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Chapter 9
Net Present Value and Other
Investment Criteria
Prepared and Taught by Lecturer : YIN SOKHNG
E-mail: [email protected]
Tel:(855) 16889872 / 17989972
Chapter Outline
9.1 Net Present Value (NPV)
9.2 The Payback Rule (PR)
9.3 The Discounted Payback Period Rule (DPR)
9.4 The Average Accounting Return (AAR)
9.5 The Internal Rate of Return (IRR)
9.6 The Profitability Index (PI)
9.7 The Practice of Capital Budgeting
2Instructed by YIN SOKHENG, Master in Finance
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Accepting positive NPV projects benefits
shareholders.NPV uses cash flows
NPV uses all the cash flows of the project
NPV discounts the cash flows properly
The difference between the market value of aproject and its cost
How much value is created from undertakingan investment?
9.1 Net Present Value
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The Net Present Value (NPV) Rule
Net Present Value (NPV) =Initial Investment (costs)
+ PV of future CFs
Estimating NPV: 1. Estimate initial costs
2. Estimate future cash flows: how much? and when?
3. Estimate discount rate
Minimum Acceptance Criteria: Accept if NPV > 0
Ranking Criteria: Choose the highest NPV
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Good Attributes of the NPV Rule
1. Uses cash flows
2. Uses ALL cash flows of the project
3. Discounts ALL cash flows properly
Reinvestment assumption: the NPV rule
assumes that all cash flows can be reinvested
at the discount rate.
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For example of NPV
Year Cash flow (net income)
0 $9,0001 6,000
2 4,000
3 3,000
4 2,000
Initial cash flow = $9,000; IR = 10%; Do you
Recommend this project?
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For example of NPV
PV = 6,000 /(1.1) + 4,000 /(1.1)2 + 3,000
/(1.1)3 + 2,000 /(1.1)4 = $12,377
NPV = $12,3779,000 = $3,377
EX2: IBM Company has two projects to invest:
1. Project (A) is initial cost of $350,000 and
cash inflow in year one is $400,000
2. Project (B) invests in treasury bill with 7%
of interest rate, Do you recommend?
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For example of NPV
PV of Project (B)= 400,000 / (1.07) =
$373,832
NPV = $373,832350,000 = $23,832
Invest in project (A) is best
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9.2 The Payback Period
How long does it take the project to pay
back its initial investment?
Computation
Estimate the cash flows
Subtract the future cash flows from the initial cost
until the initial investment has been recovered
Payback Period = number of years to recover
initial costs
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The Payback Period Rule
Decision RuleAccept if the payback
period is less than some preset limit Minimum Acceptance Criteria:
set by management
Ranking Criteria:
set by management
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The Payback Period Rule
Disadvantages:
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 criteriamay not have a positive NPV
Advantages:
Easy to understand Biased toward liquidity
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Computing Payback For The
Project
Assume we will accept the project if it pays
back within two years.
Year 1: 165,00063,120 = 101,880 still to recover
Year 2: 101,88070,800 = 31,080 still to recover
Year 3: 31,08091,080 = -60,000project pays
back in year 3
Do we accept or reject the project?
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Payback Period
Assume ABC Co. plans to invest in a project
that has a $50,000 initial outlay. It is estimatedthat the project will provide regular cashinflows of $30,000 in year 1, $20,000 in year 2,
$10,000 in year 3, and $5,000 in year 4.
Payback period = 2 years
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For example of Payback period
Year A B C D E
0 -100 -200 -200 -200 -50
1 30 40 40 100 100
2 40 20 20 100 -50,000
3 50 10 10 10 -200
4 60 130 200
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For example of Payback period
Payback period (A) = 2 years + (10070 )/ 50 = 2.6 years
Payback period (B) = Never payback
Payback period ( C) = 4 years
Payback period (D) = 2 years
Payback period (E) = 6 months
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9.3 The Discounted Payback
Period Rule
How long does it take the project to pay
back its initial investment taking the timevalue of money into account?
By the time you have discounted the cash
flows, you might as well calculate the NPV.
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9.4 The Average Accounting Return Rule
Another attractive but fatally flawed approach.
Ranking Criteria and Minimum Acceptance Criteriaset by management
Disadvantages: Ignores the time value of money
Uses an arbitrary benchmark cutoff rate
Based on book values, not cash flows and market values
Advantages: The accounting information is usually available
Easy to calculate
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InvestentofValueBookAverage
IncomeNetAverageAAR
Book value is a started investment
Average book value of Investment
= a stated investment / 2
Decision Rule: Accept the project if the AARis greater than a preset rate.
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Computing AAR For The Project
Assume we require an average accounting
return of 25%
Average Net Income:
(13,620 + 3,300 + 29,100) / 3 = 15,340
AAR = 15,340 / 72,000 = .213 = 21.3%
Do we accept or reject the project?
