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1
Prof-Parashar DaveDepartment-commerce
Capital-BudgetingTechniques
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2Capital Budgeting Concepts❖ Capital Budgeting involves evaluation of (and
decision about) projects. Which projects should be accepted? Here, our goal is to accept a project which maximizes the shareholder wealth. Benefits are worth more than the cost.
❖ The Capital Budgeting is based on forecasting.❖ Estimate future expected cash flows.❖ Evaluate project based on the evaluation method.❖ Classification of Projects
❖ Mutually Exclusive - accept ONE project only❖ Independent - accept ALL profitable projects.
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3Capital Budgeting Concepts
❖ Initial Cash Outlay - amount of capital spent to get project going.
Cash Flows
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4Capital Budgeting Concepts
❖ Initial Cash Outlay - amount of capital spent to get project going.
❖ If spend $10 million to build new plant then the Initial Outlay (IO) = $10 million
Cash Flows
CF0 = Cash Flow time 0 = -10 million
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5Capital Budgeting Concepts
❖ Initial Cash Outlay - amount of capital spent to get project going.
❖ If spend $10 million to build new plant then the Initial Outlay (IO) = $10 million
Cash Flows
CFn = Sales - Costs
❖Annual Cash Inflows--after-tax CF❖Cash inflows from the project
CF0 = Cash Flow time 0 = -10 million
We will determine these in Chapter 10
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6Capital Budgeting Methods
❖ Number of years needed to recover your initial outlay.
Payback Period
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7Capital Budgeting Methods
❖ Number of years needed to recover your initial outlay.
Payback Period
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
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8Capital Budgeting Methods
❖ Number of years needed to recover your initial outlay.
Payback Period
0 1 2 3 4
3,500 3,500 3,500 3,500(10,000)
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
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9Capital Budgeting Methods
❖ Number of years needed to recover your initial outlay.
Payback Period
0 1 2 3 4
3,500-6,500
3,500 3,500 3,500(10,000)Cumulative CF
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
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10Capital Budgeting Methods
❖ Number of years needed to recover your initial outlay.
Payback Period
0 1 2 3 4
3,500-6,500
3,500-3,000
3,500 3,500(10,000)Cumulative CF
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
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11Capital Budgeting Methods
❖ Number of years needed to recover your initial outlay.
Payback Period
0 1 2 3 4
3,500-6,500
3,500-3,000
3,500+500
3,500(10,000)Cumulative CF
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
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12Capital Budgeting Methods
❖ Number of years needed to recover your initial outlay.
Payback Period
0 1 2 3 4
3,500-6,500
3,500-3,000
3,500+500
3,500(10,000)
Payback 2.86 yearsCumulative CF
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
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13Capital Budgeting Methods
❖ Number of years needed to recover your initial outlay.
Payback Period
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
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14Capital Budgeting Methods
❖ Number of years needed to recover your initial outlay.
Payback Period
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
0 1 2 3 4
500 500 4,600 10,000(10,000)
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15Capital Budgeting Methods
❖ Number of years needed to recover your initial outlay.
Payback Period
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
0 1 2 3 4
500-9,500
500 4,600 10,000(10,000)Cumulative CF
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16Capital Budgeting Methods
❖ Number of years needed to recover your initial outlay.
Payback Period
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
0 1 2 3 4
500-9,500
500-9,000
4,600 10,000(10,000)Cumulative CF
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17Capital Budgeting Methods
❖ Number of years needed to recover your initial outlay.
Payback Period
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
0 1 2 3 4
500-9,500
500-9,000
4,600-4,400
10,000(10,000)Cumulative CF
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18Capital Budgeting Methods
❖ Number of years needed to recover your initial outlay.
Payback Period
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
0 1 2 3 4
500-9,500
500-9,000
4,600-4,400
10,000+5,600
(10,000)Cumulative CF
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19Capital Budgeting Methods
❖ Number of years needed to recover your initial outlay.
Payback Period
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
0 1 2 3 4
500-9,500
500-9,000
4,600-4,400
10,000+5,600
(10,000)
Payback = 3.44 yearsCumulative CF
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20Capital Budgeting Methods
❖ Number of years needed to recover your initial outlay.
