Rate                                            Project B 22
A Real World Capital
Budgeting Puzzle:
   Poterba and Summers (1982) showed
empirically that firms use much higher
hurdle rates than what finance theory
would predict, i.e. they compute NPV at
discount rates way above the cost of
capital.

   Why would they do that?
23
Capital Budgeting in the Real
   Some firms face financial constraints (e.g.
right now, it is difficult to tap into equity
markets).
   Division managers have more detailed
knowledge than headquarters. They often
overstate their situation to get funding.
   However, there are limits to overstatements
(post-audits of forecasts, divisions have to
meet their own projections)
24
Capital Budgeting in the Real
   Thus, NPV rule cannot be applied directly.
   However, applying NPV-rule with higher cost
of capital can account for some of the
overstatements.
   It is important to design incentive schemes
•   Efficient capital allocation and investments.
•   High managerial effort in the interest of
shareholders.

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Summary and Conclusions
   This chapter evaluates the most popular
alternatives to NPV:
   Payback period
   Accounting rate of return
   Internal rate of return
   Profitability index
   We see how all other investment rules
in existence are inferior to NPV.
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