FINA1003 / FINA1310 CORPORATE FINANCE
Faculty of Business and Economics
University of Hong Kong
Dr. Shiyang Huang
Lecture 8: Capital Budgeting
Course Overview
• Introduction
• Part I: Valuation
• Time Value of Money, Discounted Cash Flow Valuation,
Bond and Stock Valuation.
• Part II: Risk and Return
• Historical Risk and Return Relationships, CAPM.
• Part III: Capital Budgeting
• Real Investment Decisions, Cost of Capital.
• Part IV: Financing Decisions
• Raising Capital, Tradeoff between Equity and Debt.
What’s next?
• Capital Budgeting: involves making decisions about
real asset investments.
•
Chapter 9: Net Present Value and Other Investment Criteria
•
Chapter 10/11: Estimating cash flows for a potential
investment.
•
Chapter 14: Estimating a required rate of return for a
potential investment = opportunity cost of capital. (need
chapters 10 & 11 to help us with chapter 12)
Learning Objectives
• Understand how to calculate and use capital budgeting
decision techniques: Payback, Discounted Payback,
NPV, ARR, IRR, & PI.
• Understand the advantages and disadvantages of each
technique.
• Understand which project to select when there is a
ranking conflict between NPV and IRR.
Example: Penn West Exploration announces
its 2013 capital budget
•
Reuters, Wed Jan 9, 2013 9:19pm EST
•
Penn West is one of the largest conventional oil and natural gas
producers in Canada. It operates a significant portfolio of light oil in
Canada
•
The focus of the 2013 capital budget is to improve capital efficiencies by
focusing capital on those projects that, on average, are expected to
produce flowing barrel efficiencies in the $35,000 to $40,000 per barrel
per day range while also attaining a minimum 20 percent internal rate of
return target... The 2013 Base Capital Budget is $900 million and
includes an option to layer in up to $300 million of incremental capital
weighted in the second half of the year. This incremental capital is
subject to commodity price and crude oil differential realizations,
demonstrating expected capital efficiencies and ongoing strategic
portfolio management. Penn West will announce in advance, if we plan
to spend beyond the Base Capital Budget of $900 million…
CFO Decision Tools
Good Investment Criteria
• Adjusts for time value of money
• Adjusts for risk
• Provides information on whether we are creating
value for the firm
Key Takeaways
• Net Present Value (NPV) Rule
• Alternatives to the NPV Rule
•
Payback, Discounted Payback, ARR, IRR, & PI.
Reading : Chapter 9
Net Present Value
• The difference between the market value of a
project and its cost
• How much value is created from undertaking
an investment?
 The first step is to estimate the expected future cash flows.
 The second step is to estimate the required return for projects of this
risk level.
 The third step is to find the present value of the cash flows and
subtract the initial investment.
Net Present Value
Objective: Increase Firm’s Current Market Value
•
•
Project has Cash Flows of
{𝐶𝐶𝐹𝐹0 , 𝐶𝐶𝐹𝐹1 , … , 𝐶𝐶𝐹𝐹𝑇𝑇 }
Current market value of project is
𝑪𝑪𝑭𝑭
𝑵𝑵𝑵𝑵𝑵𝑵 = 𝑪𝑪𝑭𝑭𝟎𝟎 + 𝟏𝟏+𝒓𝒓𝟏𝟏 + ⋯ +
𝑪𝑪𝑭𝑭𝑻𝑻
𝟏𝟏+𝒓𝒓 𝑻𝑻
Decision Rule:
• For independent projects: accept a project if NPV>0
• For mutually exclusive projects: take the one with positive and
highest NPV
• “Mutually exclusive” means accepting one rules out the others
Net Present Value Rule
To compute the NPV of a project, we need to consider:
• Cash Flows (Chapters 10)
• Discount Rates (Chapter 14)
Advantages of NPV
• Depends on forecasted cash flows from the project
and the opportunity cost of capital
• Time value of money
• Compensation for bearing risk
• Net present values are additive
• NPV(Project A + Project B)
=NPV(Project A)+ NPV(Project B)
• If project A & B are independent
Our Case Study
• We want to help Mr. Chan, Inc. analyze the following business opportunities
by using the following cash flow information. Assume Chan’s discount rate
is 12%, the average book value = 25,000.
