BFF2140 Corporate Finance 1
Lecture 4: Capital Budgeting Part I
Chief Examiner/Lecturer: Dr Amale Scally
MONASH
BUSINESS
SCHOOL
Teaching Week Four
Capital Budgeting I:
Techniques for evaluation
Readings
Chapter 8, pp. 217-241, 245-247
MONASH
BUSINESS
SCHOOL
Learning Objectives
❑ Differentiate between independent & mutually exclusive projects.
❑ Differentiate between conventional and non-conventional cash flows.
❑ Compute and understand the roles of the main methods of project
evaluation.
❑ Understand the advantages and disadvantages of these methods.
❑ Understand why NPV is preferred method.
What is capital budgeting?
What is capital budgeting?
• As a financial manager one key duty is to choose investments
that are worth undertaking (recall the goal of the firm!).
• This may involve choosing between two or more alternatives.
• Capital budgeting is very important to the firm and its future.
• Capital is a limited resource, and resources should be allocated
among the best investment alternatives.
• Capital expenditures are long term in nature. This means long
term decisions need to be made.
• A sound process to evaluate, compare, selects projects is thus
essential.
What is capital budgeting?
•
•
•
•
Analysis of potential additions to fixed assets.
Long-term decisions; involve large expenditures.
These decisions are often hard to reverse.
Highlights that the investment decision is the most important
duty of a financial manager.
What is capital budgeting?
• Capital budgeting involves:
1. Estimating CFs (inflows & outflows).
2. Assessing the riskiness of CFs.
3. Determining an appropriate discount rate
4. Finding NPV and/or IRR.
5. Acceptance of project if NPV > 0 and/or IRR > r ( WACC).
Types of Investment Decisions
➢ INDEPENDENT PROJECTS
• Projects that, if accepted or rejected, will not affect the
cash flows of another project.
➢ MUTUALLY EXCLUSIVE PROJECTS
• Projects that, if accepted, preclude the acceptance of
competing projects.
Types of Project Cash Flows
➢ Conventional CF Project (C)
Typically, a negative CF (initial cost outlay) is followed by a
series of positive cash inflows – hence there is one change of
signs (-ve to +ve)
➢ Nonconventional CF Project (NC)
Two or more changes of signs – the most common is an
outlay, followed by positive CFs, then a terminal cost in order
to complete the project (e.g., repair damaged site)
Project Cash Flows (continued)
Inflow (+) or Outflow (-) in Year
0
1
2
3
4
5
C
-
+
+
+
+
+
C
-
+
+
+
+
-
-
-
-
+
+
+
C
+
+
+
-
-
-
C
-
+
+
-
+
-
NC
NC
NC
Alternative Decision Methods
➢ Non-discounting methods
▪ Payback
➢ Discounting methods
▪ Discounted pay back
▪ Net Present Value (NPV)
▪ Internal Rate of Return (IRR)
▪ Profitability Index (PI)
Payback Period Method
The number of years required to recover a
project’s cost, ie:
How long it takes to get our money back.
Decision Rule: An investment is acceptable if
its calculated payback is less than a prespecified cut-off rate.
Example 1:
Payback Period Method
Cash flows for projects L and S are given below: (This slide
will be used to explain Payback, NPV and IRR concepts.)
Assume cost of capital (when required) = 10%
YEAR
0
Project L
-$100
Project S
-$100
1
2
$10
$60
$70
$50
3
$80
$20
Example 1:
Payback Period for Project L
0
1
Ct
Cumulative
-$100
-$100
$10
-$90
PaybackL
=
2 + (30/80)
2
2.4
$60 $100
-$30 $0
3
$80
$50
= 2.375 years
Example 1 :
Payback Period for Project S
0
1
1.6
2
3
Ct
-$100
$70 $100 $50
$20
Cumulative
-$100
-$30
$40
PaybackS
= 1 + (30/50) = 1.6 years
$0 $20
Payback Period Method
Advantages:
1.
2.
Provides an indication of a project’s risk and liquidity
Easy to calculate and understand YEAR
Project L
Project S
Disadvantages:
1.
2.
3.
0
-$100
-$100
1
$10
$70
2
$60
$50
3
$80
$20
4
$100,000,000
$0
Ignores the time value of money
Ignores CFs occurring after the payback period
Arbitrary choice of a cutoff date
Example 1 (continued):
Discounted Payback (uses discounted rather than raw CFs.)
(Project L Illustration)
0
10%
1
2
3
$80
Ct
-$100
$10
$60
PV(Ct)
-$100
$9.09
$49.59
$60.11
Cumulative
-$100
-$90.91
-$41.32
$18.79
Discounted
payback
= 2
+ 41.32/60.11 = 2.687 yrs
Recover investment and capital costs in 2.687yrs.