Payback Period
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
0 1 2 3 4
500-9,500
500-9,000
4,600-4,400
10,000+5,600
(10,000)
Payback 3.44 yearsCumulative CF
Evaluation:Company sets maximum acceptable payback. If Max PB = 3 years, accept project A and reject project C
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21•Payback Method
The payback method is not a good method as it does not consider the time value of money.
Which project should you choose?
CF0 CF1 CF2 CF3A -100,000 90,000 9,000 1,000
B -100,000 1,000 9,000 90,000
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22•Payback Method
The Discounted payback method can correct this shortcoming of the payback method.
To find the discounted pay back(1) Find the PV of each cash flow on the time line.(2) Find the payback using the discounted CF and NOT
the CF.
Example In Table 9-2
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23•Payback Method
Also, the payback method is not a good method as it does not consider the cash flows beyond the payback period.
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24Payback Method
Also, the payback method is not a good method as it does not consider the cash flows beyond the payback period.
Which project should you choose?CF0 CF1 CF2 Cf3 CF4
A -100000 90000 10000 0 0B -100000 90000 9000 80000 1000000
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25Payback Method
Also, the payback method is not a good method as it does not consider the cash flows beyond the payback period.
Which project should you choose? CF0 CF1 CF2 Cf3 CF4A -100,000 90,000 10,000 0 0B -100,000 90,000 9,000 80,000 100,0000
These two shortcomings often result in an incorrect decisions.
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26Capital Budgeting Methods
Methods that consider time value of money and all cash flows
Net Present Value:Present Value of all costs and benefits of a project.
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27Capital Budgeting Methods
Present Value of all costs and benefits of a project.Concept is similar to Intrinsic Value of a security but
subtracts cost of the project.
Net Present Value
NPV = PV of Inflows - Initial Outlay
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28Capital Budgeting Methods
❖ Present Value of all costs and benefits of a project.❖ Concept is similar to Intrinsic Value of a security but
subtracts of cost of project.
Net Present Value
NPV = PV of Inflows - Initial Outlay
NPV = + + +···+ – CF1 (1+ k )
CF2 (1+ k )
2 CF3 (1+ k )
3 CFn (1+ k )
n
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29Capital Budgeting MethodsNet Present Value
0 1 2 3 4
500 500 4,600 10,000(10,000)
k=10%
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
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30Capital Budgeting MethodsNet Present Value
0 1 2 3 4
500 500 4,600 10,000(10,000)
455
k=10%
$500 (1.10)
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
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31Capital Budgeting MethodsNet Present Value
0 1 2 3 4
500 500 4,600 10,000(10,000)
455413
k=10%
$500 (1.10) 2
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
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32Capital Budgeting MethodsNet Present Value
0 1 2 3 4
500 500 4,600 10,000(10,000)
455413
3,456
k=10%
$4,600 (1.10) 3
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
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33Capital Budgeting MethodsNet Present Value
0 1 2 3 4
500 500 4,600 10,000(10,000)
455
6,830
4133,456
k=10%
$10,000 (1.10) 4
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
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34Capital Budgeting MethodsNet Present Value
0 1 2 3 4
500 500 4,600 10,000(10,000)
455
$11,1546,830
4133,456
k=10%
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
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35Capital Budgeting MethodsNet Present Value
0 1 2 3 4
500 500 4,600 10,000(10,000)
455
6,830
4133,456
k=10%
PV Benefits > PV Costs
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
$11,154 > $ 10,000
$11,154
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36Capital Budgeting MethodsNet Present Value
0 1 2 3 4
500 500 4,600 10,000(10,000)
455
6,830
4133,456
k=10%
PV Benefits > PV Costs
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
$11,154 > $ 10,000NPV > $0
$1,154 > $0
$11,154$1,154 = NPV
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37Capital Budgeting MethodsNet Present Value
0 1 2 3 4
3,500(10,000)
k=10%
3,500 3,500 3,500
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
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38Capital Budgeting MethodsNet Present Value
0 1 2 3 4
3,500(10,000)
k=10%
3,500 3,500 3,500
NPV = + + + – 10,000 3,500 (1+ .1 )
3,500 (1+ .1)2
3,500 (1+ .1 )
3 3,500 (1+ .1 )
4
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
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39Capital Budgeting MethodsNet Present Value
0 1 2 3 4
3,500(10,000)
k=10%
3,500 3,500 3,500
NPV = + + + – 10,000 3,500 (1+ .1 )
3,500 (1+ .1)2
3,500 (1+ .1 )
3 3,500 (1+ .1 )
4
PV of 3,500 Annuity for 4 years at 10%
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
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40Capital Budgeting MethodsNet Present Value
0 1 2 3 4
3,500(10,000)
k=10%
3,500 3,500 3,500
NPV = + + + – 10,000 3,500 (1+ .1 )
3,500 (1+ .1)2
3,500 (1+ .1 )
3 3,500 (1+ .1 )
4
= 3,500 x PVIFA 4,.10 - 10,000
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
= 11,095 – 10,000 = $1,095
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41Capital Budgeting Methods
❖ If projects are independent then accept all projects with NPV ≥ 0.