Time
Coffee shop CF Sandwich shop CF
0
(20,000)
(20,000)
1
15,000
6,000
2
15,000
7,000
3
13,000
6,000
4
3,000
6,000
Computing NPV for the Project
Time
Coffee shop CF
PV(CF)
Sandwich shop CF
0
(20,000)
(20,000)
1
15,000
13,393
6,000
5,357
2
15,000
11,958
7,000
5,580
3
13,000
9,253
6,000
4,271
4
3,000
1,907
6,000
3,813
NPV
16,510
(20,000)
PV(CF)
(20,000)
(979)
Calculating NPVs with a Spreadsheet
• Spreadsheets are an excellent way to compute NPVs,
especially when you have to compute the cash flows as
well.
• Using the NPV function
• The first component is the required return entered as a decimal
• The second component is the range of cash flows beginning
with year 1
• Subtract the initial investment after computing the NPV
Example of Net Present Value
Suppose a proposed project is expected to generate the
following cash flows:
Year 0: -165,000
Year 1: 63,120
Year 2: 70,800
Year 3: 91,080
Your required rate of return for assets of this risk level is 12%
per year.
Should you accept the project?
We should accept the project
Example of Net Present Value
Should you accept the project?
NPV=12,627. We should accept the project
Key Takeaways
• Net Present Value (NPV) Rule
• Alternatives to the NPV Rule
Reading : Chapter 9
Alternatives to NPV
In practice, other investment rules are also used for capital
budgeting
1.
2.
3.
4.
Internal Rate of Return (IRR)
Profitability Index (PI)
Payback Period
Average Accounting Return
• These rules were used historically
• They sometimes give the same answer as NPV, but
sometimes do not (these alternatives have shortcomings)
• Bottom line: NPV rule dominates these alternatives!
Internal Rate of Return
• This is the most important alternative to NPV
• It is often used in practice and is intuitively appealing
• It is based entirely on the estimated cash flows and is
independent of interest rates found elsewhere
Internal Rate of Return
• Determined by cash flow process completely
• IRR is the solution to:
𝑪𝑪𝑭𝑭𝟏𝟏
𝑪𝑪𝑭𝑭𝟐𝟐
+
𝑪𝑪𝑭𝑭𝟎𝟎 +
𝟏𝟏 + 𝑰𝑰𝑰𝑰𝑰𝑰
𝟏𝟏 + 𝑰𝑰𝑰𝑰𝑰𝑰
𝑪𝑪𝑭𝑭𝒕𝒕
+ ⋯+
𝟐𝟐
𝟏𝟏 + 𝑰𝑰𝑰𝑰𝑰𝑰
IRR estimated by trial and error
𝒕𝒕
= 𝟎𝟎
• IRR is the discount rate that will yield a zero for the NPV
calculation
Decision Rule:
• For independent projects: accept a project if IRR > IRR*
(the threshold IRR)
• For mutually exclusive projects: among the projects with
IRR>IRR*, accept one with the highest IRR
Internal Rate of Return Example
Suppose a proposed project is expected to generate the following
cash flows:
Year 0: -165,000
Year 1: 63,120
Year 2: 70,800
Year 3: 91,080
What is the IRR of this project?
Solving for −165,000 +
𝐼𝐼𝐼𝐼𝐼𝐼 = 16.13%
63,120
(1+𝐼𝐼𝐼𝐼𝐼𝐼)
70,800
+
(1+𝐼𝐼𝐼𝐼𝐼𝐼)2
+
91,080
1+𝐼𝐼𝐼𝐼𝐼𝐼 3
= 0 gives
If the required rate of return is 12%, should we accept the project?
Yes, since IRR>12%
Our Case Study: IRR
• We want to help Mr. Chan, Inc. analyze the following business
opportunities by using the following cash flow information.
Assume Chan's opportunity cost of capital is 12%, the average
book value = 25,000.
Time
Coffee shop CF Sandwich shop CF
0
(20,000)
(20,000)
1
15,000
6,000
2
15,000
7,000
3
13,000
6,000
4
3,000
6,000
Computing IRR for the Project
• If you do not have a financial calculator, then this becomes
a trial-and-error process
• Calculating IRRs with a spreadsheet
• Enter the cash flows as you did with NPV
• Use IRR function
• IRR of Coffee shop= 54.7% > 12%
• IRR of Sandwich shop = 9.6% < 12%
Computing IRR for the Project
NPV Profile for the Project
30,000
25,000
IRR = 54.7%
20,000
NPV
15,000
10,000
Coffee shop
5,000
Sandwich shop
(5,000)
0
1%
11%
21%
31%
41%
51%
(10,000)
(15,000)
Discount rate
61%
71%
Decision Criteria Test - IRR
• Does the IRR rule account for the time value of money?
