Notes on Capital Budgeting
I. CAPITAL BUDGETING METHODS.
A. Payback method. Number of years to recover the investment amount.
1. Example:
Project A Project B
Investment ($1000) ($1000)
Year 1 $500 $100
Year 2 400 200
Year 3 300 300
Year 4 200 400
Year 5 100 500
Year 6 10 600
Year 7 10 0
2. Decision rule:
Accept project if the payback years 0
Reject project if NPV opportunity cost of capital
Reject if IRR < opportunity cost of capital
If mutual exclusive projects: Accept the project with the highest IRR.
3. Problems with IRR methods.
a) Size problem if projects are mutually exclusive:
Project Large Project Small
Investment ($1.0 million) ($1.00)
Year 1 CF $1.25 million $1.50
Using IRR
Using NPV
@ 10% rate
b) Multiple solutions problem.
Project
Investment: ($22)
Yrs 1 – 4 +$15
Yr 5 -$40
IRR = 6% and 28% Suppose opportunity cost of capital is 10%?
c) Reinvestment Assumption: The IRR implicitly assumes that all
future cash flows from the project are reinvested at the IRR rate of
return. The NPV implicitly assumes that all future cash flows are
reinvested at the opportunity cost of capital.
If projects are mutually exclusive, the IRR assumption will lead to
conflicting decisions compared to the NPV.
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II. Capital Budgeting Issue - PROJECTS WITH DIFFERENT LIVES.
A. Example:
Machine 1 (M1) M1* Machine 2 (M2)
Investment ($1000) ($1800)
Years 1 – 6 $400 $400
Year 6 ($1200)
Year 7 – 12 $400 $400
NPV @ 10% NPV(M1) =$742 NPV(M2) =$926
NPV(M1+M1*) = $1048
B. Main issue:
1. The important point is that it is not the life of the machine that dictates the
investment decision, but the investment horizon of what the machine is
used for. For example, if this machine is used to produce Pokemon cards,
we must decide on which machine to invest in based on how long we
expect the Pokemon craze to last.
2. Alternatively for a high tech firm, it is important to decide how long their
latest product will be marketable before it becomes obsolete. For the
investment decision we will consider the sale of the production machine at
the 3 year point or put it to other use.
3. An Alternative Method. Use EAC (Equivalent Annual Cost) to evaluate
machines with different lives.
EAC is defined as an annuity cash flow that is equivalent to the NPV of a
project. It is calculated as:
EAC = PV of cost / (PV of annuity at k% for the life of
machine)
where k% is the opportunity cost of capital.
Annuity of the NPV(M1) = $1000 / (PV of annuity at 10% for 6 yrs)
= $1000 / (4.355)
= $229.62
Calculate the annuity of the NPV(M2) = $
Think of EAC as the RENTAL COST if you were to rent (or lease) the
machine instead of purchasing it.
Choose the machine that is less costly.
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Try another problem:
Machine A Machine B
Cost of machine $15 $10
Cost to maintain
In year 1 $ 4 $ 6
In year 2 4 6
In year 3 4 0
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III. INCREMENTAL CASH FLOW ANALYSIS FOR CAPITAL BUDGETING
A. Existing firm New product
Sales $10,000 $1,000
- CofGS 4,000 300
Gross Profits $ 6,000 $ 700
- Operating Exp - 1,000 - 300
- Depreciation Exp 1,000 - 200
Operating Profits $ 4,000 $ 200
- Interest Exp ------- -----
Profits Bef taxes $ 4,000 $ 200
Taxes (40%) -1,600 - 80
PAT $ 2,400 $ 120
Incremental Cash Flow = PAT + Depreciation Exp
= (1-T)[Sales-CoGS-OE-D] + D
= (1 - T)[Sales - CoGS-OE] - (1-T)D + D
-D +TD +D
Incremental Cash Flow = CF= (1-T)[Sales - CoGS - OE] + TD
B. Additional Net Working Capital
Existing firm New product
Accounts Receivable $4,000 $ 100
Inventory 5,000 600
Accounts Payable 6,000 300
$3,000 $ 400
C. EXCLUDE: Research & Development, Test marketing, Survey, etc. that are
SUNK COST or costs that are irreversible.
