1. Project Decision Making
MGT 326 Ch 8:Investment Decision Rules (bdh2e)
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
MGT 326 Ch 8:Investment Decision Rules (bdh2e)
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, R&D, 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:
Since the results of capital budgeting decisions last many years…
the firm loses some financial flexibility
they are strategic decisions
Erroneous forecasts of requirements can have serious consequences
if too much is invested the firm will incur unnecessarily high depreciation and other expenses
if not enough is invested:
purchased equipment may not be modern enough to enable the firm to be competitive
if capacity is in adequate, the firm may lose market share
Timing is important; the firm must acquire and bring into operation assets when needed; must be pro-active

3. Project (Decision) Types:
MGT 326 Ch 8:Investment Decision Rules (bdh2e)
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:
Payback Period
Discounted Payback Period
Net Present Value (NPV)
Internal Rate of Return (IRR)
Modified Internal Rate of Return (MIRR)

4. Net Present Value (NPV) Method
MGT 326 Ch 8:Investment Decision Rules (bdh2e)
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 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 > 0 means you make money; the profit is greater than the cost
An NPV < 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 > 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)
MGT 326 Ch 8:Investment Decision Rules (bdh2e)
Net Present Value (NPV) Method (continued)
Example (Uneven CFs): What is the NPV of a project with the following annual cash flows if the firm’s WACC =10%? 1 2 3 4
-3,000
1,363.64
991.74
601.05
204.90
161.33
1,500
1,200
800
300
10% 1 per.
10% 2per.
10% 3 per.
10% 4 per.
Financial Calculator:
I/Y=10, CF0=-3000, CF1=1500, CF2=1200, CF3=800, CF4=300; NPV = Is this project acceptable?
Example (Uniform CFs): What is the NPV of a project with the following annual cash flows if the firm’s WACC =10%?
500
500
500
500 1 2 3 4
1,500
NPV = [P/Y=1, N=4, I/Y=10, PMT=500; CPT, PV] =
= 84.93

6. Net Present Value (NPV) Method (continued)
CE 350 Project Decison Making
Net Present Value (NPV) Method (continued)
Example: What is the NPV of a project with the following monthly cash flows if the firm’s WACC =6.0000%?
x $1,000 4 5 6 1 2 3
$350
$390
$480
$660
$820
$940
-$2,000

7. Net Present Value (NPV) Method (continued)
CE 350 Project Decison Making
Net Present Value (NPV) Method (continued)
Example: What is the NPV of a project with the following quarterly cash flows if the firm’s WACC = %?
$500
$ x $1,000 1 2 34 35 36
$11,000.00

8. CE 350 Project Decison Making
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.
Uncovered cost at start of full-recovery year
Total cash flow during full-recovery year
Number of years before full recovery of original investment
PB = +
Example: Find the payback period for a project
which has the following cash flows
Full-recovery year PB 1 2 3 4
Cash Flow
-3,000
1,500
1,200
800
300
Cumulative Net CF
-3,000
-3,000
+ 1,500
-1,500
-1,500
+ 1,200
-300
-300
+ 800
500
PB = /800 = years

9. Payback Period (continued) Payback Period Decision Rule:
MGT 326 Ch 8:Investment Decision Rules (bdh2e)
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 project’s 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 who’s annual cash flows are shown below:
100
100
100
100
100
100
Project A 1 2 3 4 5 6
PB = 4.5 yrs
450 90 90 90 90 90
200
Project B 1 2 3 4 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. Cum. NET Discounted Cash Flows
CE 350 Project Decison Making
Discounted Payback Period (not covered in your textbook)
Similar to Payback Period Method
Expected future cash flows are discounted by the project’s 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% 1 2 3
-100
PVCFt=0
-100
9.09
49.59
60.11
Cum. NET Discounted Cash Flows
-100
+ 9.09
-90.91
-90.91
-41.32
-41.32
18.79
Discounted
Payback
= /60.11 = yrs
Strengths & Weaknesses of the Discounted Payback Method:
Strengths
Provides an indication of a project’s 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)
CE 350 Project Decison Making
Discounted Payback Period (not covered in your textbook)
Example: A project has the following quarterly cash flows. Find the discounted payback period. WACC = % 30 25
rper = 1.5% 20 10 1 2 3 4
-70