• Does the IRR rule account for the risk of the cash flows?
• Does the IRR rule provide an indication about the
increase in value?
• Should we consider the IRR rule for our primary decision
criteria?
Advantages of IRR
• Knowing a return is intuitively appealing
• It is a simple way to communicate the value of a project
to someone who doesn’t know all the estimation details
• If the IRR is high enough, you may not need to estimate
a required return, which is often a difficult task
Comparison between NPV and IRR
IRR Rule Leads to the Same Decision as NPV if:
(1) There is only one cash outflow, which occurs at time 0
(2) Only one project is under consideration
(3) The required returns are the same for all periods
(4) The threshold rate is set equal to the required return
Shortcomings of IRR
(1) Non-existent or multiple IRRs can occur in certain cases
(2) Incorrect rankings for projects with negative cash flows in
future periods (e.g. loans)
(3) Incorrect rankings for mutually exclusive projects; ignores
scale
⇒ Use NPV!
IRR and Nonconventional Cash Flows
• When the cash flows change sign more than once, there
is more than one IRR
• When you solve for IRR, you are solving for the root of an
equation, and when you cross the x-axis more than once,
there will be more than one return that solves the equation
• If you have more than one IRR, which one do you use to
make your decision?
Example of Non-Existent IRR
Year
0
1
2
Project 1
-105
250
-150
Project 2
105
-250
150
What are the IRRs for these two projects?
IRRs do not exist for these two projects
−105 +
250
−150
+
1 + 𝐼𝐼𝐼𝐼𝐼𝐼
1 + 𝐼𝐼𝐼𝐼𝐼𝐼
2
=0
No solution
Example of Multiple IRRs
Suppose a project is expected to generate the following cash flows:
Year 0: -20,000
Year 1: 50,000
Year 2: 30,000
Year 3: -70,000
Required rate of return is 10%.
What is the NPV of this project? What is the IRR?
NPV: −20000 +
IRR: Solve for
50000
1.1
+
30000
1.12
−
70000
1.13
−20000 +
= −2344.1
50000
1+𝑟𝑟
+
Two solutions of IRR: 14.68% and 155%
30000
1+𝑟𝑟 2
+
−70000
1+𝑟𝑟 3
=0
Example of Multiple IRRs
Only has positive NPV if 14.68%<r<155%
Example of IRR for Mutually Exclusive Projects
Suppose there are two mutually exclusive projects A and B, with
the following cash flows
Year
0
1
Project A
-10,000
20,000
Project B
-20,000
36,000
Your required return is 10%. You can only take on one project.
Which one should you choose?
𝐼𝐼𝐼𝐼𝑅𝑅𝐴𝐴 = 100% > 10%
𝐼𝐼𝐼𝐼𝑅𝑅𝐵𝐵 = 80% > 10%
IRR rule tells us to choose project A. However…
Example of IRR for Mutually Exclusive Projects
Year
0
1
Project A
-10,000
20,000
Project B
-20,000
36,000
IRR and NPV calculations
IRR
NPV
Project A
100%
8,181.82
Project B
80%
12,727.27
Project B has higher NPV even though its IRR is lower. We
should choose Project B.
Example of IRR for Mutually Exclusive Projects
One way to solve the problem is to use incremental cash flows
Year
0
1
Project A
-10,000
20,000
Project B
-20,000
36,000
Project B-A
-10,000
16,000
• Should you choose A or B?
• Do IRR and NPV give the same answer?
Conflicts Between NPV and IRR
• NPV directly measures the increase in value to the
firm
• Whenever there is a conflict between NPV and
another decision rule, you should always use NPV
• IRR is unreliable in the following situations
Nonconventional cash flows
• Mutually exclusive projects
•
Alternatives to NPV
In practice, other investment rules are also used for capital
budgeting
1.
2.
3.
4.
Internal Rate of Return (IRR)
Profitability Index (PI)
Payback Period
Average Accounting Return
• These rules were used historically
• They sometimes give the same answer as NPV, but
sometimes do not (these alternatives have shortcomings)
• Bottom line: NPV rule dominates these alternatives!
