1. Capital Budgeting Techniques FHU3213
PART 2
Capital Budgeting Techniques FHU3213

2. capital budgeting EVALUATION METHODS
Non-Discounted Cash Flow
Does not explicitly account for time value of money (i.e., Each dollar earned in the future is assumed to have the same values as each dollar that was invested many years earlier).
The methods include:
(a) Payback Period (PBP)
(b) Accounting Rate of Return (ARR) also known as
Return on Investment (ROI)
Discounted Cash Flow
Consider the time value of money. The methods used include:
(a) Net Present Value (NPV)
(b) Internal Rate of Return (IRR)
(c) Profitability Index (PI)

3. Net Present value (NPV)
NPV is the present value of an investment project’s net cash flows minus the project’s initial cash outflow.
Use frequently in capital budgeting practice
NPV = PV of Inflows - Initial Investment
CF1
(1+ k )
CF2
(1+ k )2
CF3
(1+ k )3
CFn
(1+ k )n
NPV = … – CFo
Where;
CFt Cash flow for t period
k is the appropriate discount rate/ cost of capital
CF0 initial outlays

4. Decision Rule
The present value method can be used as an accept-reject criterion.
If NPV ≥ $0, then accept the project
If NPV ≤ $0, then reject the project
accept-reject criterion can also be shown as:
PV Benefits ≥ PV Cost → Accept [NPV ≥ $0]
PV Benefits ≤ PV Cost → Reject [NPV ≤ $0]
Where, PV Benefits is present value of inflows and PV Cost is the initial investment

5. Net Present Value - Example
Boston Company is currently contemplating two project: Project A and Project B. Both projects require an initial investment of $10,000. The projected relevant cash inflows are presented in the following Table.
If the firm has a 10% cost of capital, which project should Boston preferred according to the NPV method?
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000

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

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

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

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

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

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

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

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

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

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

16. Net Present Value - Example
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
k=10%
(10,000)
3,500
3,500
3,500
3,500
NPV A = – 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%

17. Net Present Value - Example
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
k=10%
(10,000)
3,500
3,500
3,500
3,500
NPV A = – 10,000
3,500
(1+ .1 )
3,500
(1+ .1)2
3,500
(1+ .1 )3
3,500
(1+ .1 )4
NPVA= 𝐴 (1+𝑖) 𝑛 −1 𝑖 (1+𝑖) 𝑛 ,000

18. Net Present Value - Example
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
k=10%
(10,000)
3,500
3,500
3,500
3,500
NPV A = – 10,000
3,500
(1+ .1 )
3,500
(1+ .1)2
3,500
(1+ .1 )3
3,500
(1+ .1 )4
NPVA= (1+0.1) 4 − (1+0.1) ,000 = 11, – 10,000 = $1095 > 0

19. NPV Decision Rules ACCEPT A & B ACCEPT B ONLY
NPVs for Project A is $1,095
NPVs for Project B is $1,151
Accept-reject criterion:
If projects are independent then accept all projects with NPV  0.
If projects are mutually exclusive, accept higher with NPV  0.
Ranking Method:
If the project were being ranked, Project B would be considered superior than project A because it has a higher NPV
ACCEPT A & B
ACCEPT B ONLY

20. Pros and cons of npv Advantage
Resulting number is easy to interpret: shows how wealth will change if the project is accepted.
Acceptance criteria is consistent with shareholder wealth maximization.
Relatively straightforward to calculate
Disadvantage
It requires estimation of cash flows with accuracy which is very difficult under
It also requires correct estimation of cost of capital for getting correct result.

21. 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,
2 3,
3 3,500 4,600
4 3,500 10,000
10% 5%
Cost of Capital N P V
6,000
3,000
20%
15%
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

22. 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,
2 3,
3 3,500 4,600
4 3,500 10,000
10% 5%
Cost of Capital N P V
6,000
3,000
20%
15%
NPV(5%) = – 10,000
3,500
( )
3,500
(1+ .05)2
3,500
( )3
3,500
(1+ .05)4
= $2,411

23. 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,
2 3,
3 3,500 4,600
4 3,500 10,000
10% 5%
Cost of Capital N P V
6,000
3,000
20%
15%
3,500
( )
3,500
(1+ .10)2
3,500
( )3
3,500
(1+ .10)4
NPV(10%) = – 10,000
= $1,095

24. 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,
2 3,
3 3,500 4,600
4 3,500 10,000
10% 5%
Cost of Capital N P V
6,000
3,000
20%
15%
3,500
( )
3,500
(1+ .15)2
3,500
( )3
3,500
(1+ .15)4
NPV(15%) = ,000
= – $7.58

