capital budgetting techniques

1. Capital-Budgeting Chapter 11
Arbon, Gizelle
Domingo, Sheila
Maranon, Mikhael
Montibon, Stephanie
Tedoco, Chelsea

2. CAPITAL BUDGETING
CONCEPTS
• Here CAPITAL refers to long term assets used in production,
while a BUDGET is a plan that outlines projected expenditures
during some future period.
• Thus, the “capital budget” is a summary of planned investments
in long term assets, and CAPITAL BUDGETING is the whole
process of analyzing projects and deciding which ones to
include in the capital budget.

3. STRATEGIC BUSINESS PLAN
• A long – run plan that outlines in broad terms
the firm’s basic strategy for the next 5 to 10
years.
• Provide a general guide to the operating
executives who must meet them.

4. 7 CATEGORIZE PROJECTS
• 1. Replacement: needed to continue current
operations
• 2. Replacement: cost reduction
• 3. Expansion of existing products or markets
• 4. Expansion into new products or markets
• 5. Safety and/or environment projects
• 6. Other Projects
• 7. Mergers

5. CAPITAL BUDGETING
CONCEPTS
 Capital Budgeting involves evaluation of (and decision about) projects.
Which projects should be accepted? Here, our goal is to accept a project
which maximizes the shareholder wealth. Benefits are worth more than
the cost.
 The Capital Budgeting is based on forecasting.
 Estimate future expected cash flows.
 Evaluate project based on the evaluation method.

6. CAPITAL BUDGETING
CONCEPTS
 Initial Cash Outlay - amount of capital spent to get project going.
 If spend $10 million to build new plant then the Initial Outlay (IO) = $10
million
Cash Flows
CF0 = Cash Flow time 0 = -10 million

7. CAPITAL BUDGETING
CONCEPTS
 Initial Cash Outlay - amount of capital spent to get project going.
 If spend $10 million to build new plant then the Initial Outlay (IO) = $10
million
Cash Flows
CFn = Sales - Costs
Annual Cash Inflows--after-tax CF
Cash inflows from the project
CF0 = Cash Flow time 0 = -10 million

8. CAPITAL BUDGETING METHODS
1. Regular Payback
2. Discounted payback
3. Net present value
4. Internal Rate of Return
5. Modified Internal Rate of Return

9. CAPITAL BUDGETING METHODS
METHOD #1 REGULAR PAYBACK
OR PAYBACK PERIOD
• Regular Payback – defined as the number of years required to
• recover the funds invested in a project from its cash flows
• The length of time required for an investments cash flows to cover its cost.

10. CAPITAL BUDGETING METHODS
 Number of years needed to recover your initial outlay.
Regular Payback
P R O J E C T
Time A B
0 (1,000.) (1,000.)
1 500 100
2 400 300
3 300 400
4 100 675

11. CAPITAL BUDGETING METHODS
 Number of years needed to recover your initial outlay.
Payback Period
0 1 2 3 4
500 400 300 100
(1,000)
P R O J E C T
Time A B
0 (1000.) (1000.)
1 500 100
2 400 300
3 300 400
4 100 675
Cash Flow
Payback = number of years prior to full recovery + unrecovered cost at
start of year/cash flow during full recovery year

12. CAPITAL BUDGETING METHODS
 Number of years needed to recover your initial outlay.
Payback Period
0 1 2 3 4
500
-500
400
-100
300
+200
100
+300
(1,000)
(1,000)
Payback = 2 + 100/300 = 2.33 years
Cash flow
Cumulative
CF
P R O J E C T
Time A B
0 (1000.) (1000.)
1 500 100
2 400 300
3 300 400
4 100 675

13. CAPITAL BUDGETING METHODS
 Number of years needed to recover your initial outlay.
Payback Period
P R O J E C T
Time A B
0 (1000.) (1000.)
1 500 100
2 400 300
3 300 400
4 100 675

