1. Capital Budgeting
 Overview
 Methods / decision rules
Payback, discounted payback
NPV
IRR, MIRR
Profitability Index
 Unequal lives
 Economic life

2. Why is capital budgeting?
 Long-term decisions; involve large
expenditures.
 Investing too much / not investing
 Timing
 Very important to firm’s future.
 Accurate sales forecast

3. Project Classification
 Replacement (M/CR)
 Expansion (E/N)
 Safety / environment
 R&D
 Long term contracts

4. What is the difference between
independent and mutually exclusive
projects?
Projects are:
independent, if the cash flows of
one are unaffected by the
acceptance of the other.
mutually exclusive, if the cash
flows of one can be adversely
impacted by the acceptance of the
other.

5. What is the payback period?
The number of years required to
recover a project’s cost,
or how long does it take to get the
business’s money back?

6. S -1000 500 400 300 100
L -1000 100 300 400 600

7. Strengths of Payback:
1. Provides an indication of a
project’s risk and liquidity.
2. Easy to calculate and understand.
Weaknesses of Payback:
1. Ignores the TVM.
2. Ignores CFs occurring after the
payback period.

8. Discounted Payback: Uses discounted
rather than raw CFs.

9. Rationale for the NPV Method
NPV = PV inflows - Cost
= Net gain in wealth.
Accept project if NPV > 0.
Choose between mutually
exclusive projects on basis of
higher NPV. Adds most value.

10. Using NPV method, which project(s)
should be accepted?
 If Projects S and L are mutually
exclusive, accept S because
NPVs > NPVL .
 If S & L are independent,
accept both; NPV > 0.

11. NPV
 +NPV?
 NPV and EVA

12. Internal Rate of Return: IRR
0 1 2 3
CF0 CF1 CF2 CF3
Cost Inflows
IRR is the discount rate that forces
PV inflows = cost. This is the same
as forcing NPV = 0.

13. Rationale for the IRR Method
If IRR > WACC, then the project’s
rate of return is greater than its
cost-- some return is left over to
boost stockholders’ returns.
Example: WACC = 10%, IRR = 15%.
Profitable.

14. Decisions on Projects S and L per IRR
 If S and L are independent, accept
both. IRRs > r = 10%.
 If S and L are mutually exclusive,
accept S because IRRS > IRRL .

15. NPV Profiles
find NPVL and NPVS at different discount
rates:
r NPVL NPVS
0
5
10
15

16. NPV
60
50
40
Crossover
Point
30
20
S
IRRS
10 L
0 Discount Rate (%)
0 5 10 15 20 23.6
-10
IRRL

17. To Find the Crossover Rate
1. Find cash flow differences between the
projects.
2. Find IRR. Crossover rate = 7.2%
3. Can subtract S from L or vice versa, but
better to have first CF negative.
4. If profiles don’t cross, one project
dominates the other.

18. NPV and IRR always lead to the same
accept/reject decision for independent
projects:
NPV
IRR > r r > IRR
and NPV > 0 and NPV < 0.
Accept. Reject.
r (%)
IRR

19. Mutually Exclusive Projects
NPV r <7.2: NPVL> NPVS , IRRS > IRRL
CONFLICT
L r > 7.2: NPVS> NPVL , IRRS > IRRL
NO CONFLICT
S IRRS
r 7.2 r %
IRRL

20. Two Reasons NPV Profiles Cross
1. Size (scale) differences. Smaller
project frees up funds at t = 0 for
investment. The higher the opportunity
cost, the more valuable these funds, so
high r favors small projects.
2. Timing differences. Project with faster
payback provides more CF in early
years for reinvestment. If r is high,
early CF especially good, NPVS > NPVL.

21. Reinvestment Rate Assumptions
 NPV assumes reinvest at r
(opportunity cost of capital).
 IRR assumes reinvest at IRR.
 Realistic?