NPV Decision RulesACCEPT A & B
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42Capital Budgeting Methods
❖ If projects are independent then accept all projects with NPV ≥ 0.
❖ If projects are mutually exclusive, accept projects with higher NPV.
NPV Decision RulesACCEPT A & B
ACCEPT B only
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43
10%5%0 Cost of Capital
NPV
6,000
3,000
20%15%
Net Present Value Profile❖ Graphs the Net Present Value of the project with
different required rates
NPV(0%) = + + + – 10,000 3,500 (1+ 0 )
3,500 (1+ 0)2
3,500 (1+ 0 )
3 3,500 (1+ 0)4
= $4,000
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
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44
10%5%0 Cost of Capital
NPV
6,000
3,000
20%15%
Net Present Value Profile❖ Graphs the Net Present Value of the project with
different required rates
NPV(5%) = + + + – 10,000 3,500 (1+ .05 )
3,500 (1+ .05)2
3,500 (1+ .05 )
3 3,500 (1+ .05)4
= $2,411
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
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45
10%5%0 Cost of Capital
NPV
6,000
3,000
20%15%
Net Present Value Profile❖ Graphs the Net Present Value of the project with
different required rates
NPV(10%) = + + + – 10,000 3,500 (1+ .10 )
3,500 (1+ .10)2
3,500 (1+ .10 )
3 3,500 (1+ .10)4
= $1,095
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
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46
10%5%0 Cost of Capital
NPV
6,000
3,000
20%15%
Net Present Value Profile❖ Graphs the Net Present Value of the project with
different required rates
NPV(15%) = + + + – 10,000 3,500 (1+ .15 )
3,500 (1+ .15)2
3,500 (1+ .15 )
3 3,500 (1+ .15)4
= – $7.58
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
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47
10%5%0 Cost of Capital
NPV
6,000
3,000
20%15%
Net Present Value Profile❖ Graphs the Net Present Value of the project with
different required rates
NPV(20%) = + + + – 10,000 3,500 (1+ .20 )
3,500 (1+ .20)2
3,500 (1+ .20 )
3 3,500 (1+ .20)4
= – $939
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
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48
10%5%0 Cost of Capital
NPV
6,000
3,000
20%15%
Net Present Value Profile❖ Graphs the Net Present Value of the project with
different required rates
Connect the Points
P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
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49
10%5%0 Cost of Capital
NPV
6,000
3,000
20%15%
Net Present Value Profile❖ Graphs the Net Present Value of the project with
different required rates P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
NPV(0%) = + + + – 10,000 500 (1+ 0 )
500 (1+ 0)2
4,600 (1+ 0 )
3 10,000 (1+ 0)4
= $5,600
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50
10%5%0 Cost of Capital
NPV
6,000
3,000
20%15%
Net Present Value Profile❖ Graphs the Net Present Value of the project with
different required rates P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
NPV(5%) = + + + – 10,000 500 (1+.05)
500 (1+.05)2
4,600 (1+ .05)3
10,000 (1+ .05)4
= $3,130
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51
10%5%0 Cost of Capital
NPV
6,000
3,000
20%15%
Net Present Value Profile❖ Graphs the Net Present Value of the project with
different required rates P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
NPV(10%) = + + + – 10,000 500 (1+.10)
500 (1+.10)2
4,600 (1+ .10)3
10,000 (1+ .10)4
= $1.154
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52
10%5%0 Cost of Capital
NPV
6,000
3,000
20%15%
Net Present Value Profile❖ Graphs the Net Present Value of the project with
different required rates P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
NPV(15%) = + + + – 10,000 500 (1+.15)
500 (1+.15)2
4,600 (1+ .15)3
10,000 (1+ .15)4
= –$445
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53
10%5%0 Cost of Capital
NPV
6,000
3,000
20%15%
Project B
