n
Capital Budgeting : involves making decisions about real asset investments.
n n n
Chapter 7: Net Present Value and Other Investment
Criteria
Chapter 8: Estimating cash flows for a potential investment.
Chapter 12: Estimating a required rate of return for a potential investment = opportunity cost of capital.
(need chapters 10 & 11 to help us with chapter 12)
Net Present Value & Other
Investment Criteria
n n n n
Project Types
Capital Budgeting Decision Criteria n
Net Present Value (NPV) n n
Payback Period
Internal Rate of Return (IRR) n
Profitability Index (PI)
Equivalent Annual Cost and Equivalent Annual
Annuity
Capital Rationing
1

q
Understand how to calculate and use capital budgeting decision techniques:
Payback, NPV, IRR, & PI.
q q
Understand the advantages and disadvantages of each technique.
Understand which project to select when there is a ranking conflict between NPV and IRR.
n n n
Which of the following investment opportunities would you prefer?
#1) Give me $1 now and I’ll give you $2 at the end of class.
#2) Give me $100 now and I’ll give you
$150 at the end of class.
n n
Independent Projects – don’t affect acceptance of other projects
Mutually Exclusive Projects – interact with other projects or accomplish the same objective n n
Normal Projects -only one sign change in sequence of cash flows
Non-normal Projects - multiple sign changes in cash flow series.
2

n
We want to help Marge Simpson, Inc. analyze the following business opportunities by using the following cash flow information. Assume Marge's opportunity cost of capital is 12%.
Time Falafel-Full How 'Bout A Pretzel?
0
1
2
3
4
(20,000)
15,000
15,000
13,000
3,000
(20,000)
2,000
2,500
3,000
50,000
Net Present Value - Present value of cash flows minus initial investments.
Opportunity Cost of Capital - Expected rate of return given up by investing in a project
NPV = PV - required investment
NPV
=
C
0
+
C t
( 1
+ r ) t
NPV
=
C
0
+
( 1
C
+
1 r ) 1
+
( 1
C
+
2 r ) 2
C t
( 1
+ r ) t
3

Terminology
C = Cash Flow t = time period of the investment r = “opportunity cost of capital” n
The Cash Flow could be positive or negative at any time period.
Net Present Value Rule
Managers increase shareholders’ wealth by accepting all projects that are worth more than they cost.
Therefore, they should accept all projects with a positive net present value.
Time Falafel-Full PV(CF) How 'Bout A Pretzel?
PV(CF)
0 (20,000) (20,000) (20,000) (20,000)
1
2
3
4
15,000
15,000
13,000
3,000
13,393
11,958
9,253
1,907
2,000
2,500
3,000
50,000
1,786
1,993
2,135
31,776
NPV 16,510 17,690 n n
Calculator Steps. Falafel-Full: CF0 = -20,000, C01 =
15,000, F01 = 2, C02 = 13,000, F02 = 1, C03 = 3,000.
NPV: I = 12, CPT NPV = 16,510
Pretzel: CF0 = -20,000, C01 = 2,000, F01=1, C02 =
2,500, F02=1, C03 = 3,000, F03=1, C04 = 50,000. NPV: I
= 12, CPT NPV = 17,690
4

n n n n
Excel’s NPV function is goofed up. =NPV(r, range of cash flows)
Assumes first cash flow in range occurs at t = 1.
See spreadsheet.
Solution to this spreadsheet problem: exclude initial cost (t = 0 cash flow) from NPV cell range and add initial cost (if already negative) to the
NPV function.
n n
If projects are independent, Marge should select both.
n
Both have positive NPV.
If the projects are mutually exclusive, select How ‘Bout A Pretzel?
n
Pretzel NPV > Falafel NPV.
n n n
Measures how long it takes to recovers a project’s cost.
Easy to calculate and a good measure of a project’s risk and liquidity.
Decision Rule: Accept if PB < some maximum period of time.
5

