Capital Budgeting

1
Capital Budgeting

• For 9.220

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Outline

• Introduction
• Net Present Value (NPV)
• Payback Period Rule (PP)
• Discounted Payback Period Rule
• Average Accounting Return (AAR)
• Internal Rate of Return Rule (IRR)
• Profitability Index Rule (PI)
• Special Situations
• Mutually Exclusive, Differing Scales
• Capital Rationing
• Summary and Conclusions

3
Recall the Flows of funds and decisions important
to the financial manager
Financing Decision
Investment Decision
Reinvestment
Refinancing
Financial Manager
Financial Markets
Real Assets
Returns from Investment
Returns to Security Holders
Capital Budgeting is used to make the Investment
Decision
4
Introduction

• Capital Budgeting is the process of determining
  which real investment projects should be accepted
  and given an allocation of funds from the firm.
• To evaluate capital budgeting processes, their
  consistency with the goal of shareholder wealth
  maximization is of utmost importance.

5
Capital Budgeting Mutually Exclusive versus
Independent Project

• 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.

6
The Net Present Value (NPV) Rule

• Net Present Value (NPV)
• Total PV of future CFs - Initial Investment
• Estimating NPV
• 1. Estimate future cash flows how much? and
  when?
• 2. Estimate discount rate
• 3. Estimate initial costs
• Minimum Acceptance Criteria
• Accept if NPV gt 0
• Ranking Criteria Choose the highest NPV

7
NPV - An Example

• Assume you have the following information on
• Project X
• Initial outlay -1,100 Required return 10
• Annual cash revenues and expenses are as
  follows
• Year Revenues
  Expenses
• 1 1,000 500
• 2 2,000 1,300
• 3 2,200 2,700
• 4 2,600 1,400
• Draw a time line and compute the NPV of project
  X.

8
The Time Line NPV of Project X
0
1
2
3
4
Initial outlay (1,100)
Revenues 2,000 Expenses 1,300 Cash flow 700
Revenues 1,000 Expenses 500 Cash flow 500
Revenues 2,200 Expenses 2,700 Cash flow (500)
Revenues 2,600 Expenses 1,400 Cash flow 1,200
1,100.00 454.54 578.51 -375.66 819.62 377.
02
1 500 x 1.10
1 700 x 1.10 2
1 - 500 x
1.10 3
1 1,200 x
1.10 4
NPV
NPV -C0 PV0(Future CFs) -C0
C1/(1r) C2/(1r)2 C3/(1r)3 C4/(1r)4
______ ______ ______ _______ _______
377.02 gt 0
9
NPV in your HP 10B Calculator
First, clear previous data, and check that your
calculator is set to 1 P/YR
CLEAR ALL
The display should show 1 P_Yr Input data (based
on above NPV example)
INPUT
Yellow
Display should show CF 0
/-
CFj
1,100
Key in CF0
Display should show CF 1
CFj
500
Key in CF1
Display should show CF 2
CFj
700
Key in CF2
Display should show CF 3
Key in CF3
/-
CFj
500
Display should show CF 4
CFj
1,200
Key in CF4
I/YR
Key in r
10
NPV
Display should show 377.01659723
Compute NPV
PRC
Yellow
10
NPV Strengths and Weaknesses

• Strengths
• Resulting number is easy to interpret shows how
  wealth will change if the project is accepted.
• Acceptance criteria is consistent with
  shareholder wealth maximization.
• Relatively straightforward to calculate
• Weaknesses
• An improper NPV analysis may lead to the wrong
  choices of projects when the firm has capital
  rationing this will be discussed later.