Profitability Index
• Measures the benefit per unit cost, based on the time
value of money
• A profitability index of 1.1 implies that for every $1 of
investment, we create an additional $0.10 in value
• This measure can be very useful in situations in which
we have limited capital
Profitability Index
• An index instead of a dollar amount
• Profitability Index (PI) is the ratio of the present value of
future cash flows and the initial cost of a project
𝑷𝑷𝑷𝑷
𝑷𝑷𝑷𝑷
𝑷𝑷𝑷𝑷 =
=
−𝑪𝑪𝑭𝑭𝟎𝟎
𝑰𝑰𝟎𝟎
Decision Rule:
• For independent projects: accept a project if PI>1 (this is
identical to the NPV rule)
• For mutually exclusive projects: among the projects with
PI>1, accept one with the highest PI
Comparison between NPV and PI
PI Rule Leads to the Same Decision as NPV if:
(1) There is only one cash outflow, which is at time 0
(2) Only one project is under consideration
Shortcomings of PI:
• PI scales projects by their initial investments. The scaling
can lead to wrong ranking when comparing mutually
exclusive projects
⇒ Use NPV!
Example of PI for Mutually Exclusive Projects
Year
0
1
Project A
-10,000
20,000
Project B
-20,000
36,000
𝑟𝑟 = 10%
PI, IRR and NPV
PI
IRR
NPV
Project A
1.82
100%
8,181.82
Project B
1.64
80%
12,727.27
Example of PI for Mutually Exclusive Projects
Using incremental cash flows
Year
0
1
Project A
-10,000
20,000
Project B
-20,000
36,000
Project B-A
-10,000
16,000
𝑟𝑟 = 10%
• PI of (B-A) = ?
• Should you choose A or B?
Alternatives to NPV
In practice, other investment rules are also used for capital
budgeting
1. Internal Rate of Return (IRR)
2. Profitability Index (PI)
3. Payback Period
4. Average Accounting Return
• These rules were used historically
• They sometimes give the same answer as NPV, but
sometimes do not (these alternatives have shortcomings)
• Bottom line: NPV rule dominates these alternatives!
Payback Period
• Minimum length of time such that the sum of cash flows
from a project is positive.
• Payback Period is the minimum 𝑘𝑘 such that
𝑪𝑪𝑭𝑭𝟏𝟏 + 𝑪𝑪𝑭𝑭𝟐𝟐 + ⋯ + 𝑪𝑪𝑭𝑭𝒌𝒌 ≥ −𝑪𝑪𝑭𝑭𝟎𝟎 = 𝑰𝑰𝟎𝟎
Decision Rule:
• For independent projects: accept if 𝑘𝑘 is less than or equal
to some fixed threshold 𝑡𝑡 ∗ (hurdle period)
• For mutually exclusive projects: among all the projects
with 𝑘𝑘 ≤ 𝑡𝑡 ∗ , accept the one that has the minimum payback
period
Computing Payback for the Project
(Assume Chan’s max is 2 years)
Time Coffee shop CF Cumulative CF
Sandwich shop CF Cumulative CF
0
(20,000)
(20,000)
(20,000)
(20,000)
1
15,000
(5,000)
6,000
(14,000)
2
15,000
10,000
7,000
(7,000)
3
13,000
23,000
6,000
(1,000)
4
3,000
26,000
6,000
5,000
• Coffee shop PB = less than 2 years
• Sandwich shop PB = less than 4 years
• Chan should choose Coffee shop using Payback Period!
Decision Criteria Test - Payback
• Does the payback rule account for the time value of money?
• Does the payback rule account for the risk of the cash flows?
• Does the payback rule provide an indication about the
increase in value?
• Should we consider the payback rule for our primary
decision rule?
NO!
Another Example of Payback Period
r=10%
Suppose hurdle period is 2 years. What does the payback rule
imply?