Time
0
1
2
3
4
Falafel-Full
(20,000)
15,000
15,000
13,000
3,000
Cumulative CF How 'Bout A Pretzel?
Cumulative CF
(20,000)
(5,000)
10,000
23,000
26,000
(20,000)
2,000
2,500
3,000
50,000
(20,000)
(18,000)
(15,500)
(12,500)
37,500 n n n
Falafel PB = less than 2 years
Pretzel PB = less than 4 years
Marge should choose Falafel using
Payback Period.
n n n
Ignores time value of money!
Ignores cash flows beyond payback period.
Not a good investment decision technique.
n n n n n n
Internal Rate of Return is a project’s expected rate of return on its investment.
IRR is the interest rate where the PV of the project’s cash flows equals its cost.
In other words, the IRR is the rate where a project’s
NPV = 0.
?CF
t
/(1 + IRR) t = Cost
Decision Rule: Accept if IRR > r (opportunity cost of capital).
Non-normal projects have multiple IRRs. Don’t use IRR to decide on non-normal projects.
6

Time Falafel-Full How 'Bout A Pretzel?
0
1
2
3
4
(20,000)
15,000
15,000
13,000
3,000
(20,000)
2,000
2,500
3,000
50,000 n n n n
Best to use calculator. Calculator Steps.
Falafel-Full: CF0 = -20,000, C01 = 15,000, F01 = 2, C02 =
54.7%
Pretzel: CF0 = -20,000, C01 = 2,000, F01=1, C02 = 2,500,
F02=1, C03 = 3,000, F03=1, C04 = 50,000. Press IRR, then
CPT: IRR = 33.3% r = 12%. If independent projects: select both, IRRs
> 12%. Mutually exclusive: select Falafel; higher
IRR.
n n n
For normal independent projects, all three methods give same accept/reject decision.
n
NPV > 0 yields IRR > r in order to lower
NPV to 0.
However, these methods can rank mutually exclusive projects differently.
What to do, then?
n n n
A graph which shows a project’s NPV at different interest rates (opportunity cost of capital).
Can illustrate ranking conflicts between NPV and
IRR.
Below is a table of NPVs for Marge’s projects.
r
0%
5%
10%
12%
15%
25%
35%
55%
Falafel-Full How 'Bout A Pretzel?
26,000 37,500
21,589
17,849
16,510
14,649
9,485
5,529
(68)
27,899
20,289
17,690
14,190
5,216
(874)
(8,201)
7

Marge's NPV Profiles
40,000
30,000
IRR(P) IRR(F)
20,000
10,000
0
-10,000 0% 10% 20% 30% 40% 50% 60%
-20,000
Cost of Capital (r)
Falafel-Full
How 'Bout A
Pretzel?
n n n n
For each year, subtract one project’s cash flows from the other.
If there is a change of signs of these cash flow differences, a ranking conflict exists.
Find IRR of these cash flow differences to find rate where the two projects have the same NPV = crossover rate.
At a cost of capital less than this crossover rate, a ranking conflict between NPV and
IRR exists.
3
2
4
1
0
Time Falafel-Full How 'Bout A Pretzel? Falafel - Pretzel
(20,000) (20,000)
15,000 2,000 13,000 C01
15,000
13,000
3,000
2,500
3,000
50,000
12,500
10,000
(47,000)
C02
C03
C04
IRR = Crossover Rate 14.1%
Marge's NPV Profiles
40,000
30,000
IRR(P) IRR(F)
20,000
10,000
0
-10,000 0% 10% 20% 30% 40% 50% 60%
-20,000
Cost of Capital (k)
Falafel-Full
How 'Bout A
Pretzel?
n n n n
NPV but lower IRR = Ranking Conflict.
At cost of capital greater than 14.1%, Falafel has the higher NPV and IRR.
Why? Cash flow timing differences in this case.
Other cause: initial cost differences, but not here.
8

n n n
Shareholder Wealth Maximization : n
Want to add more value to the firm than less.
Result: Choose project with highest
NPV when NPV/IRR ranking conflict exists for mutually exclusive projects.
Also, IRR has the multiple IRR problem for non-normal projects like the following.
n
Acme is considering the following project which would market these roller blades to coyotes trying to catch road runners. Acme expects a cash inflow in the year 1, but an outflow in the 2 nd (last) year of the project due to liability claims from injured cartoon coyotes. Acme’s opportunity cost of capital is 13%.
Year
Cash Flow
NPV = -1.95
0
(5)
1
30
IRR = 26.8%
2
(30)
4
-1
0% 50% 100% 150% 200% 250% 300% 350% 400% 450% 500% 550%
-6 n n
At Acme’s 13% opportunity cost of capital, the project has a negative NPV even though the IRRs is greater than
13%.
Because of this conflict, don’t use IRR to make decisions for non-normal projects! (or look for a first IRR that is less than cost of capital)
9

