1. Cash Flows and Other Issues in Capital Budgeting
Chapter 10
Cash Flows and Other Issues in Capital Budgeting

2. Overview Capital Rationing Cash Flow Estimation
Comparing Projects with Unequal Lives

3. Capital Rationing
Suppose that you have evaluated 5 capital investment projects for your company.
Suppose that the VP of Finance has given you a limited capital budget.
How do you decide which projects to select?

4. Capital Rationing
You could rank the projects by IRR:

5. Capital Rationing IRR You could rank the projects by IRR: 5% 10% 15%
20%
25% $ 5 1 2 3 4

6. Capital Rationing IRR You could rank the projects by IRR: 5% 10% 15%
20%
25% $
Our budget is limited
so we accept only
projects 1, 2, and 3. 1 2 3 4 5 $X

7. Capital Rationing IRR You could rank the projects by IRR: 5% 10% 15%
20%
25% $
Our budget is limited
so we accept only
projects 1, 2, and 3. 1 2 3 $X

8. Capital Rationing
Ranking projects by IRR is not always the best way to deal with a limited capital budget.
It’s better to pick the largest NPVs.
Let’s try ranking projects by NPV.

9. Problems with Project Ranking
1) Mutually exclusive projects of unequal size (the size disparity problem)
The NPV decision may not agree with IRR or PI.
Solution: select the project with the largest NPV.

10. Size Disparity example
Project A
year cash flow
0 (135,000)
,000
,000
,000
required return = 12%
IRR = 15.89%
NPV = $9,110
PI = 1.07
Project B
year cash flow
0 (30,000)
,000
,000
,000
required return = 12%
IRR = 23.38%
NPV = $6,027
PI = 1.20

11. Size Disparity example
Project A
year cash flow
0 (135,000)
,000
,000
,000
required return = 12%
IRR = 15.89%
NPV = $9,110
PI = 1.07
Project B
year cash flow
0 (30,000)
,000
,000
,000
required return = 12%
IRR = 23.38%
NPV = $6,027
PI = 1.20

12. Problems with Project Ranking
2) The time disparity problem with mutually exclusive projects.
NPV and PI assume cash flows are reinvested at the required rate of return for the project.
IRR assumes cash flows are reinvested at the IRR.
The NPV or PI decision may not agree with the IRR.
Solution: select the largest NPV.

13. Time Disparity example
Project A
year cash flow
0 (48,000)
,200
,400
,000
,000
required return = 12%
IRR = 18.10%
NPV = $9,436
PI = 1.20
Project B
year cash flow
0 (46,500)
,500
,000
,400
,400
required return = 12%
IRR = 25.51%
NPV = $8,455
PI = 1.18

14. Time Disparity example
Project A
year cash flow
0 (48,000)
,200
,400
,000
,000
required return = 12%
IRR = 18.10%
NPV = $9,436
PI = 1.20
Project B
year cash flow
0 (46,500)
,500
,000
,400
,400
required return = 12%
IRR = 25.51%
NPV = $8,455
PI = 1.18

15. Capital Budgeting Steps
1) Evaluate Cash Flows
Look at all incremental cash flows occurring as a result of the project.
Initial outlay
Differential Cash Flows over the life of the project (also referred to as annual cash flows).
Terminal Cash Flows

16. Capital Budgeting Steps
1) Evaluate Cash Flows 1 2 3 4 5 n 6
. . .

17. Capital Budgeting Steps
1) Evaluate Cash Flows
Initial
outlay 1 2 3 4 5 n 6
. . .

18. Capital Budgeting Steps
1) Evaluate Cash Flows
Initial
outlay 1 2 3 4 5 n 6
. . .
Annual Cash Flows

19. Capital Budgeting Steps
1) Evaluate Cash Flows
Terminal
Cash flow
Initial
outlay 1 2 3 4 5 n 6
. . .
Annual Cash Flows

20. Cash Flow Estimation
Need to estimate incremental after tax cash flows that the project is expected to generate.
General form: Cash Flow = Incremental Net Income + Depreciation
Other “special” cash flows
Initial costs
Extra ending or terminal cash flows at the end of the project’s expected useful life.

21. Capital Budgeting Steps
2) Evaluate the risk of the project.
We’ll get to this in the next chapter.
For now, we’ll assume that the risk of the project is the same as the risk of the overall firm.
If we do this, we can use the firm’s cost of capital as the discount rate for capital investment projects.