22. Normal Cash Flow Project:
Cost (negative CF) followed by a
series of positive cash inflows.
One change of signs.
Nonnormal Cash Flow Project:
Two or more changes of signs.
Most common: Cost (negative
CF), then string of positive CFs,
then cost to close project.
Nuclear power plant, strip mine.

23. Nonnormal CFs--two sign changes.
NPV NPV Profile
IRR2 = 400%
0 r
100 400
IRR1 = 25%

24. Logic of Multiple IRRs
1. At very low discount rates, the PV of
CF2 is large & negative, so NPV < 0.
2. At very high discount rates, the PV of
both CF1 and CF2 are low, so CF0
dominates and again NPV < 0.
3. In between, the discount rate hits CF 2
harder than CF1, so NPV > 0.
4. Result: 2 IRRs.

25. Managers like rates--prefer IRR to NPV
comparisons. Can we give them a
better IRR?
MIRR is the discount rate which
causes the PV of a project’s terminal
value (TV) to equal the PV of costs.
TV is found by compounding inflows
at WACC.
Thus, MIRR assumes cash inflows are
reinvested at WACC.

26. Why use MIRR versus IRR?
MIRR correctly assumes reinvestment
at opportunity cost = WACC. MIRR
also avoids the problem of multiple
IRRs.
Managers like rate of return
comparisons, and MIRR is better for
this than IRR.

27. Accept Project?
MIRR = 5.6% < r = 10%.
Also, if MIRR < r, NPV will be
negative

28. Mutually exclusive projects
Project C0 C1 IRR NPV @
12%
P -10000 20000
Q -50000 75000
Incremental cash flow associated with the switch?

29. Lending Vs Borrowing
Project C0 C1 IRR NPV @
10%
X -4000 6000
Y +4000 -7000

30. PI
 PI = PV of future CFs / Initial cost

31. Unequal Lives
S and L are mutually exclusive and
will be repeated. r = 10%. Which is
better? (000s)
0 1 2 3 4
Project S:
(100) 60 60
Project L:
(100) 33.5 33.5 33.5 33.5

32. S L
CF0 -100,000 -100,000
CF1 60,000 33,500
Nj 2 4
I 10 10
NPV 4,132 6,190
NPVL > NPVS. But is L better?

33.  Note that Project S could be
repeated after 2 years to generate
additional profits.
 Can use either replacement chain
or equivalent annual annuity
analysis to make decision.

34. Replacement Chain Approach (000s)
Project S with Replication:
0 1 2 3 4
Project S:
(100) 60 60
(100) 60 60
(100) 60 (40) 60 60
NPV = 7,547.

35. Or, use NPVs:
0 1 2 3 4
4,132 4,132
3,415 10%
7,547
Compare to Project L NPV = 6,190.

36. If the cost to repeat S in two years
rises to $105,000, which is best? (000s)
0 1 2 3 4
Project S:
(100) 60 60
(105) 60 60
(45)
NPVS = $3,415 < NPVL = $6,190.
Now choose L.

37. Economic Life
Consider another project with a 3-year
life. If terminated prior to Year 3, the
machinery will have positive salvage
value.
Year CF Salvage Value
0 (5,000) 5,000
1 2,100 3,100
2 2,000 2,000
3 1,750 0

38. CFs Under Each Alternative (000s)
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

39. Assuming a 10% cost of capital, what is
the project’s optimal, or economic life?
NPV(no) = -123.
NPV(2) = 215.
NPV(1) = -273.

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

41. 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

42. 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...)

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

44. 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...)

45. Reason: Companies want to avoid the
direct costs (i.e., flotation costs) and
the indirect costs of issuing new
capital.
(More...)

46. Reason: Companies don’t have
enough managerial, marketing, or
engineering staff to implement all
positive NPV projects.
(More...)

47. Reason: Companies believe that the
project’s managers forecast
unreasonably high cash flow estimates,
so companies “filter” out the worst
projects by limiting the total amount of
projects that can be accepted.