2
3
0
1
4 n
To replace the Budweiser sign that the ferret dropped in the frog pond, Louie the Lizard is evaluating two new signs. Louie must purchase and care for a replacement sign indefinitely.
Here are the annual costs for the two replacement signs.
n
Which sign should Louie choose given an opportunity cost of capital of 11%?
Year Frying Frogs Lizards Leaping over Frogs
4,000
1,000
1,000
6,000
900
700
700
700
Equivalent Annual Cost - The cost per period with the same present value as the cost of buying and operating a machine.
Equivalent annual cost = present value of costs annuity factor
3
4
1
2
Year Frying Frogs Lizards Leaping over Frogs
0 4,000 6,000
1,000
1,000
900
700 n n n
700
700
Frying Frogs (FF) PV of costs = 5713
Lizards Leaping (LL) PV of costs = 8352
FF EAC: 5713=PV, 11=I/Y, 2=N, 0=FV, CPT PMT = 3336 n n
LL EAC: 8352=PV, 11=I/Y, 4=N, 0=FV, CPT PMT = 2692
Louie should choose the Lizards Leaping over Frogs sign because of its lower cost on an annual basis.
10

n
Comparing Projects (NPV>0) with unequal lives: Equivalent Annual
Annuity
Burns Power is considering the following mutually exclusive projects in order to increase power consumption in Springfield indefinitely.
Which project should be selected if Burns
Power’s opportunity cost of capital is 10%?
Year
Sun-Blocker
Fog-Maker
0
(50)
(30)
1
60
40
2
60
40
3
40
Equivalent annual annuity = net present va lue annuity factor n n n n n
NPV of Sun-Blocker = $54.1 m
NPV of Fog-Maker = $69.5 m
Sun-Blocker EAA: -54.1=PV, 10=I/Y, 2=N,
0=FV, CPT PMT = $31.2m
Fog-Maker EAA: -69.5=PV, 10=I/Y, 3=N, 0=FV,
CPT PMT = $27.9m
Burns should choose the Sun-Blocker because it would add the most value on an annual basis.
Sometimes you have the ability to defer an investment and select a time that is more ideal at which to make the investment decision. A common example involves a tree farm. You may defer the harvesting of trees. By doing so, you defer the receipt of the cash flow, yet increase the cash flow.
11

n n n n
Can purchase a scanner today for $400 that would provide $60 in annual benefits for 10 years. However, scanner prices are expected to decrease 20% per year.
Should you purchase the scanner today or wait if your discount rate is 10%?
PV of annual benefits: 60=PMT, 10=N, 10=I/Y,
0=FV, CPT PV = $369
NPV = $369 – Expected Scanner Cost n
6
7
4
5
2
3
Year Cost PV Benefits NPV at Purchase
0
1
400
320
369
369
-31
49
256
205
164
131
105
84
369
369
369
369
369
369
113
164
205
238
264
285
NPV Today
-31
45
93
123
140
148
149
146
Capital Rationing - Limit set on the amount of funds available for investment.
Soft Rationing - Limits on available funds imposed by management.
Hard Rationing - Limits on available funds imposed by the unavailability of funds in the capital market.
12

n n n n n
The ratio of the net present value of a project’s cash flows to its cost.
PI = NPV/Cost
Decision Rule: Accept if PI > 0
PI can be used to rank projects under capital rationing conditions. Accept highest PI projects under the capital constraint to maximize NPV.
CAUTION: PI can rank mutually exclusive projects that have different initial costs differently than NPV.
n n n n
Want a method the uses the time value of money with all project cash flows: NPV,
PI, IRR.
IRR can give erroneous decision for nonnormal projects.
Overall, NPV is the best and preferred method.
However, under capital rationing (budget restraint), ranking projects by PI can be useful in helping to maximize NPV under capital constraint.
13