11
The Payback Period Rule

• How long does it take the project to pay back
  its initial investment?
• Payback Period of years to recover costs of
  project
• Minimum Acceptance Criteria set by management
• Ranking Criteria set by management

12
Discounted Payback - An Example

• Initial outlay -1,000
• r 10
• PV
  of
• Year Cash flow Cash flow
• 1 200 182
• 2 400 331
• 3 700 526
• 4 300 205
• Accumulated
• Year discounted cash flow
• 1 182
• 2 513
• 3 1,039
• 4 1,244
• Discounted payback period is just under 3 years

13
Average Accounting Return (AAR)

• Also known as Accounting Rate of Return (ARR)
• Method using accounting data on profits and
  book value of the investment
• AAR Average Net Income / Average Book Value
• If AAR gt some target book rate of return, then
  accept the project

14
Average Accounting Return (AAR)

• You want to invest in a machine that produces
  squash balls.
• The machine costs 90,000.
• The machine will die after 3 years (assume
  straight line depreciation, the annual
  depreciation is 30,000).
• You estimate for the life of the project
• Year 1 Year 2 Year 3
• Sales 140 160 200
• Expenses 120 100 90
• EBD 20 60 110

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Calculating Projected NI
Year 1 Year 2 Year 3 Sales 140 160 200 Expenses
120 100 90 E.B.D. Depreciation E.B.T. Taxes
(40) NI
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We calculate (i) Average NI (ii) Average
book value (BV) of the investment
(machine) time-0 time-1 time-2 time-3 BV of
investment 90 60 30 0 gt Average BV
(divide by 4 - not 3) (iii) The
Average Accounting Return AAR
44.44 Conclusion If target AAR lt 44.44 gt
accept If target AAR gt 44.44 gt reject
17
The Internal Rate of Return (IRR) Rule

• IRR the discount rate that sets the NPV to zero
• Minimum Acceptance Criteria
• Accept if IRR gt required return
• Ranking Criteria Select alternative with the
  highest IRR
• Reinvestment assumption the IRR calculation
  assumes that all future cash flows are reinvested
  at the IRR

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Internal Rate of Return - An Example
Initial outlay -2,200 Year
Cash flow 1 800 2 900
3 500 4 1,600 Find the IRR such that NPV
0 ______ _______
______ _______ 0

(1IRR)1 (1IRR)2
(1IRR)3 (1IRR)4
800 900 500
1,600 2,200

(1IRR)1 (1IRR)2 (1IRR)3
(1IRR)4
19
IRR in your HP 10B Calculator
First, clear previous data, and check that your
calculator is set to 1 P/YR
CLEAR ALL
The display should show 1 P_Yr Input data (based
on above NPV example)
INPUT
Yellow
Display should show CF 0
/-
CFj
2,200
Key in CF0
Display should show CF 1
CFj
800
Key in CF1
Display should show CF 2
CFj
900
Key in CF2
Display should show CF 3
CFj
500
Key in CF3
Display should show CF 4
CFj
1,600
Key in CF4
IRR/YR
Display should show 23.29565668
Compute IRR
CST
Yellow
20
Internal Rate of Return and the NPV Profile

• The NPV Profile
• Discount rates NPV
• 0 1,600.00
• 5 1,126.47
• 10 739.55
• 15 419.74
• 20 152.62
• 25 -72.64
• IRR is between 20 and 25 -- about 23.30
• If required rate of return (r) is lower than IRR
  gt accept the project (e.g. r 15)
• If required rate of return (r) is higher than IRR
  gt reject the project (e.g. r 25)

21
The Net Present Value Profile
Net present value
Year Cash flow 0 2,200
1 800 2 900 3 500 4 1,600
1,600.00
1,126.47
739.55
419.74
159.62
Discount rate
0
72.64
2
6
10
14
18
22
IRR23.30
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IRR Strengths and Weaknesses

• Strengths
• IRR number is easy to interpret shows the return
  the project generates.
• Acceptance criteria is generally consistent with
  shareholder wealth maximization.
• Weaknesses
• Does not distinguish between investing and
  financing scenarios
• IRR may not exist or there may be multiple IRR
• Problems with mutually exclusive investments

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IRR for Investment and Financing Projects
Initial outlay 4,000 Year
Cash flow 1 -1,200 2 -800
3 -3,500 Find the IRR such that NPV 0
_______ _______
_______ 0