22. Capital Budgeting Steps
Accept or Reject the Project.
Calculate Project’s NPV and IRR to make this decision.

23. Imperial Defense Co. Death Star Replacement Project
Six years ago in a galaxy far, far away, the Imperial Defense Co. (IDC) built the original Death Star at a cost of $100 billion. This original project is being depreciated on a simplified straight-line basis over a 10-year period to zero.
IDC is considering building a new and improved Death Star at a cost of $160 billion and would require an initial increase in net working capital of $15 billion over the old Death Star. The old death star can be sold for scrap today for $20 billion.

24. IDC Death Star Replacement Project Info(cont.)
The new Death Star is estimated to have a 4-year class and expected useful life and will be depreciated using the simplified straight-line method. The new Death Star is expected to increase “protection” revenues by $50 billion in year 1 and $90 billion in years 2 through 4 Rebel defense expenses are expected to increase by $10 billion in year 1, $20 billion in year 2, $30 billion in year 3 and $40 billion in year 4.
The new Death Star has an estimated salvage value of $30 billion at the end of its 4-yr useful life and the original Death Star has a $5 billion salvage value at the end of its useful life.

25. Death Star Replacement Project Tasks
Estimate the cash flows of the replacement project assuming a marginal tax rate of 40%.
Should the old Death Star be replaced if Imperial Defense Co.’s cost of capital is 10%.

26. Replacement Project CF Analysis
Assume old project is sold today and replaced be the new one.
Receive inflow from the sale of old project today, but give up any future expected inflows (opportunity costs).
General form: Increase in Net Income + (Depreciation on New - Depreciation on Old) – Increase in Net Working Capital

27. Step 1: Evaluate Cash Flows
a) Initial Outlay: What is the cash flow at “time 0?”
General Steps
(Purchase price of the asset)
+ (shipping and installation costs)
(Depreciable asset)
+ (Investment in working capital)
+ After-tax proceeds from sale of old asset
Net Initial Outlay

28. After-tax Proceeds from sale of Old Death Star($billion)
After-tax Proceeds from sale of Old Death Star($billion). Tax Rate = 40%
Salvage value = $20
Original Cost and Depreciable asset = $100
Annual Old Depreciation = $100/10 = $10
Book value = depreciable asset - total amount depreciated.
Book value = $100 – 6($10) = $40.
Capital gain = SV - BV
= $20 - $40 = ($20)
Tax refund = $20 x .4 = $8
Total After Tax Proceeds = Salvage Value + Tax Refund = $20 + $8 = $28

29. Initial Outlay of Death Star Replacement ($billion)
($160) Cost of New Depreciable Asset
($15) Increase in Net Working Capital After-tax Proceeds from sale of
+ $28 replaced asset
($147) Initial Outlay

30. Step 1: Evaluate Cash Flows
b) Annual Cash Flows: What incremental cash flows occur over the life of the project?

31. For Each Year, Calculate:
Incremental revenue
- Incremental costs
- Depreciation increase on project
Incremental earnings before taxes
- Tax on incremental EBT
Incremental earnings after taxes
+ Depreciation increase reversal
- annual increase in net working capital(none here)
Annual Cash Flow

32. Death Star Replacement Project Depreciation($billion)
Annual Depreciation on Old = $100/10 = $10
Annual Depreciation on New = $160/4 = $40
Annual Increase in Depreciation due to Replacement = $40 - $10 = $30 for years 1 through 4.

33. Death Star Replacement Project Annual Free Cash Flows($billion)
Year
Inc in Rev
-Inc in Exp
-Inc in Dep
EBT
-Tax(40%)
EAT
+Inc in Dep
Cash Flow

34. Step 1: Evaluate Cash Flows
c) Terminal Cash Flow: What is the cash flow at the end of the project’s life?
New Salvage value
-/+ Tax effects of new capital gain/loss
- Old Salvage value
- (-/+) Tax effects of old capital gain/loss
+ Recapture of all increase in net working capital
Terminal Cash Flow

35. Tax Effects of Sale of Asset ($billion)
New Salvage value = $30
Book value = depreciable asset - total amount depreciated.
Book value = $160 - $160 = $0.
Capital gain = SV - BV = $ = $30
New Tax payment = $30 x .4 = $12
Old Salvage Value = Opportunity Cost = $5
Old Book Value = $0
Old Capital Gain = $5.
Old Tax Payment = $5 x .4 = $2
Net Old Salvage Value = $5 – $2 = $3

36. Death Star Replacement Terminal Cash Flows ($billion)
at t=4
New Salvage Value $30
-Taxes on New SV = .4(30-0) $12
-Old Net Salvage Value $3
+Recovery of Net Working Capital $15
Total Terminal CF (t = 4) $30

37. Death Star Replacement Project Decision Time ($billion)
Year Cash Flow
(147) CF0
C01
C02
C03
= C04
NPV at 10% = $15.59 Billion, PI = 1.11
IRR = 14.3%, MIRR = 12.8%

38. Other Incremental Cash Flow Issues
Sunk costs = exclude. Ask yourself if rejecting the project affects this cost.
Financing costs = EXCLUDE. Already included in WACC.
Opportunity Costs = INCLUDE. Generally revenues forgone from using land or building for another purpose other than the project.