25. 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,
2 3,
3 3,500 4,600
4 3,500 10,000
10% 5%
Cost of Capital N P V
6,000
3,000
20%
15%
3,500
( )
3,500
(1+ .20)2
3,500
( )3
3,500
(1+ .20)4
NPV(20%) = – 10,000
= – $939

26. 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,
2 3,
3 3,500 4,600
4 3,500 10,000
10% 5%
Cost of Capital N P V
6,000
3,000
20%
15%
Connect the Points

27. 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,
2 3,
3 3,500 4,600
4 3,500 10,000
6,000 N P V
3,000
Cost of Capital 5%
10%
15%
20%
500
(1+ 0 )
500
(1+ 0)2
4,600
(1+ 0 )3
10,000
(1+ 0)4
NPV(0%) = – 10,000
= $5,600

28. 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,
2 3,
3 3,500 4,600
4 3,500 10,000
6,000 N P V
3,000
Cost of Capital 5%
10%
15%
20%
500
(1+.05)
500
(1+.05)2
4,600
(1+ .05)3
10,000
(1+ .05)4
NPV(5%) = – 10,000
= $3,130

29. 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,
2 3,
3 3,500 4,600
4 3,500 10,000
6,000 N P V
3,000
Cost of Capital 5%
10%
15%
20%
500
(1+.10)
500
(1+.10)2
4,600
(1+ .10)3
10,000
(1+ .10)4
NPV(10%) = – 10,000
= $1.154

30. 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,
2 3,
3 3,500 4,600
4 3,500 10,000
6,000 N P V
3,000
Cost of Capital 5%
10%
15%
20%
500
(1+.15)
500
(1+.15)2
4,600
(1+ .15)3
10,000
(1+ .15)4
NPV(15%) = – 10,000
= –$445

31. 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,
2 3,
3 3,500 4,600
4 3,500 10,000
10% 5%
Cost of Capital N P V
6,000
3,000
20%
15%
Project B
Connect the Points

32. 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,
2 3,
3 3,500 4,600
4 3,500 10,000
10% 5%
Cost of Capital N P V
6,000
3,000
20%
15%
Project B

33. Net Present Value Profile
Compare NPV of the two projects for different required rates
Crossover point
6,000 N P V
Project B
3,000
Project A
Cost of Capital 5%
10%
15%
20%

34. Net Present Value Profile
Compare NPV of the two projects for different required rates
Crossover point
6,000 N P V
Project B
3,000
For any discount rate < crossover point choose B
Project A
Cost of Capital 5%
10%
15%
20%

35. Net Present Value Profile
Compare NPV of the two projects for different required rates
Crossover point
6,000 N P V
Project B
For any discount rate > crossover point choose A
3,000
For any discount rate < crossover point choose B
Project A
Cost of Capital 5%
10%
15%
20%

36. Internal Rate of Return (IRR):
IRR measures the rate of the return on a project
The IRR can be determined by setting up an NPV equation and solving for discount rate that make the NPV = 0
Equivalently, IRR is solved by determining the rate that equates the PV of cash inflows to the PV of cash outflows. =

37. Internal Rate of Return (IRR)
IRR of Project A and Project B from previous example. The IRR for project A (14%) and B (15%) were determined in which NPV = 0
6,000
Project B N P V
3,000
IRRA 15%
NPV = $0
IRRB 14%
Cost of Capital 5%
10%
15%
20%

38. Internal Rate of Return (IRR)
Determine the mathematical solution for IRR

39. Internal Rate of Return (IRR)
Determine the mathematical solution for IRR
CF1
(1+ IRR )
CF2
(1+ IRR )2
CFn
(1+ IRR )n
0 = NPV = – IO

40. Internal Rate of Return (IRR)
Determine the mathematical solution for IRR
CF1
(1+ IRR )
CF2
(1+ IRR )2
CFn
(1+ IRR )n
0 = NPV = – IO
CF1
(1+ IRR )
CF2
(1+ IRR )2
CFn
(1+ IRR )n
IO =
Outflow = PV of Inflows

41. Internal Rate of Return (IRR)
Determine the mathematical solution for IRR
CF1
(1+ IRR )
CF2
(1+ IRR )2
CFn
(1+ IRR )n
0 = NPV = – IO
CF1
(1+ IRR )
CF2
(1+ IRR )2
CFn
(1+ IRR )n
IO =
Outflow = PV of Inflows
Solve for Discount Rates

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

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

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

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

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

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

48. Internal rate of return (IRR)
The calculation by hand of the IRR from the above equation is not an easy task as it involves a complex trial-and-error techniques.
IRR can be easily solve using financial calculator or spreadsheet.
The IRR for project B is 13.55
The IRR for project A is 14.6

49. Decision rule for IRR Independent Projects Accept Projects with
IRR required rate
Mutually Exclusive Projects
Accept project with highest
These criteria guarantee that the firm will earn at least its required return.

