Project Decision Making

1

• Project Decision Making
• Learning Objectives
• Explain the Cost-Benefit Analysis Concept
• Compute the NPV of a Project
• Conduct NPV Analysis of Projects With Unequal
  Lengths
• Compute the NPV of a Project Using Risk Adjusted
  Discount Rate
• Compute the IRR of a Project
• Compute the Payback Period of a Project
• Compute the Discounted Payback Period of a
  Project
• Compute the MIRR of a Project
• Use the Above Methods to Make a Project
  Investment Decision
• Understand the Limitations of the Above Methods
• Interpret NPV Profiles
• Explain Why WACC is Used as the Discount Rate For
  NPV Calculations

2

• Project Decision Making
• The process of planning and evaluating
  expenditures of capital for assets whose
  resulting cash flows are expected to extend
  beyond one year
• Theis decision process is also called Capital
  Budgeting
• Used to decide which projects to adopt
• Involves Long-term / Strategic Decisions
• Project duration of several years
• Errors in forecasting requirements have long
  lasting effects
• Projects in question typically involves large
  capital expenditures
• The larger the firm, the larger the expenditures
• Typically involves the purchase of fixed assets
  (i.e. plant equipment) that will produce some
  sort of future cash flow stream
• However, the capital budgeting process can be
  applied to any outflow of cash that produces a
  series of future cash flows
• transportation, automation/MIS, RD, etc.
• costs of market expansion efforts, new product
  lines, etc.
• outsourcing
• marketing
• Used to evaluate a single project or choose
  between 2 or more projects
• Importance of Capital Budgeting

3

• Project (Decision) Types
• Replacement Projects whether to purchase capital
  assets to take the place of existing assets to
  maintain or improve existing operations.
• maintenance of business replacement of equipment
  necessary to continue current business operations
• cost reduction includes replacement of
  serviceable but obsolete equipment with more cost
  effective equipment
• Expansion Projects whether to purchase capital
  projects and add them to existing assets to
  increase existing operations.
• existing products or markets
• new products or markets
• Safety and/or Environmental Projects
• Research Development Projects
• future cash flows very uncertain
• the norm is to add very subjective estimates to
  more solid cash flows
• Long-term contracts
• Other office buildings, parking lots, executive
  aircraft, etc.
• Project Categories
• Independent Projects Projects whose cash flows
  are not affected by decisions made about other
  projects i.e. you can do as many of the projects
  as you can afford
• Mutually Exclusive Projects A set of projects
  where the acceptance of one project means the
  others cannot be accepted
• Five Techniques

4

• Net Present Value (NPV) Method
• Definition The sum of all project cash flows is
  the Net Present Value
• The value of any financial asset is determined by
  discounting all future cash flows to the present
  (i.e. find the PV _at_ t 0) and adding them up
• Process Discount all future expected cash flows
  to time zero (t 0) then add them to any initial
  investments
• Rationale
• An NPV gt 0 means you make money the profit is
  greater than the cost
• An NPV lt 0 means you lose money the cost is
  greater than the profit
• An NPV of 0 means you break even
• Accept only projects with NPV gt 0
• When comparing mutually exclusive projects, the
  one with the highest NPV is the one with the
  highest potential benefit to the firm.
• If all the cash flows of mutually exclusive
  projects are negative, they will have negative
  NPVs. Still, you choose the project with the
  hichest NPV
• Formula

• The discount rate r for computing NPV is usually
  the Weighted Average Cost of Capital (WACC) (from
  Ch 12)
• The discount rate can be the Opportunity Cost of
  Capital (from Ch 5)