14. CAPITAL BUDGETING METHODS
 Number of years needed to recover your initial outlay.
Payback Period
P R O J E C T
Time A B
0 (1000.) (1000.)
1 500 100
2 400 300
3 300 400
4 100 675
0 1 2 3 4
100 300 400 675
(1,000)
Cash Flow
Formula is: Payback = number of years prior to full recovery +
unrecovered cost at start of year/cash flow during full recovery year

15. CAPITAL BUDGETING METHODS
 Number of years needed to recover your initial outlay.
Payback Period
P R O J E C T
Time A B
0 (1000.) (1000.)
1 500 100
2 400 300
3 300 400
4 100 675
0 1 2 3 4
100
-900
300
-600
400
-200
675
+475
(1,000)
(1,000)
Payback = 3 + 200/675 = 3.30 years
Cash flow
Cumulative CF

16. • FLAWS OF PAYBACK METHOD
- All dollars received in different years are given the same
weight (i.e., the time value of money is ignored)
- Cash Flows beyond the payback year are given no
consideration regardless of how large they might be
- Unlike NPV (Net Present Value), which tells us how
much wealth a project adds, and the IRR, which tells us
how much a project yields over the cost of capital, the
payback merely tells us how much a project yields over
the cost of capital

17. METHOD #2
DISCOUNTED PAYBACK METHOD
The length of time required for an investment’s cash flows,
discounted at the investment’s cost of capital, to cover its
cost.

18. Discounted Payback Example
P R O J E C T
Time A B
0 (1000.) (1,000.)
1 500 100
2 400 300
3 300 400
4 100 675

19. CAPITAL BUDGETING METHODS
 At 10% Cost of Capital
Discounted Payback Period
0 1 2 3 4
500 400 300 100
(1,000)
P R O J E C T
Time A B
0 (1000.) (1000.)
1 500 100
2 400 300
3 300 400
4 100 675
Cash Flow

20. CAPITAL BUDGETING METHODS
Discounted Payback Period
0 1 2 3 4
500
455
-545
400
331
-215
300
+225
11
100
68
79
(1,000)
(1,000)
(1,000)
Discounted Payback = 2 + 215/255 = 2.95 years
Cash Flow
Discounted Cash Flow
Cumulative discounted CF
P R O J E C T
Time A B
0 (1000.) (1000.)
1 500 100
2 400 300
3 300 400
4 100 675
Formula is: Payback = number of years prior to full recovery +
unrecovered cost at start of year/cash flow during full recovery year

21. CAPITAL BUDGETING METHODS
 At 10% Cost of Capital
Discounted Payback Period
P R O J E C T
Time A B
0 (1000.) (1000.)
1 500 100
2 400 300
3 300 400
4 100 675

22. CAPITAL BUDGETING METHODS
Discounted Payback Period
P R O J E C T
Time A B
0 (1000.) (1000.)
1 500 100
2 400 300
3 300 400
4 100 675
0 1 2 3 4
100 300 400 675
(1,000)
Cash Flow

23. CAPITAL BUDGETING METHODS
Discounted Payback Period P R O J E C T
Time A B
0 (1000.) (1000.)
1 500 100
2 400 300
3 300 400
4 100 675
0 1 2 3 4
100
91
-909
300
248
-661
400
301
-361
675
461
100
(1,000)
(1,000)
(1,000)
Discounted Payback = 3 + 361/461 = 3.78 years
Cash Flow
Discounted Cash Flow
Cumulative discounted CF
Formula is: Payback = number of years prior to full recovery +
unrecovered cost at start of year/cash flow during full recovery year

24. Method #3
Net Present Value
A method of ranking investment
proposals using the NPV, which is
equal to the present value of the
project’s free cash flows discounted
at the cost of capital

25. CAPITAL BUDGETING METHODS
• Methods that consider time value of money and all
cash flows
• Net Present Value:
• Present Value of all costs and benefits of a project.