In your own time calculate the discounted payback for Project S.
ANSWER: Recover investment and capital costs in 1.88 yrs.
Net Present Value (NPV) Method
• The required rate of return (r) is the minimum return that a
project must earn in order to be acceptable.
• The cost of capital (k) is often used as the minimum required
rate of return for capital budgeting purposes.
• The cost of capital (k) is the cost of investment funds, usually
viewed as a weighted average of the cost of funds from all
sources.
Net Present Value (NPV) Method
NPV: Sum of the PVs of inflows and outflows
minus cost CF0 which is often negative.
n NCFt
NPV = 
t
t = 0 (1 + k )
Decision Rule: Accept a project if NPV > 0.
Example 1 (continued):
What’s Project L’s NPV?
YEAR
Project L
Project S
0
-$100
-$100
1
$10
$70
2
$60
$50
3
$80
$20
Project L:
0
1
2
3
$10
$60
$80
10%
-$100.00
$9.09
$49.59
$60.11
$18.78 = NPVL
NPVS = $19.99.
Example 1 (continued):
What is Project L’s NPV?
YEAR
Project L
Project S
0
-$100
-$100
1
$10
$70
2
$60
$50
3
$80
$20
Example 1 (continued):
What is Project S’s NPV?
YEAR
Project L
Project S
0
-$100
-$100
1
$10
$70
2
$60
$50
3
$80
$20
Rationale for the NPV Method
NPV
= PV (Benefits or Inflows) – PV (Costs)
= Net gain in wealth.
Accept project if NPV > 0
• Choose between mutually exclusive projects on the basis of
higher NPV. (Recall Corporate Objective – Lecture 1 Intro).
• The project with the highest NPV adds greatest value
– If Projects S and L are mutually exclusive: Accept S because NPVs >
NPVL .
– If S & L are independent: Accept both as NPV > 0 for both projects
Strengths and Weakness
of the NPV Method
Advantages
– Uses cash flows (not earnings)
– Uses ALL cash flows of a project
– Discounts cash flows properly
Disadvantages
– Relies on accurate estimate of cash flows (teaching week 5) and
the discount rate (teaching week 10)
– Projects likely to be replicated with maturity of differing lengths
(teaching week 5)
NPV Example 1– Excel Application
Calculating NPV at various discount rates (Project L)
NPV Example 1 – Excel Application
Creating the NPV Profile for Project L
Internal Rate of Return (IRR)
0
1
CF0
Cost
CF1
2
CF2
Inflows
• IRR is the discount rate that forces PV inflows = cost
This is the same as forcing the NPV = 0
• IRR is popular because it provides a single number that
summarises the merit of a project.
3
CF3
Internal Rate of Return (IRR)
IRR: Enter NPV = 0, solve for IRR.
n
NCFt
IRR  NPV = 
=0
t
t =0 (1 + irr)
Decision Rule: If IRR > k, accept project; If IRR < k, reject project
YEAR
Example 1 (continued):
What is Project L’s IRR?
0
IRR = ?
-100.00
PV1
Project L
Project S
0
-$100
-$100
1
$10
$70
2
$60
$50
3
$80
$20
1
2
3
10
60
80
PV2
PV3
0 = NPV
IRRL = 18.13%.
IRRS = 23.56%.
Example 1 (continued):
What is Project L’s IRR?
YEAR
Project L
Project S
0
-$100
-$100
1
$10
$70
2
$60
$50
3
$80
$20
Example 1 (continued):
What is Project S’s IRR?
YEAR
Project L
Project S
0
-$100
-$100
1
$10
$70
2
$60
$50
3
$80
$20
Rationale for the IRR Method
If IRR > k, then the project’s rate of return is greater
than its cost - some return is left over to boost
stockholders’ returns.
Illustration:
If k = 10% and IRR = 15%, the project is profitable.
IRR Example 1– Excel Application
Calculating IRR (Project L)
• IRR = 18.13%
Decisions on Projects S and L
using the IRR Method
• If S and L are independent projects:
➢ Accept both because IRRs > k , if k = 10%.
• If S and L are mutually exclusive projects:
➢ Accept S because IRRS > IRRL
NOTE:
There are some potential errors (pitfalls) with the use of IRR in
deciding between mutually exclusive projects.