5
Net Present Value (NPV) Method (continued) Exampl
e (Uneven CFs) What is the NPV of a project with
the following annual cash flows if the firms
WACC 10?
0
1
2
3
4
1,500
800
1,200
-3,000 1,363.64 991.74 601.05 204.90 161.33
300
discount _at_ 10 1 per.
discount _at_ 10 2per.
discount _at_ 10 3 per.
discount _at_ 10 4 per.
Financial Calculator I/Y10, CF0-3000,
CF11500, CF21200, CF3800, CF4300 NPV
161.33 Is this project acceptable? Example
(Uniform CFs) What is the NPV of a project with
the following annual cash flows if the firms
WACC 10?
500
500
500
500
1,500
NPV -1500 P/Y1, N4, I/Y10, PMT500 CPT,
PV -1500 1584.93 84.93
6
Net Present Value (NPV) Method (continued) Exampl
e What is the NPV of a project with the
following monthly cash flows if the firms WACC
6.0000?
x 1,000
7
Net Present Value (NPV) Method (continued) Exampl
e What is the NPV of a project with the
following quarterly cash flows if the firms WACC
8.0000?
500
x 1,000
34
35
36
1
2
0
11,000.00
8

• Payback Period
• Payback Period (PB) The length of time it takes
  to recover the original costs (of the project)
  from expected cash flows
• Rationale The sooner investment costs are
  recovered, the better
• Process Simply add up the expected cash flows
  until they equal (or exceed) the original
  investment. The number of years it take to do
  this is the payback period.

Number of years beforefull recovery oforiginal
investment
PB

Example Find the payback period for a project
which has the following cash flows
Full-recovery year
PB
0
1
2
3
4
Cash Flow
800
1,200
-3,000
300
1,500
Cumulative Net CF
-1,500 1,200 -300
-300 800 500
-3,000
-3,000 1,500 -1,500
PB 2 300/800 2.38 years

9

• Payback Period (continued)
• Payback Period Decision Rule
• When evaluating a single project, the project is
  acceptable if the Payback Period is less than any
  pre-specified time limit
• When evaluating 2 or more mutually exclusive
  projects, the one with the shortest Payback
  Period is preferrable, assuming that it is less
  than any pre-specified time limit
• Strengths Weaknesses of the Payback Method
• Strengths
• Provides an indication of a projects liquidity
  risk (how long will invested capital be tied up)
• Weaknesses
• Ignores the Time Value of Money
• Ignores the CFs occurring after the payback
  period
• Example Consider two projects whos annual cash
  flows are shown below

100
100
100
100
100
100
Project A
0
2
3
4
1
5
6
PB 4.5 yrs
450
200
90
90
90
90
90
Project B
0
2
3
4
1
5
6
PB 5 yrs
450
Project A has a shorter PB period but is it
really the more preferable project? Compute NPV
of each project (assume WACC 8)
NPVA 12.28
NPVB 35.38
10

• Discounted Payback Period (not covered in your
  textbook)
• Similar to Payback Period Method
• Expected future cash flows are discounted by the
  projects cost of capital
• Thus the discounted payback period is defined as
  the number of years required to recover the
  investment from discounted net cash flows
• Example A project has the following annual cash
  flows. Find the discounted payback period

80
60
10
r 10
0
2
1
3
-100
PVCFt0
-100
9.09
49.59
60.11
Cum. NET Discounted Cash Flows
-100 9.09 -90.91
-90.91 49.59 -41.32
-41.32 60.11 18.79
Discounted Payback
2 41.32/60.11 2.69 yrs

• Strengths Weaknesses of the Discounted Payback
  Method
• Strengths
• Provides an indication of a projects liquidity
  risk
• Recognizes time value of money
• Recognizes WACC
• Weaknesses
• Ignores the CFs occurring after the payback
  period

11
Discounted Payback Period (not covered in your
textbook) Example A project has the following
quarterly cash flows. Find the discounted
payback period. WACC 6.0000
30
25
rper 1.5
20
10
-70
12

• Internal Rate of Return
• Definition
• The discount rate that forces the PV of a
  projects expected cash flows to equal its
  initial cost
• It is also the discount rate that forces the
  projects NPV to equal 0 (do some algebra
  subtract the initial cost form both sides of the
  equation and you get an NPV equation)
• The IRR is the ROR of the project
• A project is internal to a firm it is an
  internal investment
• Rationale Projects that have an IRR greater
  than r (the opportunity cost) are acceptable
  investments
• The project produces returns in excess of that
  which is required