26. CAPITAL BUDGETING METHODS
• Present Value of all costs and benefits of a project.
• Concept is similar to Intrinsic Value of a security but subtracts cost of the
project.
Net Present Value
NPV = PV of Inflows - Initial Outlay

27. CAPITAL BUDGETING METHODS
 Present Value of all costs and benefits of a project.
 Concept is similar to Intrinsic Value of a security but subtracts of cost of
project.
Net Present Value
NPV = PV of Inflows - Initial Outlay
NPV = + + +···+ – IO
CF1
(1+ k )
CF2
(1+ k )2
CF3
(1+ k )3
CFn
(1+ k )n

28. CAPITAL BUDGETING METHODS
Net Present Value
0 1 2 3 4
500 500 4,600 10,000
(10,000)
k=10%
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000

29. CAPITAL BUDGETING METHODS
Net Present Value
0 1 2 3 4
500 500 4,600 10,000
(10,000)
455
k=10%
$500
(1.10)
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000

30. CAPITAL BUDGETING METHODS
Net Present Value
0 1 2 3 4
500 500 4,600 10,000
(10,000)
455
413
k=10%
$500
(1.10) 2
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000

31. CAPITAL BUDGETING METHODS
Net Present Value
0 1 2 3 4
500 500 4,600 10,000
(10,000)
455
413
3,456
k=10%
$4,600
(1.10) 3
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000

32. CAPITAL BUDGETING METHODS
Net Present Value
0 1 2 3 4
500 500 4,600 10,000
(10,000)
455
6,830
413
3,456
k=10%
$10,000
(1.10) 4
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000

33. CAPITAL BUDGETING METHODS
Net Present Value
0 1 2 3 4
500 500 4,600 10,000
(10,000)
455
$11,154
6,830
413
3,456
k=10%
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000

34. CAPITAL BUDGETING METHODS
Net Present Value
0 1 2 3 4
500 500 4,600 10,000
(10,000)
455
6,830
413
3,456
k=10%
PV Benefits > PV Costs
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000
$11,154 > $ 10,000
$11,154

35. CAPITAL BUDGETING METHODS
Net Present Value
0 1 2 3 4
500 500 4,600 10,000
(10,000)
455
6,830
413
3,456
k=10%
PV Benefits > PV Costs
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000
$11,154 > $ 10,000
NPV > $0
$1,154 > $0
$11,154
$1,154 = NPV

36. CAPITAL BUDGETING METHODS
Net Present Value
0 1 2 3 4
3,500
(10,000)
k=10%
3,500 3,500 3,500
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000

37. CAPITAL BUDGETING METHODS
Net Present Value
0 1 2 3 4
3,500
(10,000)
k=10%
3,500 3,500 3,500
NPV = + + + – 10,000
3,500
(1+ .1 )
3,500
(1+ .1)2
3,500
(1+ .1 )3
3,500
(1+ .1 )4
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000

38. CAPITAL BUDGETING METHODS
Net Present Value
0 1 2 3 4
3,500
(10,000)
k=10%
3,500 3,500 3,500
NPV = + + + – 10,000
3,500
(1+ .1 )
3,500
(1+ .1)2
3,500
(1+ .1 )3
3,500
(1+ .1 )4
PV of 3,500 Annuity for 4 years at 10%
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000

39. CAPITAL BUDGETING METHODS
Net Present Value
0 1 2 3 4
3,500
(10,000)
k=10%
3,500 3,500 3,500
NPV = + + + – 10,000
3,500
(1+ .1 )
3,500
(1+ .1)2
3,500
(1+ .1 )3
3,500
(1+ .1 )4
= 3,500 x PVIFA 4,.10 - 10,000
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000
= 11,095 – 10,000 = $1,095

40. CAPITAL BUDGETING METHODS
 If projects are independent then accept all
projects with NPV  0.
NPV Decision Rules ACCEPT A & B

41. CAPITAL BUDGETING METHODS
 If projects are independent then accept all
projects with NPV  0.
 If projects are mutually exclusive, accept
projects with higher NPV.
NPV Decision Rules
ACCEPT A & B
ACCEPT B only

