1. The Basics of Capital Budgeting
Chapter 10
The Basics of Capital Budgeting

2. Topics
Methods
NPV
IRR, MIRR
Payback, discounted payback
EAS (EAA)

3. What is capital budgeting?
Analysis of potential projects.
Long-term decisions; involve large expenditures.

4. Steps in Capital Budgeting
Estimate cash flows (inflows & outflows).
Determine r = WACC for project.
Evaluate

5. Capital Budgeting Project Categories
Replacement to continue profitable operations
Replacement to reduce costs
Expansion of existing products or markets
Expansion into new products/markets
Contraction decisions
Safety and/or environmental projects
Mergers
Other

6. Independent versus 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.

7. Net present value (NPV) rule
FI Corporate Finance leng Ling
Net present value (NPV) rule
Accept project if
Net present value > 0
What is Net present value?
Net present value
= Benefits minus Costs

8. How do we measure benefits & costs?
NPV = B – C =

9. NPV: Sum of the PVs of All Cash Flows
Cost often is CF0 and is negative.
NPV = Σ N
t = 0
CFt
(1 + r)t
t = 1
– CF0

10. Cash Flows for Franchises L and S10 80 60 1 2 3
10%
L’s CFs: 70 20 50
S’s CFs:

11. What’s Franchise L’s NPV?10 80 60 1 2 3
10%
L’s CFs:
9.09
49.59
60.11
= NPVL
NPVS = $19.98.

12. Calculator Solution: Enter Values in CF Register for L
-100 10 60 80
CF0
CF1
NPV
CF2
CF3 I
= = NPVL

13. Rationale for the NPV Method
NPV = PV inflows – Cost
This is net gain in wealth, so accept project if NPV > 0.
Choose between mutually exclusive projects on basis of higher positive NPV. Adds most value.

14. Using NPV method, which franchise(s) should be accepted?
If Franchises S and L are mutually exclusive, accept S because NPVs > NPVL.
If S & L are independent, accept both; NPV > 0.
NPV is dependent on cost of capital.

15. Internal Rate of Return: IRR1 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.

16. NPV: Enter r, Solve for NPVΣ N
t = 0
CFt
(1 + r)t

17. IRR: Enter NPV = 0, Solve for IRRΣ N
t = 0
CFt
(1 + IRR)t
IRR is an estimate of the project’s rate of return, so it is comparable to the YTM on a bond.

18. What’s Franchise L’s IRR?10 80 60 1 2 3
IRR = ?
PV3
PV2
PV1
0 = NPV
Enter CFs, then press IRR: IRRL = 18.13%. IRRS = 23.56%.

19. 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%.
So this project adds extra return to shareholders.

20. Decisions on Franchises S and L per IRR
If S and L are independent, accept both: IRRS > r and IRRL > r.
If S and L are mutually exclusive, accept S because IRRS > IRRL.
IRR is not dependent on the cost of capital used.

21. NPV and IRR: No conflict for independent projects.
r > IRR
and NPV < 0.
Reject.
NPV ($)
r (%)
IRR
IRR > r
and NPV > 0
Accept.

22. Reinvestment Rate Assumptions
NPV assumes reinvest at r (opportunity cost of capital).
IRR assumes reinvest at IRR.
Reinvest at opportunity cost, r, is more realistic, so NPV method is best. NPV should be used to choose between mutually exclusive projects.

23. Modified Internal Rate of Return (MIRR)
MIRR is the discount rate that causes the PV of a project’s terminal value (TV) to equal the PV of costs.
TV is found by compounding all inflows at WACC.
Thus, MIRR assumes cash inflows are reinvested at WACC.

24. MIRR for Franchise L: First, Find PV and TV (r = 10%)
10.0
80.0
60.0 1 2 3
10%
66.0
12.1
158.1
-100.0
TV inflows
PV outflows

25. Second, Find Discount Rate that Equates PV and TV
MIRR = 16.5%
158.1 1 2 3
-100.0
TV inflows
PV outflows
MIRRL = 16.5%
$100 =
$158.1
(1+MIRRL)3

26. BAII: Step 1, Find PV of Inflows
First, enter cash inflows in CF register:
CF0 = 0, CF1 = 10, CF2 = 60, CF3 = 80
Second, enter I = 10.
Third, find PV of inflows:
Press NPV =

27. Step 2, Find TV of Inflows
Enter PV = , N = 3, I/YR = 10, PMT = 0.
Press FV = = FV of inflows.

28. Step 3, Find PV of Outflows
For this problem, there is only one outflow, CF0 = -100, so the PV of outflows is -100.
For other problems there may be negative cash flows for several years, and you must find the present value for all negative cash flows.