WARNING
PITFALLS WITH
THE INTERNAL RATE OF RETURN
WARNING
YEAR
IRR Method Pitfall 1:
Mutually Exclusive Projects
Construct an NPV Profile
Project L
Project S
0
-$100
-$100
1
$10
$70
2
$60
$50
3
$80
$20
Find NPVL and NPVS at different discount rates assuming projects
are mutually exclusive:
Cost of capital (k)
0%
5%
10%
15%
20%
NPV (Project L)
$50.00
$33.05
$18.78
$6.67
-$3.70
NPV (Project S)
$40.00
$29.29
$19.98
$11.83
$4.63
Cost of capital (k)
NPV (Project L)
NPV (Project S)
0%
$50.00
$40.00
5%
$33.05
$29.29
10%
$18.78
$19.98
15%
$6.67
$11.83
20%
-$3.70
$4.63
NPV Profile
60
NPV ($)
50
40
30
20
S
IRRS = 23.56%
L
10
0
Discount Rate (%)
0
-10
5
10
15
20
23.6
IRRL = 18.13%
YEAR
Project L
Project S
NPV Profile
60
NPV ($)
50
0
-$100
-$100
$0
1
$10
$70
-$60
2
$60
$50
$10
3
$80
$20
$60
Crossover
Point = 8.68%
40
30
20
S
IRRS = 23.56%
L
10
0
Discount Rate (%)
0
-10
5
10
15
20
Cash Flow
L-S
23.6
IRRL = 18.13%
About the Crossover Point
• Crossover Point is the discount rate at which the NPV for the two
projects are equal (it can be thought of as the rate of indifference).
• It is also the IRR of the incremental cash flows
k1 < 8.68: NPVL> NPVS , IRRS > IRRL
CONFLICT
k2 > 8.68: NPVS> NPVL , IRRS > IRRL
NO CONFLICT
Conflict between IRR and NPV
40
• When k is larger than the crossover rate, IRR & NPV lead to
the same decision
• When k is smaller than the crossover rate there is conflict
between IRR and NPV
Which should we use?
➢ NPV is always preferred as it measures additional wealth
obtained.
To Find the Crossover Rate
1.
Find cash flow differences between the projects (i.e. find the
incremental cash flows – the change in cash flow).
2.
Incremental CF’s L-S
YEAR
Project L
Project S
Cash Flow
L-S
0
-$100
-$100
$0
1
$10
$70
-$60
2
$60
$50
$10
3
$80
$20
$60
and calculate the IRR of incremental cash flow = 8.68%
3.
You Can subtract S from L or vice versa, but better to have first CF
negative
4. If profiles don’t cross, one project dominates the other.
Two Reasons NPV Profiles Cross
1. Size (scale) differences.
Smaller project frees up funds at T = 0 for investment.
The higher the opportunity cost, the more valuable these funds,
so high k favours small projects.
2. Timing differences.
Project with faster payback provides more CF in early years
for reinvestment.
If k is high, early CFs are especially good, NPVS > NPVL
Reinvestment Rate Assumptions
• NPV assumes reinvestment at k (opportunity cost of capital).
• IRR assumes reinvestment at IRR.
• Reinvestment at opportunity cost, k, is more realistic, so NPV
method is best.
• NPV should always be used to choose between mutually
exclusive projects (CASH IS KING).
IRR Method Pitfall 2:
Multiple rates of returns
Example 2
Assume a company cost of capital of 15%.
4
What are they? (Hint: Search between 20% and 70%)
IRR Method Pitfall 2:
Multiple rates of returns
From our text:
“In cases where there is more than one IRR, the spreadsheet or
calculator will simply produce the first one that it finds, with no
mention that there could be others!” (Berk et al., 2018, p. 230)
IRR Method Pitfall 2:
Multiple rates of returns
If only we could use a more powerful calculator
Like the Sharp EL738
Clear the memory before any operation [2ndF] then [ALPHA] then [0] then [0]
252 [+/-]
1431
3035 [+/-]
2850
1000 [+/-]
[2ndF]
[COMP]
30
[2ndF]
[COMP]
[ENT]
[ENT]
[ENT]
[ENT]
[ENT]
[CFi]
25%
[ENT]
[CFi]
33.33%
40
[2ndF]
[COMP]
50
[2ndF]
[COMP]
60
[2ndF]
[COMP]
[ENT]
[ENT]
42.86%
[ENT]
[ENT]
42.86%
[ENT]
[ENT]
66.67%
We can’t identify these IRRs using the HP 10bII +
IRR Method Pitfall 2:
Multiple rates of returns
From our text:
“In cases where there is more than one IRR, the spreadsheet or
calculator will simply produce the first one that it finds, with no
mention that there could be others!” (Berk et al., 2018, p. 230)
“Thus, it always pays to create the NPV profile.” (Berk et al.,
2018, p. 230)
We have four IRRs.
Non-conventional CFs - four sign changes.