42. 10%
5%
0 Cost of Capital
N
P
V
6,000
3,000
20%
15%
NET PRESENT VALUE PROFILE
 Graphs the Net Present Value of the project with different required rates
NPV(0%) = + + + – 10,000
3,500
(1+ 0 )
3,500
(1+ 0)2
3,500
(1+ 0 )3
3,500
(1+ 0)4
= $4,000
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000

43. 10%
5%
0
Cost of Capital
N
P
V
6,000
3,000
20%
15%
NET PRESENT VALUE PROFILE
 Graphs the Net Present Value of the project with different required rates
NPV(5%) = + + + – 10,000
3,500
(1+ .05 )
3,500
(1+ .05)2
3,500
(1+ .05 )3
3,500
(1+ .05)4
= $2,411
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000

44. 10%
5%
0 Cost of Capital
N
P
V
6,000
3,000
20%
15%
NET PRESENT VALUE PROFILE
 Graphs the Net Present Value of the project with different required rates
NPV(10%) = + + + – 10,000
3,500
(1+ .10 )
3,500
(1+ .10)2
3,500
(1+ .10 )3
3,500
(1+ .10)4
= $1,095
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000

45. 10%
5%
0 Cost of Capital
N
P
V
6,000
3,000
20%
15%
NET PRESENT VALUE PROFILE
 Graphs the Net Present Value of the project with different required rates
NPV(15%) = + + + – 10,000
3,500
(1+ .15 )
3,500
(1+ .15)2
3,500
(1+ .15 )3
3,500
(1+ .15)4
= – $7.58
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000

46. 10%
5%
0 Cost of Capital
N
P
V
6,000
3,000
20%
15%
NET PRESENT VALUE PROFILE
 Graphs the Net Present Value of the project with different required rates
NPV(20%) = + + + – 10,000
3,500
(1+ .20 )
3,500
(1+ .20)2
3,500
(1+ .20 )3
3,500
(1+ .20)4
= – $939
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000

47. 10%
5%
0 Cost of Capital
N
P
V
6,000
3,000
20%
15%
NET PRESENT VALUE PROFILE
 Graphs the Net Present Value of the project with different required rates
Connect the Points
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000

48. 10%
5%
0 Cost of Capital
N
P
V
6,000
3,000
20%
15%
NET PRESENT VALUE PROFILE
 Graphs the Net Present Value of the project with different required rates
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000
NPV(0%) = + + + – 10,000
500
(1+ 0 )
500
(1+ 0)2
4,600
(1+ 0 )3
10,000
(1+ 0)4
= $5,600

49. 10%
5%
0 Cost of Capital
N
P
V
6,000
3,000
20%
15%
NET PRESENT VALUE PROFILE
 Graphs the Net Present Value of the project with different required rates
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000
NPV(5%) = + + + – 10,000
500
(1+.05)
500
(1+.05)2
4,600
(1+ .05)3
10,000
(1+ .05)4
= $3,130

50. 10%
5%
0 Cost of Capital
N
P
V
6,000
3,000
20%
15%
NET PRESENT VALUE PROFILE
 Graphs the Net Present Value of the project with different required rates
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000
NPV(10%) = + + + – 10,000
500
(1+.10)
500
(1+.10)2
4,600
(1+ .10)3
10,000
(1+ .10)4
= $1.154

51. 10%
5%
0 Cost of Capital
N
P
V
6,000
3,000
20%
15%
NET PRESENT VALUE PROFILE
 Graphs the Net Present Value of the project with different required rates
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000
NPV(15%) = + + + – 10,000
500
(1+.15)
500
(1+.15)2
4,600
(1+ .15)3
10,000
(1+ .15)4
= –$445

52. 10%
5%
0 Cost of Capital
N
P
V
6,000
3,000
20%
15%
Project B
NET PRESENT VALUE PROFILE
 Graphs the Net Present Value of the project with different required rates
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000
Connect the Points