29. Step 4, Find “IRR” of TV of Inflows and PV of Outflows
Enter FV = , PV = -100, PMT = 0, N = 3.
Press I/YR = 16.50% = MIRR.

30. 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.

31. FI 3300 - Corporate Finance leng Ling
Apply NPV, IRR
Assume a discount rate of 11%. Compute the NPV, IRR and decide whether the project should be accepted or rejected.
Project C0 C1 C2 C3 C4 C5
T=0
T=1
T=2
T=3
T=4
T=5 A
-1000
400
500
Verify that NPV = , IRR = 31.79%,
Since NPV>0, IRR>11%, accept the project

32. Conceptual problem: NPV and IRR
FI Corporate Finance leng Ling
Conceptual problem: NPV and IRR
Consider a project with an initial outflow at time 0 and positive cash flows in all subsequent years. As the discount rate is decreased the _____________.
IRR remains constant while the NPV increases.
IRR decreases while the NPV remains constant.
IRR increases while the NPV remains constant.
IRR remains constant while the NPV decreases.
IRR decreases while the NPV decreases.

33. Computational problem: NPV and IRR
FI Corporate Finance leng Ling
Computational problem: NPV and IRR
You are attempting to reconstruct a project analysis of a co-worker who was fired. You have found the following information:
The IRR is 12%.
The project life is 4 years.
The initial cost is $20,000.
In years 1, 3 and 4 you will receive cash inflows of $6,000.
You know there will be a cash flow in year 2, but the amount is not in the file.
The appropriate discount rate is 10%.
What is the NPV of the project?

34. Condition 1: Cash inflows occur before cash outflows
Thus far, we have considered projects with normal cash flows, (i.e., a single cash outflow in year 0 followed by cash inflows in all future years).
With normal cash flows, IRR works fine.
However, if you have cash inflow first, followed by cash outflow, then IRR will be negative.
Result: You cannot use IRR to make the accept/reject decision.
Use NPV to get the correct decision.

35. Condition 2: Cash flows change signs more than once
FI Corporate Finance leng Ling
Condition 2: Cash flows change signs more than once
Consider the following project cash flows: t = 0, -$400, t = 1, $2,500, t = 2, -$3,000. Suppose that the company’s cost of capital is 70 percent.
NPV = $ The project is, acceptable.
There are two IRR’s for this project: 61.98%, 363%. Look at the NPV profile (next slide).
When there are multiple IRRs, the IRR method loses meaning and is NOT appropriate.
However, the NPV method still gives the correct accept/reject decision.
Using the BA II Plus, students will get the first IRR = 61.98%, but this is misleading.

36. 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?

37. Payback for Franchise L10 80 60 1 2 3
-100 =
CFt
Cumulative
-90
-30 50
PaybackL
2 + $30/$80 = years
2.4

38. Payback for Franchise S70 20 50 1 2 3
-100
CFt
Cumulative
-30 40
PaybackS
1 + $30/$50 = years
1.6 =

39. Applying the PBP criterion
FI Corporate Finance leng Ling
Applying the PBP criterion
Compute the payback periods for the following two projects.
Project C0 C1 C2 C3 C4 C5 A
-9000
2000
3000
4000
5000
6000 B
-11000
Verify that PBP for A = 3 years, PBP for B = 3.4 years (assume cash flows occur evenly throughout the year)

40. FI 3300 - Corporate Finance leng Ling
NPV + PBP Problem
Bantam Industries is considering a project which has the following cash flows:
Year Cash flow ?
$2,000
$3,000
$3,000
$1,500
The project has a payback period of 2 years. The firm's cost of capital is 12%.
What is the project's net present value?
Verify that NPV = 2,265.91

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

42. PBP does not consider cash flows after the critical number
FI Corporate Finance leng Ling
PBP does not consider cash flows after the critical number
A firm uses two years as the critical number for the payback period.
This firm is faced with two projects whose cash flows are:
Project C0 C1 C2 C3 A
-1000
500
510 10 B
99,000,000
According to the payback rule, project A will be accepted and B will be rejected.
But, if you consider all cash flows, including those after 2 years, then project B is more attractive.

43. Discounted Payback: Uses Discounted CFs10 80 60 1 2 3
CFt
Cumulative
-100
-90.91
-41.32
18.79
Discounted
payback
2 + $41.32/$ = 2.7 yrs
PVCFt
10%
9.09
49.59
60.11 =
Recover investment + capital costs in 2.7 yrs.

