CAPITAL BUDGETING

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CAPITAL BUDGETING
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• Capital budgeting is finance terminology for the
  process of deciding whether or not to undertake
  an investment project. There are two standard
  concepts used in capital budgeting
• Net present value (NPV) and
• Internal rate of return (IRR).

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The NPV Rule for Judging Investments and Projects

• Suppose you are considering a project that has
  cash flows CF0, CF1, CF2, . . . , CFN. Suppose
  that the appropriate discount rate for this
  project is r. Then the NPV of the project is

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NPV CF0 /(1 r )0 CF1/(1 r )1 CF2/(1 r
)2 CFN/(1 r )N Rule A project is
worthwhile by the NPV rule if its NPV gt
0. Suppose we apply the NPV criterion to
projects A and B
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Project A involves buying expensive machinery
that produces a better product at a lower cost.
The machines for project A cost 1,000 and, if
purchased, you anticipate that the project will
produce cash flows of 500 per year for the next
five years. Project Bs machines are cheaper,
costing 800, but they produce smaller annual
cash flows of 420 per year for the next five
years. Well assume that the correct discount
rate is 12.
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TWO PROJECTS TWO PROJECTS TWO PROJECTS TWO PROJECTS
Discount rate 12    
       
Year Project A Project B  
0 -1000 -800  
1 500 420  
2 500 420  
3 500 420  
4 500 420  
5 500 420  
       
NPV 802.39 714.01 lt-- NPV(B2,C6C10)C5
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Both projects are worthwhile, since each has a
positive NPV. If we have to choose between the
two projects, then project A is preferred to
project B because it has the higher NPV.
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The IRR Rule for Judging Investments

• An alternative to using the NPV criterion for
  capital budgeting is to use the internal rate of
  return (IRR). IRR is defined as the discount rate
  for which the NPV equals zero.

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TWO PROJECTS TWO PROJECTS TWO PROJECTS TWO PROJECTS
Discount rate 0.12  
   
Year Project A Project B  
0 -1000 -800  
1 500 420  
2 B6 C6  
3 B7 C7  
4 B8 C8  
5 B9 C9  
   
IRR IRR(B5B10) IRR(C5C10)  
   
       
Prepared by Dr. Charbaji for the Training Program Prepared by Dr. Charbaji for the Training Program Prepared by Dr. Charbaji for the Training Program Prepared by Dr. Charbaji for the Training Program
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TWO PROJECTS TWO PROJECTS TWO PROJECTS TWO PROJECTS
Discount rate 12  
   
Year Project A Project B  
0 -1000 -800  
1 500 420  
2 500 420  
3 500 420  
4 500 420  
5 500 420  
   
IRR 41 44 lt-- IRR(C5C10)
   
       
Prepared by Dr. Charbaji for the Training Program Prepared by Dr. Charbaji for the Training Program Prepared by Dr. Charbaji for the Training Program Prepared by Dr. Charbaji for the Training Program
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Both project A and project B are worthwhile,
since each has an IRR gt 12, which is our
relevant discount rate. If we have to choose
between the two projects then, project B is
preferred to project A because it has a
higher IRR.
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NPV or IRR, Which to Use?
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Discountrate NPV
0 1,100.00
2 928.16
4 774.84
6 637.67
8 514.62
10 403.94
12 304.16
14 213.97
16 132.28
18 58.10
20 -9.39
22 -70.92
24 -127.14
26 -178.60
28 -225.80
30 -269.16
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Do NPV and IRR Produce the Same Project
Rankings? NPV and IRR do not necessarily rank
projects the same!
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Ranking mutually exclusive projects by NPV and
IRR can lead to possibly contradictory
results. Where a conflict exists between NPV
and IRR then, the project with the larger NPV
is preferred. The NPV criterion is
the correct criterion to use for capital
budgeting.
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TABLE OF NPVs AND DISCOUNT RATES TABLE OF NPVs AND DISCOUNT RATES TABLE OF NPVs AND DISCOUNT RATES
  Project ANPV Project BNPV
0 B5NPV(A23,B6B10) C5NPV(A23,C6C10)
0.02 B5NPV(A24,B6B10) C5NPV(A24,C6C10)
0.04 B5NPV(A25,B6B10) C5NPV(A25,C6C10)
0.06 B5NPV(A26,B6B10) C5NPV(A26,C6C10)
0.08 B5NPV(A27,B6B10) C5NPV(A27,C6C10)
0.1 B5NPV(A28,B6B10) C5NPV(A28,C6C10)
0.12 B5NPV(A29,B6B10) C5NPV(A29,C6C10)
0.14 B5NPV(A30,B6B10) C5NPV(A30,C6C10)
0.16 B5NPV(A31,B6B10) C5NPV(A31,C6C10)
0.18 B5NPV(A32,B6B10) C5NPV(A32,C6C10)
0.2 B5NPV(A33,B6B10) C5NPV(A33,C6C10)
0.22 B5NPV(A34,B6B10) C5NPV(A34,C6C10)
0.24 B5NPV(A35,B6B10) C5NPV(A35,C6C10)
0.26 B5NPV(A36,B6B10) C5NPV(A36,C6C10)
0.28 B5NPV(A37,B6B10) C5NPV(A37,C6C10)
0.3 B5NPV(A38,B6B10) C5NPV(A38,C6C10)
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• When the discount rate is low, project A has a
  higher NPV than project B.
• But when the discount rate is high,
  project B has a higher NPV.
• There is a crossover point that marks the
  disagreement/agreement range.
• Project As NPV is more sensitive to changes in
  the discount rate than project Bs NPV. The
  reason for this is that project A has
  substantially more of its cash flows at later
  dates than project B.

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The Modified Internal Rate of Return MIRR
avoids the problem of multiple IRRs
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Year Project A Project B Discount 0.1
0 -100 -100
1 130 230
2   -132
NPV 18.2 0.00
IRR 30.00 10.00
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0 (2.0)
0.02 (1.4)
0.04 (0.9)
0.06 (0.5)
0.08 (0.2)
0.1 0.0
0.12 0.1
0.14 0.2
0.16 0.2
0.18 0.1
0.2 0.0
0.22 (0.2)
0.24 (0.4)
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MIRR