S
L
CF
0
-100
-100
CF
1
60
33.5
N
J
2
4
I/YR
10
10
NPV
4.132
6.190

56
Put Projects on Common Basis
•
Note that Franchise S could be repeated after
2 years to generate additional profits.
•
Use replacement chain to put on common life.
•
Note: equivalent annual annuity analysis is
alternative method.

57
Replacement Chain Approach (000s)
Franchise S with Replication
NPV = $7.547.
0
1
2
3
4
S:
-100
60
-100
60
60
-100
-40
60
60
60
60

58
Suppose Cost to Repeat S in Two Years Rises
to $105,000
NPV
S
= $3.415 < NPV
L
= $6.190.
Now choose L.
0
1
2
3
4
S:
-100
60
60
-105
-45
60
60
10%

59
Equivalent Annual Annuity Approach (EAA)
•
Convert the PV into a stream of annuity
payments with the same PV.
•
S: N=2, I/YR=10, PV=-4.132, FV = 0. Solve for
PMT = EAA
S
= $2.38.
•
L: N=4, I/YR=10, PV=-6.190, FV = 0. Solve for
PMT = EAA
L
= $1.95.
•
S has higher EAA, so it is a better project.

EAA and Chain Problem
•
Problem 4

61
Economic Life versus Physical Life
•
Consider another project with a 3-year life.
•
If terminated prior to Year 3, the machinery
will have positive salvage value.
•
Should you always operate for the full physical
life?
•
See next slide for cash flows.

62
Economic Life versus Physical Life
(Continued)
Year
CF
Salvage
Value
0
-$5,000
$5,000
1
2,100
3,100
2
2,000
2,000
3
1,750
0

63
CFs Under Each Alternative (000s)
Years:
0
1
2
3
1. No termination
-5
2.
1
2
1.75
2. Terminate 2 years
-5
2.
1
4
3. Terminate 1 year
-5
5.
2

64
NPVs under Alternative Lives (Cost of Capital
= 10%)
•
NPV(3 years)
=
-$123.
•
NPV(2 years)
=
$215.
•
NPV(1 year)
=
-$273.

65
Conclusions
•
The project is acceptable only if operated for 2
years.
•
A project’s engineering life does not always
equal its economic life.

Economic Life vs. Physical Life Problem
•
Problem 7.

67
Choosing the Optimal Capital Budget
•
Finance theory says to accept all positive NPV
projects.
•
Two problems can occur when there is not
enough internally generated cash to fund all
positive NPV projects:
–
An increasing marginal cost of capital.
–
Capital rationing

68
Increasing Marginal Cost of Capital
•
Externally raised capital can have large
flotation costs, which increase the cost of
capital.
•
Investors often perceive large capital budgets
as being risky, which drives up the cost of
capital.
(More...)

69
•
If external funds will be raised, then the NPV
of all projects should be estimated using this
higher marginal cost of capital.

70
Capital Rationing
•
Capital rationing occurs when a company
chooses not to fund all positive NPV projects.
•
The company typically sets an upper limit on
the total amount of capital expenditures that
it will make in the upcoming year.
(More...)

71
•
Reason:
Companies want to avoid the direct
costs (i.e., flotation costs) and the indirect
costs of issuing new capital.
•
Solution:
Increase the cost of capital by
enough to reflect all of these costs, and then
accept all projects that still have a positive
NPV with the higher cost of capital.

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- Fall '14
- Interest, Interest Rate, Net Present Value