44. Example of discounted payback period criterion
FI Corporate Finance leng Ling
Example of discounted payback period criterion
Example: Suppose that the discount rate is 10 percent. Project A has the following cash flows and discounted cash flows. Find A’s discounted PBP.
Project A C0 C1 C2 C3
Cash flow
-9000
3000
6000
9000
Discounted cash flow
2727
4959
6762
Verify that discounted payback period = years

45. Normal vs. Nonnormal Cash Flows
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.
For example, nuclear power plant or strip mine.

46. When There are Nonnormal CFs and More than One IRR, Use MIRR1 2
-800,000
5,000,000
-5,000,000
PV 10% = -4,932,
TV 10% = 5,500,
MIRR = 5.6%

47. If the two projects have different lifespan, then…

48. S and L are Mutually Exclusive, r = 10%1 2 3 4
S: -100
L: -100 60
33.5
Note: CFs shown in $ Thousands

49. NPVL > NPVS, but is L better?
CF0
-100
CF1 60
33.5 NJ 2 4
I/YR 10
NPV
4.132
6.190

50. Method 1:mPut 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.

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

52. FI 3300 - Corporate Finance Leng Ling
Method 2:Equivalent annual series (EAS) or Equivalent Annual Annuity (EAA)
When projects are mutually exclusive but have unequal lives
We construct the equivalent annual series (EAS) of each project and
We choose the project with the highest EAS
A project’s EAS is the payment on an annuity whose life is the same as that of the project and whose present value, using the discount rate of the project, is equal to the project’s NPV.

53. 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 = EAAS = $2.38.
L: N=4, I/YR=10, PV=-6.190, FV = 0. Solve for PMT = EAAL = $1.95.
S has higher EAA, so it is a better project.

54. FI 3300 - Corporate Finance Leng Ling
Calculating EAS
Consider Projects J & K, with the following cash flows. The discount rate is 10%.
Project C0 C1 C2 C3 C4 J
-12000
6000 K
-18000
7000

55. FI 3300 - Corporate Finance Leng Ling
EAS for Project J
To compute Project J’s EAS, do the following:
Compute Project J’s NPV
Verify that NPV(J) = $2,921.11
Find the payment on the 3-year (life of project J) annuity whose PV is equal to $2,
Enter the following values:
N=3, I/Y=10, PV= , FV=0, Then CPT, PMT.
PMT = 1,174.62, which is Project J’s EAS.
So, finding EAS is nothing more than finding the payment of an annuity.

56. EAS for Project K Verify that Project K’s NPV= $4,189.06
Find the payment on the 4-year (life of project K) annuity whose PV is equal to $ 4,
Enter the following values:
N=4, I/Y=10, PV=- 4,189.06, FV=0, Then CPT, PMT.
PMT = 1,321.53, which is Project K’s EAS.
Recall that Project J’s EAS=
So, choose Project K since it has the higher EAS.

57. Another application of EAA
We can use the EAA concept to choose between two machines that do the same job but have different costs and lives.
Consider the following problem.

58. FI 3300 - Corporate Finance Leng Ling
Problem
Suppose that your firm is trying to decide between two machines, that will do the same job. Machine A costs $90,000, will last for ten years and will require operating costs of $5,000 per year. At the end of ten years it will be scrapped for $10,000. Machine B costs $60,000, will last for seven years and will require operating costs of $6,000 per year. At the end of seven years it will be scrapped for $5,000. Which is a better machine? (discount rate is 10 percent)

59. Step 1: compute the PV of the costs of each machine
FI Corporate Finance Leng Ling
Step 1: compute the PV of the costs of each machine
PV of costs (A)
= $90,000 + PV of $5,000 annuity for ten years - PV of the scrap (at t = 10) value of $10,000
= – = $116,867.41
PV of costs (B)
= $60,000 + PV of $6,000 annuity for seven years - PV of the scrap (at t = 7) value of $5,000
= $60,000 + $29, $2, =$86,644.72

60. Step 2: compute equivalent annual cost (EAC) series of each machine
FI Corporate Finance Leng Ling
Step 2: compute equivalent annual cost (EAC) series of each machine
The equivalent annual cost series is the payment of an annuity that has the same present value as the PV of the machine’s cost.
EAC of machine A, EAC(A):
N = 10, I/Y = 10, PV = , FV = 0. Then CPT, PMT. This yields EAC(A) = $19,
EAC of machine B, EAC(B):
N = 7, I/Y = 10, PV = , FV = 0. Then CPT, PMT. This yields EAC(B) = $17,
Choose machine B because it has the lower cost.

61. Homework Assignment
Problems: 1,2,3,4,5,6,7,9,11,13(a,b,c),16,17,21(a,b,c,d)