(1IRR)1 (1IRR)2 (1IRR)3
-1,200 -800
-3,500 - 4,000

(1IRR)1 (1IRR)2 (1IRR)3
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Internal Rate of Return and the NPV Profile for a
Financing Project

• The NPV Profile of a Financing Project
• Discount rates NPV
• 0 -1,500.00
• 5 -891.91
• 10 -381.67
• 15 50.2
• 20 418.98
• IRR is between 10 and 15 -- about 14.37
• For a Financing Project, the required rate of
  return is the cost of financing, thus
• If required rate of return (r) is lower than IRR
  gt reject the project (e.g. r 10)
• If required rate of return (r) is higher than IRR
  gt accept the project (e.g. r 15)

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The NPV Profile for a Financing Project
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Multiple Internal Rates of Return
Example 1
Assume you are considering a project for which
the cash flows are as follows Year Cash
flows 0 -900 1 1,200
2 1,300 3 -1,200
27
Multiple IRRs and the NPV Profile - Example 1
IRR272.25
IRR1-29.35
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Multiple IRRs in your HP 10B Calculator
First, clear previous data, and check that your
calculator is set to 1 P/YR
CLEAR ALL
The display should show 1 P_Yr Input data (based
on above NPV example)
INPUT
Yellow
Display should show CF 0
/-
CFj
900
Key in CF0
Display should show CF 1
CFj
1,200
Key in CF1
Display should show CF 2
CFj
1,300
Key in CF2
Display should show CF 3
CFj
/-
1,200
Key in CF3
IRR/YR
Display should show 72.252175
CST
Yellow
Compute 1st IRR
IRR/YR
STO
CST
Yellow
/-
RCL
Yellow
30
Compute 2nd IRR by guessing it first
Display should show -29.352494
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No or Multiple IRR Problem What to do?

• IRR cannot be used in this circumstance, the only
  solution is to revert to another method of
  analysis. NPV can handle these problems.
• How to recognize when this IRR problem can occur
• When changes in the signs of cash flows happen
  more than once the problem may occur (depending
  on the relative sizes of the individual cash
  flows).
• Examples - -- -- ---

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Multiple Internal Rates of Return
Example 2
Assume you are considering a project for which
the cash flows are as follows Year Cash
flows 0 -260 1 250 2
300 3 20 4 -340
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Multiple IRRs and the NPV Profile - Example 2
IRR229.84
IRR111.52
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Multiple Internal Rates of Return
Example 3
Assume you are considering a project for which
the cash flows are as follows Year Cash
flows 0 660 1 -650
2 -750 3 -50 4
850
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Multiple IRRs and the NPV Profile - Example 3
IRR18.05
IRR233.96
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The Profitability Index (PI) Rule

• PI
• Total Present Value of future CFs / Initial
  Investment
• Minimum Acceptance Criteria Accept if PI gt 1
• Ranking Criteria Select alternative with highest
  PI

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Profitability Index - An Example

• Consider the following information on Project Y
• Initial outlay -1,100
• Required return 10
• Annual cash benefits
• Year Cash flows
• 1 500
• 2 1,000
• Whats the NPV?
• Whats the Profitability Index (PI)?

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• The NPV of Project Y is equal to
• NPV (500/1.1) (1,000/1.12) - 1,100
  (454.54 826.45) - 1,100
• 1,280.99 - 1,100 180.99.
• PI PV Cashflows/Initial Investment
• This is a good project according to the PI rule.

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The Profitability Index (PI) Rule

• Disadvantages
• Problems with mutually exclusive investments (to
  be discussed later)
• Advantages
• May be useful when available investment funds are
  limited (to be discussed later).
• Easy to understand and communicate
• Correct decision when evaluating independent
  projects

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Special situations

• When projects are independent and the firm has
  few constraints on capital, then we check to
  ensure that projects at least meet a minimum
  criteria if they do, they are accepted.
• NPV0 IRRhurdle rate PI1
• Sometimes a firm will have plenty of funds to
  invest, but it must choose between projects that
  are mutually exclusive. This means that the
  acceptance of one project precludes the
  acceptance of any others. In this case, we seek
  to choose the one highest ranked of the
  acceptable projects.
• If the firm has capital rationing, then its funds
  are limited and not all independent projects may
  be accepted. In this case, we seek to choose
  those projects that best use the firms available
  funds. PI is especially useful here.