Net Present Value Profile❖ Graphs the Net Present Value of the project with
different required rates P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
Connect the Points
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54
10%5%0 Cost of Capital
NPV
6,000
3,000
20%15%
Project B
Net Present Value Profile❖ Graphs the Net Present Value of the project with
different required rates P R O J E C TTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
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55Net Present Value Profile❖ Compare NPV of the two projects for different
required rates
10%5%0 Cost of Capital
NPV
6,000
3,000
20%15%
Project B
Crossover point
Project A
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56Net Present Value Profile❖ Compare NPV of the two projects for different
required rates
10%5%0 Cost of Capital
NPV
6,000
3,000
20%15%
Project B
Crossover point
Project AFor any discount rate < crossover point choose B
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57Net Present Value Profile❖ Compare NPV of the two projects for different
required rates
10%5%0 Cost of Capital
NPV
6,000
3,000
20%15%
Project B
Crossover point
For any discount rate > crossover point choose A
Project AFor any discount rate < crossover point choose B
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58Capital Budgeting MethodsInternal Rate of Return❖ Measures the rate of return that will make the PV of
future CF equal to the initial outlay.
Definition:The IRR is that discount rate at which NPV = 0
IRR is like the YTM. It is the same cocept but the term YTM is used only for bonds.
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59Capital Budgeting MethodsInternal Rate of Return❖ Measures the rate of return that will make the PV of
future CF equal to the initial outlay.
The IRR is the discount rate at which NPV = 0
10%5%0 Cost of Capital
NPV
6,000
3,000
20%15%
Project B
NPV = $0
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60Capital Budgeting MethodsInternal Rate of Return❖ Measures the rate of return that will make the PV of
future CF equal to the initial outlay.Or, the IRR is the discount rate at which NPV = 0
10%5%0 Cost of Capital
NPV
6,000
3,000
20%15%
Project B
NPV = $0 IRRA ≈ 15%
IRRB ≈ 14%
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61Capital Budgeting MethodsInternal Rate of Return❖ Determine the mathematical solution for IRR
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62Capital Budgeting MethodsInternal Rate of Return❖ Determine the mathematical solution for IRR
0 = NPV = + +···+ – CF1 (1+ IRR )
CF2 (1+ IRR )
2 CFn (1+ IRR )
n
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63Capital Budgeting MethodsInternal Rate of Return❖ Determine the mathematical solution for IRR
0 = NPV = + +···+ – CF1 (1+ IRR )
CF2 (1+ IRR )
2 CFn (1+ IRR )
n
= + +···+
CF1 (1+ IRR )
CF2 (1+ IRR )
2 CFn (1+ IRR )
n
Outflow = PV of Inflows
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64Capital Budgeting MethodsInternal Rate of Return❖ Determine the mathematical solution for IRR
0 = NPV = + +···+ – CF1 (1+ IRR )
CF2 (1+ IRR )
2 CFn (1+ IRR )
n
= + +···+
CF1 (1+ IRR )
CF2 (1+ IRR )
2 CFn (1+ IRR )
n
Outflow = PV of InflowsSolve for Discount Rates
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65Capital Budgeting MethodsInternal Rate of ReturnFor Project B
Cannot solve for IRRdirectly, must use Trial & Error
10,000 = + + + 500 (1+ IRR )
500 (1+ IRR )
2 10,000 (1+ IRR )
4 4,600 (1+ IRR )
3
10%5%0 Cost of Capital
NPV
6,000
3,000
20%15%
Project B
IRRB ≈ 14%
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66Capital Budgeting MethodsInternal Rate of ReturnFor Project B
Cannot solve for IRRdirectly, must use Trial & Error
10,000 = + + + 500 (1+ IRR )
500 (1+ IRR )
2 10,000 (1+ IRR )
4 4,600 (1+ IRR )
3
TRY 14%
10,000 = + + + 500 (1+ .14 )
500 (1+ .14)2
10,000 (1+ .14 )
4 4,600 (1+ .14 )
3
?