Rates < 25%
25% < Rates < 33.33%
33.33% < Rates < 42.86%
42.86% < Rates < 66.66%
Rates > 66.66%
REJECT
ACCEPT
REJECT
ACCEPT
REJECT
FAQ
❑ So what does this mean with regards testing and examination
purposes?
❑ Simple answer: We can never ask you to find the rates. All we could ask is the
following:
IRR Method Pitfall 3:
Lending or Borrowing?
Illustration
Consider the following projects A and B
Project Lending
Project Borrowing
CF (t=0)
-$1,000.00
+$1,000.00
CF (t=1)
+$1,500.00
-$1,500.00
50%
50%
+$364
-$364
IRR
NPV @10%
Each project has an IRR of 50%. Does this mean that they
are equally attractive?
IRR Method Pitfall 4:
No Feasible Solution
Illustration
Consider Project A:
YEAR
Cash Flow
0
$1,000.00
1
-$3,000.00
2
$2,500.00
NPV at 10% = $339
IRR
= None
Capital Rationing
• Capital rationing is a limit (constraint) set on funds available for
investment.
• Soft rationing limits imposed by top management
• Hard rationing - Firm is unable raise the money it requires to
undertake all profitable projects.
• Under 'hard' rationing the firm may be forced to pass up
positive NPV projects, whereas 'soft' rationing should never cost
the firm anything as top management can relax capital control at
any time.
Project Selection with Resource
Constraints
The Profitability Index is a relative measure of value.
The PI is an investment return measurement much like net present
value (NPV) with one notable difference.
=> NPV finds "the dollar amount difference" between the sum of
present values of all future cash flows and the amount of
initial investment whereas profitability index finds "the
ratio".
Value Created
NPV
Profitability Index =
=
Resource Consumed Initial Investment
Profitability Index
Chapter 8, pp. 245-247
The profitability index measures the ratio between cash flow to
investment. Therefore, the higher the ratio the more cash flow
to investment
Decision Rule:
➢ Accept a project if the profitability index is greater than 0
➢ Stay indifferent if the profitability index is zero
➢ Don't accept a project if the profitability index is below 0.
Example 2: Profitability Index
Taken Inn is planning to open cafes in several cities and has estimates the required outlay and
NPV for each of the following cities. Taken Inn is subject to hard capital rationing from its
bank who has set a limit at $1,000,000 this year. Develop a profitability index for the
following four centres and state which would be selected. All four centres plan to last for
three years and the firm uses a 10% discount rate. In which cities should Taken Inn open
cafes and why?
CITY
Sydney
INITIAL
OUTLAY
500,000
ANNUAL
INFLOWS
$220,000
Melbourne
300,000
$130,000
Perth
250,000
$100,000
Hobart
125,000
$60,000
NPV @10%
55
Profitability
Index
Example 2: Profitability Index - solution
ANNUAL
INFLOWS
$220,000
NPV @10%
CITY
Sydney
INITIAL
OUTLAY
500,000
$47,107.44
Profitability
Index
0.094
Melbourne
300,000
$130,000
$23,290.76
0.078
Perth
250,000
$100,000
-$1,314.80
-0.005
Hobart
125,000
$60,000
$24,211.12
0.194
Hobart, Sydney and Melbourne a total budget of $925,000
56
Profitability Index
Strengths and Weaknesses
Strengths:
▪ It considers time value of money
▪ It presents a relative profitability of the project. Relative profitability
allows comparison of two investments irrespective of their amount of
investment. A higher PI would indicate a better IRR and a lower PI would
have lower IRR.
Weaknesses:
▪ is also its relative indications. Two projects having vast difference in
investment and dollar return can have same PI. In such situation, therefore,
the NPV method remains the best method.
❑ Today we have been talking about the fundamental capital budgeting evaluation
techniques used in practice.
The most popular decision rules used by CFOs for listed Australian firms
Based on a survey by Truong, Partington and Peat (2004)
❑ Next week we will turn our attention to learning how to construct cash flows.
Extra problem:
General Foods (GF) owns a machine that is 6 years old and has an estimated remaining
physical life of no more than 2 years. The table below shows the net cash flows and
residual value estimates for the machine. Assume the cost of capital is 10%. When should
the machine be retired? Assume a no tax world.
End of Year
Net Cash Flow
Residual Value
6
$-
$18,000
7
$22,000
$9,000
8
$14,000
$0
Extra problem: Solution
Option One: Retire the machine at the end of year 6.
NPV = $18,000
or
Retire the machine at the end of year 7.
PV = (22000+9,000)/1.1 = $28,181.82
or
Keep the machine until the end of year 8
PV = 22,000/1.1 + 14,000/1.12 = $31,570.25
Therefore, the machine should be retired at the end of year 8 as this is
where shareholder wealth is maximised.
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