53. 10%
5%
0 Cost of Capital
N
P
V
6,000
3,000
20%
15%
Project B
NET PRESENT VALUE PROFILE
 Graphs the Net Present Value of the project with different required rates
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000

54. NET PRESENT VALUE PROFILE
 Compare NPV of the two projects for different required rates
10%
5%
0 Cost of Capital
N
P
V
6,000
3,000
20%
15%
Project B
Crossover point
Project A

55. NET PRESENT VALUE PROFILE
 Compare NPV of the two projects for different required rates
10%
5%
0 Cost of Capital
N
P
V
6,000
3,000
20%
15%
Project B
Crossover point
Project A
For any discount rate <
crossover point choose B

56. NET PRESENT VALUE PROFILE
 Compare NPV of the two projects for different required rates
10%
5%
0 Cost of Capital
N
P
V
6,000
3,000
20%
15%
Project B
Crossover point
For any discount rate >
crossover point choose A
Project A
For any discount rate <
crossover point choose B

57. METHOD #4
INTERNAL RATE OF RETURN
Is the discounted rate that forces the PV of its
inflows to equal its cost. This is equivalent to
forcing the NPV to equal zero.
The IRR is an estimate of the projects rate of
return, and it is comparable to the YTM on a
bond.

58. CAPITAL BUDGETING METHODS
 Measures the rate of return that will make the PV of future CF equal to the initial outlay.
Internal Rate of Return
Definition:
The IRR is that discount rate at which
NPV = 0
IRR is like the YTM. It is the same cocept but
the term YTM is used only for bonds.

59. CAPITAL BUDGETING METHODS
 Measures the rate of return that will make the PV of future CF equal to the initial outlay.
Internal Rate of Return
The IRR is the discount rate at which NPV = 0
10%
5%
0
Cost of Capital
N
P
V
6,000
3,000
20%
15%
Project B
NPV = $0

60. CAPITAL BUDGETING METHODS
 Measures the rate of return that will make the PV of future CF equal to the initial outlay.
Internal Rate of Return
Or, the IRR is the discount rate at which NPV = 0
10%
5%
0 Cost of Capital
N
P
V
6,000
3,000
20%
15%
Project B
NPV = $0 IRRA 15%
IRRB 14%

61. CAPITAL BUDGETING METHODS
Example:
Internal Rate of Return
0 = NPV = + +···+ – IO
CF1
(1+ IRR )
CF2
(1+ IRR )2
CFn
(1+ IRR )n

62. CAPITAL BUDGETING METHODS
Example:
Internal Rate of Return
0 = NPV = + +···+ – IO
CF1
(1+ IRR )
CF2
(1+ IRR )2
CFn
(1+ IRR )n
IO = + +···+
CF1
(1+ IRR )
CF2
(1+ IRR )2
CFn
(1+ IRR )n
Outflow = PV of Inflows

63. CAPITAL BUDGETING METHODS
Example:
Internal Rate of Return
0 = NPV = + +···+ – IO
CF1
(1+ IRR )
CF2
(1+ IRR )2
CFn
(1+ IRR )n
IO = + +···+
CF1
(1+ IRR )
CF2
(1+ IRR )2
CFn
(1+ IRR )n
Outflow = PV of Inflows
Solve for Discount Rates

64. CAPITAL BUDGETING METHODS
Internal Rate of Return
For Project B
Cannot solve for IRR
directly, must use Trial &
Error
10,000 = + + +
500
(1+ IRR )
500
(1+ IRR )2
10,000
(1+ IRR )4
4,600
(1+ IRR )3
10%
5%
0 Cost of Capital
N
P
V
6,000
3,000
20%
15%
Project B
IRRB 14%