10%5%0 Cost of Capital
NPV
6,000
3,000
20%15%
Project B
IRRB ≈ 14%
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67Capital Budgeting MethodsInternal Rate of ReturnFor Project B
Cannot solve for IRRdirectly, must use Trial & Error
10,000 = + + + 500 (1+ IRR )
500 (1+ IRR )
2 10,000 (1+ IRR )
4 4,600 (1+ IRR )
3
TRY 14%
10,000 = + + + 500 (1+ .14 )
500 (1+ .14)2
10,000 (1+ .14 )
4 4,600 (1+ .14 )
3
?
10,000 = 9,849?
PV of Inflows too low, try lower rate
10%5%0 Cost of Capital
NPV
6,000
3,000
20%15%
Project B
IRRB ≈ 14%
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68Capital Budgeting MethodsInternal Rate of ReturnFor Project B
Cannot solve for IRRdirectly, must use Trial & Error
10,000 = + + + 500 (1+ IRR )
500 (1+ IRR )
2 10,000 (1+ IRR )
4 4,600 (1+ IRR )
3
TRY 13%
10,000 = + + + 500 (1+ .13 )
500 (1+ .13)2
10,000 (1+ .13 )
4 4,600 (1+ .13 )
3
?
10%5%0 Cost of Capital
NPV
6,000
3,000
20%15%
Project B
IRRB ≈ 14%
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69Capital Budgeting MethodsInternal Rate of ReturnFor Project B
Cannot solve for IRRdirectly, must use Trial & Error
10,000 = + + + 500 (1+ IRR )
500 (1+ IRR )
2 10,000 (1+ IRR )
4 4,600 (1+ IRR )
3
TRY 13%
10,000 = + + + 500 (1+ .13 )
500 (1+ .13)2
10,000 (1+ .13 )
4 4,600 (1+ .13 )
3
?
10,000 = 10,155?
10%5%0 Cost of Capital
NPV
6,000
3,000
20%15%
Project B
IRRB ≈ 14%
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70Capital Budgeting MethodsInternal Rate of ReturnFor Project B
Cannot solve for IRRdirectly, must use Trial & Error
10,000 = + + + 500 (1+ IRR )
500 (1+ IRR )
2 10,000 (1+ IRR )
4 4,600 (1+ IRR )
3
TRY 13%
10,000 = + + + 500 (1+ .13 )
500 (1+ .13)2
10,000 (1+ .13 )
4 4,600 (1+ .13 )
3
?
10,000 = 10,155?
13% < IRR < 14%
10%5%0 Cost of Capital
NPV
6,000
3,000
20%15%
Project B
IRRB ≈ 14%
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71Capital Budgeting MethodsDecision Rule for Internal Rate of Return
Independent ProjectsAccept Projects with
IRR ≥ required rate
Mutually Exclusive ProjectsAccept project with highest IRR ≥ required rate
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72Capital Budgeting MethodsProfitability Index
PI = PV of InflowsInitial Outlay
Very Similar to Net Present Value
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73Capital Budgeting MethodsProfitability Index
PI = PV of InflowsInitial Outlay
Very Similar to Net Present Value
Instead of Subtracting the Initial Outlay from the PVof Inflows, the Profitability Index is the ratio of InitialOutlay to the PV of Inflows.
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74Capital Budgeting MethodsProfitability Index
PI = PV of InflowsInitial Outlay
Very Similar to Net Present Value
Instead of Subtracting the Initial Outlay from the PVof Inflows, the Profitability Index is the ratio of InitialOutlay to the PV of Inflows.