Example What is the IRR of a project with the
following cash flows?
3000 1,500 1,200 800
300 (1IRR) (1IRR)2
(1IRR)3 (1IRR)4 NPV 0 -3000 1,500
1,200 800
300 (1IRR) (1IRR)2 (1IRR)3
(1IRR)4 Solve for IRR (the discount rate that
satisfies (results in, fits) either of above
equations CF, 2nd CLR WORK (Clear cash flow
worksheet) -3000, ENTER ?, 1500, ENTER ?, ?,
1200, ENTER ?, ?, 800, ENTER ?, ?, 300,
ENTER IRR, CPT 13.1140
13
Internal Rate of Return (continued)

• 3000 1,500 1,200 800
  300
• (1IRR) (1IRR)2 (1IRR)3
  (1IRR)4
• IRR is similar in concept to the Yield to
  Maturity of a bond
• If IRR 13.114 then
• 3000 1,326.10 937.88 552.77 183.25

• If the initial cost of the project is 3,000 and
  it produces a 13.114 ROR, then the firm will
  break even (the initial investment is matched by
  the sum of the discounted future cash flows)
• If each of the discounted CFs are compounded at
  IRR (13.114) for the respected number of
  periods, it produces the projects CF stream

14

• Internal Rate of Return (continued)
• If a projects IRR exceeds the WACC (or
  opportunity cost of capital), the firm makes
  money
• If a projects IRR is less than the WACC (or
  opportunity cost of capital) , the firm will lose
  money
• If a projects IRR equals the WACC (or
  opportunity cost of capital), the firm breaks
  even
• Thus the projects required ROR is the firms
  WACC
• When comparing two mutually exclusive projects,
  the one with the higher IRR is preferred
• Some notes on using NPV and IRR methods
• 1. Reinvestment Rate Assumption
• Which one of these methods (NPV or IRR) is a
  safer bet? (i.e. more reliable and predictable)
• The answer depends on the interest rate at which
  cash flows can be reinvested
• the NPV method assumes that they can be
  reinvested at r,
• the IRR implies that they can be reinvested at a
  rate equal to a projects IRR
• both methods rely on expected (thus estimated)
  future cash flows
• however with NPV, we know what rate these CFs
  will be reinvested at its the opportunity cost
  of capital
• we create the IRR by forcing the NPV of the
  expected cash flows to equal zero
• thus the IRR we come up may be much greater than
  the opportunity cost of capital, thus
  establishing an unrealistic reinvestment rate for
  project CFs

15

• Some notes on using NPV and IRR methods
  (continued)
• 2. The IRR method is not suitable when a project
  has unconventional cash flows
• A conventional CF has a large outflow of cash at
  the beginning of the life span and several
  inflows of cash throughout the rest of the
  project
• An unconventional CF has an initial negative CF,
  followed by a series of positive CFs which are
  interrupted by a negative CF.
• This will produce 2 or more IRRs (one for each
  period in which the sign of the CF changes)
  (trust me on this you dont want to see the
  math)(you can use a calculator but the IRR will
  be meaningless)
• Which IRR will you use?

Unconventional Cash Flows
170k
145k
130k
94k
89k
0
4
5
6
1
2
3
50k
370k
What to do? Answer Modify the cash flows so
that there is only one negative cash flow then do
IRR. This is the Modified IRR method.
170k
145k
130k
94k
89k
0
4
5
6
1
2
3
WACC 9.5000
45.66k
50k
370k
P/Y1, N1, I/Y9.5, FV50 CPT PV PV
45.66k CF0-370, C01130, C0243.34, C030,
C04145, C05170, CO694 IRR 13.4800
89K - 45.66k
16

• Notes on NPV and IRR (continued)
• Why use IRR?
• Answer
• It suits those who want to directly express the
  benefits of a project as a rate of return
  (Corporate operation types selling a project to
  non-finance guys)
• It gives some indication of safety if future cash
  flows fall short of expectations
• WACC is only an estimate of the of a firms true
  cost of capital
• What if WACC is too low of an estimate of a
  firms cost of capital? Projects with relatively
  high IRR have greater margins of safety the than
  projects whose IRRs barely exceed a firms WACC
• Conclusions When evaluating which of 2 or more
  mutually exclusive projects, NPV is preferred
  over IRR
• Prof. Jims Recommendations
• Always use NPV first
• Use IRR and Discounted Payback Period as tie
  breakers