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Example of AAR
Assume we require an average accounting return of25%
Assume that net earnings for the next 4 years areestimated to be $10,000, 15,000, $20,000, and$30,000, respectively. If the initial investment is$100,000, find the average rate of return
Average net earnings = 10,000 + 15,000 + 20,000 +30,000 / 4 = $18,750
Average Book value = 100,000 / 2 = $50,000
AAR = $18,750 / $50,000 = 37.5% Do we accept or reject the project?
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9.5 The Internal Rate of Return (IRR)
Rule 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
Reinvestment assumption: All future cash flows assumed reinvested at the IRR.
Disadvantages: Does not distinguish between investing and borrowing. IRR may not exist or there may be multiple IRR Problems with mutually exclusive investments
Advantages: Easy to understand and communicate
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The Internal Rate of Return:
ExampleConsider the following project:
0 1 2 3
$50 $100 $150
-$200
The internal rate of return for this project is 19.44%
32 )1(
150$
)1(
100$
)1(
50$0
IRRIRRIRRNPV
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The NPV Payoff Profile for This Example
Discount Rate NPV
0% $100.00
4% $71.04
8% $47.32
12% $27.79
16% $11.65
20% ($1.74)
24% ($12.88)
28% ($22.17)
32% ($29.93)36% ($36.43)
40% ($41.86)
If we graph NPV versus discount rate, we can see the
IRR as the x-axis intercept.
IRR = 19.44%
($60.00)($40.00)
($20.00)
$0.00
$20.00
$40.00
$60.00
$80.00
$100.00
$120.00
-1% 9% 19% 29% 39%
NPV
Discount rate
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Problems with the IRR Approach
Multiple IRRs. Are We Borrowing or Lending?
The Scale Problem
The Timing Problem
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Multiple IRRs
There are two IRRs for this project:
0 1 23
$200 $800
-$200 - $800
($150.00)
($100.00)
($50.00)
$0.00
$50.00
$100.00
-50% 0% 50% 100% 150% 200%
Discount rate
NPV
100% = IRR2
Which one
should we use?
0% = IRR1
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The Scale Problem
Would you rather make 100% or 50% on your
investments?
What if the 100% return is on a $1 investment
while the 50% return is on a $1,000
investment?
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The Timing Problem
0 1 2 3
$10,000 $1,000 $1,000
-$10,000
Project A
0 1 2 3
$1,000 $1,000 $12,000
-$10,000
Project B
The preferred project in this case depends on the discount rate, not
the IRR.
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The Timing Problem
($4,000.00)
($3,000.00)
($2,000.00)
($1,000.00)
$0.00
$1,000.00
$2,000.00
$3,000.00
$4,000.00
$5,000.00
0% 10% 20% 30% 40%
Discount rate
NPV
Project A
Project B10.55% = crossoverrate
16.04% = IRRA12.94% = IRRB
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Calculating the Crossover RateCompute 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)($2,000.00)
($1,000.00)
$0.00
$1,000.00
$2,000.00
$3,000.00
0% 5% 10% 15% 20%
Discount rate
NPV A-B
B-A
10.55% = IRR
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Mutually Exclusive vs.
Independent Project
Mutually Exclusive Projects: only ONE of several
potential projects can be chosen, e.g. acquiring anaccounting system.
RANK all alternatives and select the best one.
Independent Projects: accepting or rejecting oneproject does not affect the decision of the otherprojects. Must exceed a MINIMUM acceptance criteria.
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IRR and Mutually Exclusive
Projects
Mutually exclusive projects
If you choose one, you cant choose the other
Example: You can choose to attend graduate
school next year at either Harvard or Stanford, but
not both
Intuitively you would use the following
decision rules:
NPVchoose the project with the higher NPV
IRRchoose the project with the higher IRR
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Example With Mutually Exclusive Projects
Period Project A Project B
0 -500 -400
1 325 325
2 325 200
IRR 19.43% 22.17%
NPV 64.05 60.74
The required
return for both
projects is 10%.
Which project
should you
accept and why?
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9.6 The Profitability Index (PI) Rule
Minimum Acceptance Criteria: Accept if PI > 1
Ranking Criteria:
Select alternative with highest PI
Disadvantages:
Problems with mutually exclusive investments
Advantages:
May be useful when available investment funds are limited
Easy to understand and communicate
Correct decision when evaluating independent projects
InvestentInitial
FlowsCashFutureofPVTotalPI
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9.7 The Practice of Capital Budgeting
Varies by industry:
Some firms use payback, others use accounting
rate of return.
The most frequently used technique for large
corporations is IRR or NPV.
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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
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Example of Investment Rules
Project A Project BCF0 -$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 -81.25120% -18.93 -92.52
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Project AProject B
($200)
($100)
$0
$100
$200
$300
$400
-15% 0% 15% 30% 45% 70% 100% 130% 160% 190%
Discount rates
N
PV
IRR 1(A) IRR (B)
NPV Profiles
Cross-over Rate
IRR 2(A)
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