+ + +···+
CF1 (1+ k )
CF2 (1+ k )
2 CF3 (1+ k )
3 CFn (1+ k )
n
PI =
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75Capital Budgeting MethodsProfitability Index for Project B P R O J E C T
Time A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
+ + + 500 (1+ .1 )
500 (1+ .1)2
4,600 (1+ .1 )
3 10,000 (1+ .1 )
4
10,000PI =
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76Capital Budgeting MethodsProfitability Index for Project B P R O J E C T
Time A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
+ + + 500 (1+ .1 )
500 (1+ .1)2
4,600 (1+ .1 )
3 10,000 (1+ .1 )
4
10,000PI =
PI = 11,15410,000 = 1.1154
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77Capital Budgeting MethodsProfitability Index for Project B P R O J E C T
Time A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
+ + + 500 (1+ .1 )
500 (1+ .1)2
4,600 (1+ .1 )
3 10,000 (1+ .1 )
4
10,000PI =
PI = 11,15410,000 = 1.1154
Profitability Index for Project A
10,000PI =
3,500 x PVIFA 4, .10
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78Capital Budgeting MethodsProfitability Index for Project B P R O J E C T
Time A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
+ + + 500 (1+ .1 )
500 (1+ .1)2
4,600 (1+ .1 )
3 10,000 (1+ .1 )
4
10,000PI =
PI = 11,15410,000 = 1.1154
Profitability Index for Project A
10,000PI =
PI = 11,095 10,000 = 1.1095
3,500( ) 1
.10(1+.10)4 1
.10
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79Capital Budgeting MethodsProfitability Index Decision Rules❖ Independent Projects
❖ Accept Project if PI ≥ 1❖ Mutually Exclusive Projects
❖ Accept Highest PI ≥ 1 Project
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80Comparison of Methods
Project A Project B ChoosePayback < 3 years < 4 years ANPV $1,095 $1,154 BIRR 14.96% 13.50% API 1.1095 1.1154B
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81Comparison of Methods❖ Time Value of Money
❖ Payback - Does not adjust for timing differences (ignore Discounted Payback)
❖ NPV, IRR and PI take into account the time value of money
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82Comparison of Methods❖ Time Value of Money
❖ Payback - Does not adjust for timing differences❖ NPV, IRR and PI take into account the time value of
money❖ Relevant Cash Flows?
❖ NPV, IRR and PI use all Cash Flows❖ Payback method ignores Cash Flows that occur
after the Payback Period.
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83Comparison of Methods❖ Time Value of Money
❖ Payback - Does not adjust for timing differences ❖ NPV, IRR and PI take into account the time value of
money❖ Relevant Cash Flows?
❖ NPV, IRR and PI use all Cash Flows❖ Payback method ignores Cash Flows that occur
after the Payback Period.
0 1 2
5,000 5,000(10,000)
Project 1
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84Comparison of Methods❖ Time Value of Money
❖ Payback - Does not adjust for timing differences ❖ NPV, IRR and PI take into account the time value of
money❖ Relevant Cash Flows?
❖ NPV, IRR and PI use all Cash Flows❖ Payback method ignores Cash Flows that occur
after the Payback Period.
0 1 2
5,000 5,000(10,000)
Project 1
0 1 2 3
5,000 5,000(10,000)
Project 2
10,000
Both Projects haveIdentical Payback
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85Comparison of MethodsNPV & PI indicated accept Project B while IRR indicated that
Project A should be accepted. Why?Sometimes there is a conflict between the decisions based on
NPV and IRR methods. The conflict arises if there is difference in the timing of CFs or
sizes of the projects (or both).The cause of the conflict is the underlying reinvestment rate
assumption.Reinvestment Rate Assumptions
❖ NPV assumes cash flows are reinvested at the required rate, k.
❖ IRR assumes cash flows are reinvested at IRR.Reinvestment Rate of k more realistic as most projects earn
approximately k (due to competition)NPV is the Better Method for project evaluation
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86IRR
Because of its unreasonable reinvestment rate assumption, IRR method can result in bad decisions.
Another problem with IRR is that if the sign of the cash flow changes more than once, there is a possibility of multiple IRR. See p 340.
The problem of unreasonable assumption can be addressed by using Modified IRR
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87MIRR
To find MIRR1.Find the FV of all intermediate CFs using the cost of
capital (the hurdle rate) as the interest rate.2.Add all FV.3. Find that discount rate which makes the PV of the
FV equal to the PV of outflows.
Drop MIRR computations.
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88
Thank you