39
Using IRR and PI correctly when projects are
mutually exclusive and are of differing scales
Year Cash flows of Project A Cash flows of Project B
0 -100,000 -50
1 150,000 100

• Consider the following two mutually exclusive
  projects. Assume the opportunity cost of capital
  is 12

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Incremental Cash Flows Solving the Problem with
IRR and PI

• As you can see, individual IRRs and PIs are not
  good for comparing between two mutually exclusive
  projects.
• However, we know IRR and PI are good for
  evaluating whether one project is acceptable.
• Therefore, consider one project that involves
  switching from the smaller project to the larger
  project. If IRR or PI indicate that this is
  worthwhile, then we will know which of the two
  projects is better.
• Incremental cash flow analysis looks at how the
  cash flows change by taking a particular project
  instead of another project.

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Using IRR and PI correctly when projects are
mutually exclusive and are of differing scales
Year Cash flows of Project A Cash flows of Project B Incremental Cash flows of A instead of B (i.e., A-B)
0 -100,000 -50 -99,950
1 150,000 100 149,900
42
Using IRR and PI correctly when projects are
mutually exclusive and are of differing scales

• IRR and PI analysis of incremental cash flows
  tells us which of two projects are better.
• Beware, before accepting the better project, you
  should always check to see that the better
  project is good on its own (i.e., is it better
  than do nothing).

43
IRR, NPV, and Mutually Exclusive Projects
Year
0 1 2 3
4 Project A 350 50
100 150 200 Project B 250
125 100 75 50
44
IRR, NPV, and the Incremental Project
Year
0 1 2 3
4 Project A 350 50
100 150 200 Project B 250
125 100 75
50 (A-B)
The Crossover Rate IRRA-B 8.07
45
Capital Rationing

• Recall If the firm has capital rationing, then
  its funds are limited and not all independent
  projects may be accepted. In this case, we seek
  to choose those projects that best use the firms
  available funds. PI is especially useful here.
• Note capital rationing is a different problem
  than mutually exclusive investments because if
  the capital constraint is removed, then all
  projects can be accepted together.
• Analyze the projects on the next page with NPV,
  IRR, and PI assuming the opportunity cost of
  capital is 10 and the firm is constrained to
  only invest 50,000 now (and no constraint is
  expected in future years).

46
Capital Rationing Example(All numbers are in
thousands)
Year Proj. A Proj. B Proj. C Proj. D Proj. E
0 -50 -20 -20 -20 -10
1 60 24.2 -10 25 12.6
2 0 0 37.862 0 0
NPV 4.545 2.0 2.2 2.727 1.4545
IRR 20 21 14.84 25 26
PI 1.0909 1.1 1.11 1.136 1.145
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Capital Rationing Example Comparison of Rankings

• NPV rankings (best to worst)
• A, D, C, B, E
• A uses up the available capital
• Overall NPV 4,545.45
• IRR rankings (best to worst)
• E, D, B, A, C
• E, D, B use up the available capital
• Overall NPV NPVEDB6,181.82
• PI rankings (best to worst)
• E, D, C, B, A
• E, D, C use up the available capital
• Overall NPV NPVEDC6,381.82
• The PI rankings produce the best set of
  investments to accept given the capital rationing
  constraint.

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Capital Rationing Conclusions

• PI is best for initial ranking of independent
  projects under capital rationing.
• Comparing NPVs of feasible combinations of
  projects would also work.
• IRR may be useful if the capital rationing
  constraint extends over multiple periods (see
  project C).

49
Summary and Conclusions

• Discounted Cash Flow (DCF) techniques are the
  best of the methods we have presented.
• In some cases, the DCF techniques need to be
  modified in order to obtain a correct decision.
  It is important to completely understand these
  cases and have an appreciation of which technique
  is best given the situation.