65. CAPITAL BUDGETING METHODS
Internal Rate of Return
For Project B
Cannot solve for IRR
directly, must use Trial &
Error
10,000 = + + +
500
(1+ IRR )
500
(1+ IRR )2
10,000
(1+ IRR )4
4,600
(1+ IRR )3
TRY 14%
10,000 = + + +
500
(1+ .14 )
500
(1+ .14)2
10,000
(1+ .14 )4
4,600
(1+ .14 )3
?
10%
5%
0 Cost of Capital
N
P
V
6,000
3,000
20%
15%
Project B
IRRB 14%

66. CAPITAL BUDGETING METHODS
Internal Rate of Return
For Project B
Cannot solve for IRR
directly, must use Trial &
Error
10,000 = + + +
500
(1+ IRR )
500
(1+ IRR )2
10,000
(1+ IRR )4
4,600
(1+ IRR )3
TRY 14%
10,000 = + + +
500
(1+ .14 )
500
(1+ .14)2
10,000
(1+ .14 )4
4,600
(1+ .14 )3
?
10,000 = 9,849
?
PV of Inflows too low, try lower rate
10%
5%
0 Cost of Capital
N
P
V
6,000
3,000
20%
15%
Project B
IRRB 14%

67. CAPITAL BUDGETING METHODS
Internal Rate of Return
For Project B
Cannot solve for IRR
directly, must use Trial &
Error
10,000 = + + +
500
(1+ IRR )
500
(1+ IRR )2
10,000
(1+ IRR )4
4,600
(1+ IRR )3
TRY 13%
10,000 = + + +
500
(1+ .13 )
500
(1+ .13)2
10,000
(1+ .13 )4
4,600
(1+ .13 )3
?
10%
5%
0 Cost of Capital
N
P
V
6,000
3,000
20%
15%
Project B
IRRB 14%

68. CAPITAL BUDGETING METHODS
Internal Rate of Return
For Project B
Cannot solve for IRR
directly, must use Trial &
Error
10,000 = + + +
500
(1+ IRR )
500
(1+ IRR )2
10,000
(1+ IRR )4
4,600
(1+ IRR )3
TRY 13%
10,000 = + + +
500
(1+ .13 )
500
(1+ .13)2
10,000
(1+ .13 )4
4,600
(1+ .13 )3
?
10,000 = 10,155
?
10%
5%
0 Cost of Capital
N
P
V
6,000
3,000
20%
15%
Project B
IRRB 14%

69. CAPITAL BUDGETING METHODS
Internal Rate of Return
For Project B
Cannot solve for IRR
directly, must use Trial &
Error
10,000 = + + +
500
(1+ IRR )
500
(1+ IRR )2
10,000
(1+ IRR )4
4,600
(1+ IRR )3
TRY 13%
10,000 = + + +
500
(1+ .13 )
500
(1+ .13)2
10,000
(1+ .13 )4
4,600
(1+ .13 )3
?
10,000 = 10,155
?
13% < IRR < 14%
10%
5%
0 Cost of Capital
N
P
V
6,000
3,000
20%
15%
Project B
IRRB 14%

70. CAPITAL BUDGETING METHODS
Decision Rule for Internal Rate of Return
Independent Projects
Accept Projects with
IRR required rate
Mutually Exclusive Projects
Accept project with highest
IRR required rate

71. METHOD #5
MODIFIED INTERNAL RATE OF
RETURN
The discount rate at which the present value of
a project’s cost is equal to the present value of
its terminal value, where the terminal value is
found as the sum of the future values of the
cash inflows, compounded at the firm’s cost of
capital.

72. CONCLUSIONS ON CAPITAL
BUDGETING METHODS
NPV is the sing best criterion, because it provides
a direct measure of value the project adds to
shareholder wealth

73. CONCLUSIONS ON CAPITAL
BUDGETING METHODS
IRR and MIRR measures the profitability
expressed as a percentage rate of return, which is
interesting to decision makers.

74. CONCLUSIONS ON CAPITAL
BUDGETING METHODS
Lastly, Payback and discounted payback provide
indications of a project’s liquidity and risk.