D. INCLUDE: Indirect (or incidental costs/benefits) effects that could arise
because of the NEW PRODUCT.
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E. INCLUDE: Opportunity Costs such as opportunity cost of leasing land or
building if project is rejected.
1. Example:
WRONG WAY TO COMPARE is to look at before & after project.
Before Take Project After CF before vs after
Firm owns land Firm still owns land $0
2. CORRECT WAY TO COMPARE is with or without project:
Before Take Project After CF with Project
Firm owns land Firm still owns land $0
Before Rejects Project After CF w/o
Project
Firm owns land Firm sells land for $1mil $1 mil
Incremental CF = +$1 mil
3. Another example: EROSION
If SUN Microsystems introduces SUN4 it will erode the sale of SUN3.
Before Take on Sun4 After CF with SUN4
Sun sells $1m SUN3 Sun sells $0.5 m SUN3 ($0.5 m)
Before Rejects Sun4 After CF without SUN4
Sun sells $1m SUN3 Sun sells $0.5 m SUN3 ($0.5 m)
(Apollo's Domain4000) technological
advancement takes SUN3's mkt share)
Incremental CF = $ 0 m
4. KEY QUESTION: Will this cost/benefit exist only because of the Project?
If your answer is NO then it is an irrelevant cost/benefit.
If your answer is YES, then it is a relevant cost/benefit.
The cost/benefit can be directly attributable to the Project
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To answer the question above depends on:
Barriers to entry: How costly is it for competitors to enter the "new" market?
Competition: How competitive is the market for the "new" product?
Substitutability: What other products can be substituted for the "new"
product?
If Barriers are very costly then EROSION is probably attributable to the new
Project.
If competition is fierce then EROSION is probably not attributable to the new
Project.
If substitutability is easy, then EROSION is probably not attributable to the
new Project.
F. INCLUDE Real overhead costs but not Accounting Allocated Overhead costs.
G. INCLUDE: EXCESS CAPACITY using the EAC method.
1. Example 1:
Suppose Sun has a silicon compression machine (SCM) that is used to
manufacture Sun3. If Sun4 is produced, it will also use the SCM to produce it
and will share the existing SCM. The SCM is a year old with a 5 year life and
cost $100 million. Sun3 is using half of its SCM capacity and is expected to grow
at 15% annually. A new SCM could be purchased for $150 million today. The
new SCM would have a 5 year life and the opportunity cost is 10%. IF Sun3 and
Sun4 are produced at the same time using the existing SCM, it will reach full
capacity in 3 years. How should the excess capacity issue be resolved?
STEP 1: Calculate EAC for the old SCM:
EAC = PV of cost/[PV of AN, 10%, 5]
STEP 2: Calculate EAC for the new SCM:
STEP 3: Calculate the number of years it takes to reach full capacity with SUN3
only.
100 units (1+g)T = 200 units
STEP 4: Determine the incremental cost if Sun4 is adopted. Again use the "With
or without" principle.
Year 0 1 2 3 4 5
Only Sun3
Sun3&Sun4
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Cost to Sun4
2. Example 2:
Suppose a billing company, Bill-4-You, uses Computer A to provide a billing
service to small businesses in a regional area. Computer A was purchased 2 years
ago at the cost of $100,000 and has 5 year life (3 years left). The firm currently
uses about 1/3 of its capacity for their current clients. Bill-4-You is considering a
new client who is a medium sized firm and would use much of Computer A. In
fact, if the new client is accepted, the firm will reach full capacity on Computer A
in 3 years. Without the new client, the current clients of Bill-4-You will increase
its billings at a rate of 10% per year.
If a new computer is purchased to support a bigger client base, the firm would
consider purchasing Computer B at a cost of $300,000 with a 7 year life.
Discount rate is 8%.
What are the relevant costs associated with the adoption of the new client.
NOTE: The New Client is the New Project.
STEP 1:
STEP 2:
STEP 3:
STEP 4:
Year 0 1 2 3 4 5
Only Old Clients
Old & New Clients
Cost to New Client
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