50. Internal rate of return (IRR): the example continued
Comparing the IRR for projects A and B given the 10% cost of capital, we can see both projects are acceptable because:
The IRRA = 14.6 > 10.0% cost of capital
The IRRB = > 10.0% cost of capital
Comparing the two projects’ IRRs, we would prefer project A over project B because IRRA = 14.6% > IRRA = 13.55%.

51. Pros and cons of irr Disadvantage Advantage
It considers the time value of money and it also takes into account the total cash flows generated by any project over the life of the project.
IRR is a very much acceptable capital budgeting method in real life as it measures profitability of the projects in percentage and can be easily compared with the opportunity cost of capital..
Disadvantage
Requires knowledge of finance to use.
Difficult to calculate – need financial calculator.
It is possible that there exists no IRR or multiple IRRs for a project and there are several special cases when the IRR analysis needs to be adjusted in order to make a correct decision (these problems will be addressed later).

52. Profitability INDEX PI = Very Similar to Net Present Value
PV of Inflows
Initial Outlay
PI =

53. Profitability INDEX + + +. . .+ PI = PI = IO
Very Similar to Net Present Value
PV of Inflows
Initial Investment
PI =
Instead of Subtracting the Initial investment from the PV of Inflows, the Profitability Index is the ratio of Initial Outlay to the PV of Inflows
CF1
(1+ k )
CF2
(1+ k )2
CF3
(1+ k )3
CFn
(1+ k )n
PI = IO

54. Profitability Index - example
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
Profitability Index for Project B
500
(1+ .1 )
(1+ .1)2
4,600
(1+ .1 )3
10,000
(1+ .1 )4
PIB =
10,000

55. Profitability index for project b
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
Profitability Index for Project B
500
(1+ .1 )
(1+ .1)2
4,600
(1+ .1 )3
10,000
(1+ .1 )4
PIB =
10,000
11,154
10,000
PIB = =

56. Profitability Index - example
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
Profitability Index for Project B
500
(1+ .1 )
(1+ .1)2
4,600
(1+ .1 )3
10,000
(1+ .1 )4
PIB =
10,000
11,154
10,000
PIB = =
Profitability Index for Project A
PIA= 𝐴 (1+𝑖) 𝑛 −1 𝑖 (1+𝑖) 𝑛 10,000
PIA= PV of 3,500 Annuity for 4 years at 10% 10,000

57. Profitability index for project b
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
Profitability Index for Project B
500
(1+ .1 )
(1+ .1)2
4,600
(1+ .1 )3
10,000
(1+ .1 )4
PIB =
10,000
11,154
10,000
PIB = =
Profitability Index for Project A
PIA= 𝐴 (1+𝑖) 𝑛 −1 𝑖 (1+𝑖) 𝑛 10,000
= (1+0.1) 4 − (1+0.1) ,000 = 11,095 10,000 =1.1095

58. Profitability Index Decision Rules
Independent Projects
Accept Project if PI  1
Mutually Exclusive Projects
Accept Highest PI  1 Project
Comparing the PI for projects A and B, we can see both projects are acceptable because
PI project A =  1
PI project B = 1.154 1
Comparing the two projects’ PIs, we would prefer project B over project B because PIB = > PIB =

59. Pros and cons of PI Advantage Disadvantage
PI considers the time value of money as well as all the cash flows generated
Acceptance criteria is generally consistent with shareholder wealth maximization.
Relatively straightforward to calculate.
Disadvantage
It is possible that PI cannot be used if the initial cash flow is an inflow.
Method needs to be adjusted when there are mutually exclusive projects (to be discussed later).

60. Comparison of Methods Project A Project B Choose NPV $1,095 $1,154 B
IRR 14.96% 13.50% A
PI B
NPV & PI indicated accept Project B while IRR indicated that Project A should be accepted. Why?
Reinvestment Rate
NPV assumes cash flows are reinvested at the required rate, k.
IRR assumes cash flows are reinvested at IRR.
Reinvestment Rate of k more realistic as most projects earn approximately k (due to competition)
Conclusion: NPV is the Better Method for project evaluation