Shortcomings of Payback Rule
(1) Ignores time-value of money
(2) Ignores cash flows after k
(3) t ∗ is arbitrary
(4) Biased toward short-term investments
Modification: Discounted Payback
Discounted Payback Period
• Compute the present value of each cash flow and
then determine how long it takes to pay back on a
discounted basis
Modification: Discounted Payback is minimum 𝑘𝑘 such
that
𝑪𝑪𝑭𝑭𝟏𝟏
𝑪𝑪𝑭𝑭𝟐𝟐
𝑪𝑪𝑭𝑭𝒌𝒌
+
+
⋯
+
≥ −𝑪𝑪𝑭𝑭𝟎𝟎 = 𝑰𝑰𝟎𝟎
𝟐𝟐
𝒌𝒌
𝟏𝟏 + 𝒓𝒓
𝟏𝟏 + 𝒓𝒓
𝟏𝟏 + 𝒓𝒓
Compare to a specified required
• Decision Rule - Accept the project if it pays back on
a discounted basis within the specified time
Computing Discounted Payback
Time
Coffee shop CF Cumulative CF Sandwich shop CF Cumulative CF
0
(20,000)
(20,000)
(20,000)
(20,000)
1
15,000
(6,607)
6,000
(14,643)
2
15,000
5,351
7,000
(9,063)
3
13,000
14,604
6,000
(4,792)
4
3,000
16,510
6,000
(979)
• Coffee shop Discounted PB = less than 2 years
• Sandwich shop Discounted PB = more than 4 years
• Should choose Coffee shop using Discounted Payback
Period!
Advantages and Disadvantages of
Discounted Payback
 Advantages
• Includes time value of money
• Easy to understand
• Does not accept negative
estimated NPV investments
when all future cash flows
are positive
 Disadvantages
• May reject positive NPV
investments
• Requires an arbitrary cutoff
point
• Ignores cash flows beyond the
cutoff point
• Biased against long-term
projects, such as R&D and new
products
Alternatives to NPV
In practice, other investment rules are also used for capital
budgeting
1. Internal Rate of Return (IRR)
2. Profitability Index (PI)
3. Payback Period
4. Average Accounting Return
• These rules were used historically
• They sometimes give the same answer as NPV, but
sometimes do not (these alternatives have shortcomings)
• Bottom line: NPV rule dominates these alternatives!
Average Accounting Return
• There are different definitions for average accounting return
• The one used in the book is:
• Average net income / average book value
• Note that the average book value depends on how the asset is depreciated.
• Need to have a target cutoff rate
• Decision Rule: Accept the project if the AAR is greater than a
preset rate
Computing AAR for the Project
(Assume Chan require an average accounting return of 25%)
Time
Coffee shop net income
Sandwich shop net
income
1
6,200
3,500
2
7,800
4,000
3
8,500
2,960
4
1,200
4,100
Average
5,925
3,640
 Average book value = 25,000
 Coffee shop AAR = 5,925 / 25,000 = .237 = 23.7% < 25%
 Sandwich shop AAR = 3,640 / 25,000 = .146 = 14.6% < 25%
Decision Criteria - AAR
• Does the AAR rule account for the time value of money?
• Does the AAR rule account for the risk of the cash flows?
• Does the AAR rule provide an indication about the
increase in value?
• Should we consider the AAR rule for our primary decision
rule?
Advantages and Disadvantages of AAR
 Advantages
• Easy to calculate
 Disadvantages
• Not a true rate of return; time
value of money is ignored
• Needed information will
usually be available
• Uses an arbitrary benchmark
cutoff rate
• Based on accounting net
income and book values, not
cash flows and market values
Capital Budgeting In Practice
• We should consider several investment criteria when
making decisions
• NPV and IRR are the most commonly used primary
investment criteria
• Payback is a commonly used secondary investment
criteria
Summary
 Net present value
• Difference between market value and cost
• Take the project if the NPV is positive
• Has no serious problems
• Preferred decision criterion
 Internal rate of return
• Discount rate that makes NPV = 0
• Take the project if the IRR is greater than the required return
• Same decision as NPV with conventional cash flows
• IRR is unreliable with nonconventional cash flows or mutually exclusive projects
 Profitability Index
• Benefit-cost ratio
• Take investment if PI > 1
• Cannot be used to rank mutually exclusive projects
• May be used to rank projects in the presence of capital rationing
Summary
 Payback period
• Length of time until initial investment is recovered
• Take the project if it pays back within some specified period
• Doesn’t account for time value of money, and there is an arbitrary
cutoff period
 Discounted payback period
• Length of time until initial investment is recovered on a discounted
basis
• Take the project if it pays back in some specified period
• There is an arbitrary cutoff period
Summary
 Average Accounting Return
• Measure of accounting profit relative to book value
• Similar to return on assets measure
• Take the investment if the AAR exceeds some specified
return level
• Serious problems and should not be used