17
NPV Profiles Lets examine two projects with
differing cash flows
Project S
Project L
If we plot NPVs of each project against various
values for r, we can see how the NPVs will change
when r changes

• Key Points
• The crossover point is the r that produces equal
  NPVs.
• At r greater than 9.55, Proj S has higher NPV.
• At r less than 9.55, Proj L has higher NPV.
• Note IRR suggests Proj S is always superior
• If the profiles dont cross, one project
  dominates the other

18

• NPV Profiles (continued)
• Two reasons why profiles cross
• Size (scale) differences. Smaller projects
  demand less funds at t 0 thus leave more funds
  available for other investments. The higher the
  opportunity cost, the more valuable these funds
  are, so high r favors small projects.
• Cash Flow Timing differences. Project with
  faster payback provides more CF in early years
  for reinvestment.
• Use both methods (NPV IRR) to determine
  sensitivity to r
• Find NPV and IRR of both projects.
• Construct NPV profiles and find the crossover
  point
• Accept the project that has the highest NPV with
  respect to r

19
Comparison of Projects with Unequal
Lives Example A company is planning to
modernize its production facilities and is
considering either a conveyor system (Proj C) or
some forklift trucks (Proj F)
8,000
13,000
14,000
12,000
10,000
11,000
r 11.5
Proj C
0
1
2
3
4
5
6
-40,000
NPVC 7,165, IRR 17.5
r 11.5
7,000
12,000
13,000
Proj F
0
1
2
3
-20,000
NPVF 5,391, IRR 25.2

• The NPV results hide the fact that Proj F affords
  the opportunity to make a similar investment at t
  3, thus producing another 3 years of cash flows
• To compensate for this we must use the
  replacement chain or common life approach
• this simply means extending the cash flows of the
  shorter project out to the life of the longer
  project and then computing NPV of the shorter
  project

Proj F Replacement Chain
7,000
12,000
13,000
7,000
12,000
13,000
0
1
2
3
4
5
6
-20,000
-20,000
NPVF 9,281

• This is only an issue for mutually exclusive
  projects
• Ignore the Equivalent Annual Annuity approach as
  discussed in your text book

20
Comparison of Projects with Unequal Lives
(continued)
Example A firm is considering two mutually
exclusive projects that have the annual cash
flows shown below. Based on NPV analysis, which
project should be accepted? The required rate of
return is 7.0000
Year 0 1 2 3 4 5 6
Project A CFs -60.00 18.00 18.00 18.00 18.00 18.00 18.00
Project B CFs -45.00 30.00 30.00  
21

• Risk-Adjusted Discount Rate (not in your text
  book)
• Definition The discount rate (required rate of
  return) that applies to a particular risky
  project
• Used to determine a projects NPV
• Applies the concept of risk aversion to project
  decisions
• Very subjective there is no reliable technique
  for determining appropriate risk premiums for
  projects
• Benchmark use what other firms (in same
  industry) use
• Should be consistently applied throughout the
  firm
• Process
• Determine the overall required rate of return for
  the average project(i.e. opportunity cost of
  capital)
• Classify all projects into three categories low
  risk, moderate risk and high risk
• Determine appropriate risk adjustments
• modify required rate of return appropriately
• Results riskier projects will have their NPVs
  artificially lowered because (according to the
  concept of risk aversion) riskier assets should
  have lower value compared to less risky assets

• Example A firm is considering two mutually
  exclusive projects. Project A is a low risk
  project, Project B is moderately risky while
  Project C is considered to have a high degree of
  risk.
• The firms rrequired is 7.30. The firm uses
  the risk-adjusted discount rate method to account
  for project risk. Projects posing minimal risk
  are evaluated using rrequired for the discount
  rate. 1.25 is added for moderately risky
  projects and 2.50 is added for significantly
  risky projects. What discount rates should be
  used for NPV calculations of Projects A, B and C?
• rProject A rrequired 7.30
• rProject B rrequired 1.25 7.30 1.25
  8.55
• rProject C rrequired 2.50 7.30 2.50
  9.80