12. Internal Rate of Return
MGT 326 Ch 8:Investment Decision Rules (bdh2e)
Internal Rate of Return
Definition:
The discount rate that forces the PV of a project’s expected cash flows to equal its initial cost
It is also the discount rate that forces the project’s 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?
1,500
800
1,200
-3,000
300 1 2 3 4
3000 = 1, ,
(1+IRR) (1+IRR) (1+IRR) (1+IRR)4
NPV = 0 = , ,
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. Internal Rate of Return (continued)
MGT 326 Ch 8:Investment Decision Rules (bdh2e)
Internal Rate of Return (continued)
3000 = 1, ,
(1+IRR) (1+IRR) (1+IRR) (1+IRR)4
IRR is similar in concept to the Yield to Maturity of a bond
If IRR = % then:
$3000 = $1, $ $ $183.25
If the initial cost of the project is $3,000 and it produces a % 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 project’s CF stream:
1,500
800
1,200
-3,000
300 1 2 3 4

14. Internal Rate of Return (continued)
MGT 326 Ch 8:Investment Decision Rules (bdh2e)
Internal Rate of Return (continued)
If a project’s IRR exceeds the WACC (or opportunity cost of capital), the firm makes money
If a project’s IRR is less than the WACC (or opportunity cost of capital) , the firm will lose money
If a project’s IRR equals the WACC (or opportunity cost of capital), the firm “breaks even”
Thus the project’s required ROR is the firm’s 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 project’s IRR
both methods rely on expected (thus estimated) future cash flows
however with NPV, we know what rate these CFs will be reinvested at; it’s 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)
MGT 326 Ch 8:Investment Decision Rules (bdh2e)
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 don’t 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
$130k
$145k
$89k
$94k 1 2 3 4 5 6
$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
$130k
$145k
$89k
$94k 1 2 3 4 5 6
WACC = %
$45.66k
$50k
$370k
P/Y=1, N=1, I/Y=9.5, FV=50; CPT PV; PV = 45.66k
CF0=-370, C01=130, C02=43.34, C03=0, C04=145, C05=170, CO6=94; IRR = %
= $89K - $45.66k

16. Notes on NPV and IRR (continued) Why use IRR? Answer:
MGT 326 Ch 8:Investment Decision Rules (bdh2e)
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 firm’s true cost of capital
What if WACC is too low of an estimate of a firm’s cost of capital? Projects with relatively high IRR have greater margins of safety the than projects whose IRRs barely exceed a firm’s WACC
Conclusions: When evaluating which of 2 or more mutually exclusive projects, NPV is preferred over IRR
Prof. Jim’s Recommendations:
Always use NPV first
Use IRR and Discounted Payback Period as tie breakers

17. NPV Profiles Let’s examine two projects with differing cash flows
MGT 326 Ch 8:Investment Decision Rules (bdh2e)
NPV Profiles
Let’s examine two projects with differing cash flows
600
300
400
200 1 2 3 4
-1,000 5
100
Project S
200
400 1 2 3 4
-1,000 5
600
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
Crossover Point:
NPVS = NPVL
@ r = 9.55%
IRRL = 18.9%
IRRS = 25.7%
NPV
Discount Rate (r)
PROJ L
PROJ S
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 don’t cross, one project dominates the other

18. NPV Profiles (continued)
MGT 326 Ch 8:Investment Decision Rules (bdh2e)
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
MGT 326 Ch 8:Investment Decision Rules (bdh2e)
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)
r =11.5%
8,000
14,000
13,000
12,000
11,000
10,000
Proj C 1 2 3 4 5 6
-40,000
NPVC = $7,165, IRR = 17.5%
r =11.5%
7,000
13,000
12,000
Proj F 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
13,000
12,000
7,000
13,000
12,000 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)
CE 350 Project Decison Making
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 %
Year 1 2 3 4 5 6
Project A
CFs
-$60.00
$18.00
Project B
-$45.00
$30.00

21. Risk-Adjusted Discount Rate (not in your text book)
MGT 326 Ch 8:Investment Decision Rules (bdh2e)
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 project’s 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 firm’s 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 % 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 % = 7.30% % = 8.55%
rProject C = rrequired % = 7.30% % = 9.80%