39. Other Incremental Cash Flow Issues (continued)
Externalities = effects of a project on cash flows in other part of the firm. Can be positive or negative and should be INCLUDED as part of the project’s incremental cash flows.
Cannibalization = INCLUDE. A negative externality, occurs when the introduction of a new product diminishes the sales of existing products.

40. Mutually Exclusive Investments with Unequal Lives
Suppose our firm is planning to expand and we have to select 1 of 2 machines.
They differ in terms of economic life and capacity.
How do we decide which machine to select?

41. The after-tax cash flows are:
Year Machine Machine 2
(45,000) (45,000)
, ,000
, ,000
, ,000
,000
,000
,000
Assume a required return of 14%.

42. Step 1: Calculate NPV NPV1 = $1,433 NPV2 = $1,664
So, does this mean #2 is better?
No! The two NPVs can’t be compared!

43. Step 2: Equivalent Annual Annuity (EAA) method
If we assume that each project will be replaced an infinite number of times in the future, we can convert each NPV to an annuity.
The projects’ EAAs can be compared to determine which is the best project!
EAA: Simply annuitize the NPV over the project’s life.

44. EAA with your calculator:
Simply “spread the NPV over the life of the project”
Machine 1: PV = 1433, N = 3, I = 14,
CPT: PMT =
Machine 2: PV = 1664, N = 6, I = 14,
CPT: PMT =

45. Decision Time EAA1 = $617 EAA2 = $428 This tells us that:
NPV1 = annuity of $617 per year.
NPV2 = annuity of $428 per year.
So, we’ve reduced a problem with different time horizons to a couple of annuities.
Decision Rule: Select the highest EAA. We would choose machine #1.

46. Step 3: Convert back to NPV
Assuming infinite replacement, the EAAs are actually perpetuities. Get the PV by dividing the EAA by the required rate of return.
NPV = 617/.14 = $4,407
NPV = 428/.14 = $3,057
This doesn’t change the answer, of course; it just converts EAA to a NPV that can be compared.

47. Alternative Decision Technique: Replacement Chain Approach
Find the shortest common life between the two mutually exclusive projects with unequal lives. In our case, 6 years.
Year Machine Machine 2
(45,000) (45,000)
, ,000
, ,000
, ,000
,000
,000
,000
Assume a required return of 14%.

48. Replacement Chain Step 2
Repeat each project as often as necessary over the shortest common life. In our case, we would buy Machine 1 again at end of year 3.
Year Machine Machine 2
(45,000) (45,000)
, ,000
, ,000
,000 – 45,000 = (25,000) ,000
, ,000
, ,000
, ,000
Assume a required return of 14%.

49. Replacement Chain Step 3
Find the (extended) NPV of each project’s cash flows over the shortest common life.
For Machine 2, we already know its NPV over 6 years is $1664.
For Machine 1: ext NPV = -45, ,000/(1.14) + 20,000/(1.14)2 – 25,000/(1.14)3 + 20,000/(1.14)4 + 20,000/(1.14)5 + 20,000/(1.14)6 = $2340
Machine 1 shortcut: one-time NPV = 1443, receive this NPV each time we purchase Machine 1. Ext NPV = /(1.14)3 = $2340
Choose Machine 1 like we did with EAA: higher NPV over 6 years.
One replacement chain advantage: can assume project CFs will change when re-purchasing the project in the future.

50. Karsten Ping Golf: New Project CF Analysis
As an analyst at MAD Inc. you have been asked to work with a client seeking capital budgeting advice, Ping Golf. Ping is considering making a new line of over-sized irons aimed at mid to high handicap golfers (known as mere mortal golfers or most of the people who play golf). These new irons would be called the Ping Kings, and would have a 3-year product life. Ping has already researched and designed these new golf clubs. Ping has given MAD Inc. the following information in order for you to estimate the project’s cash flows.

51. Ping cash flow information
Ping has already spent $500,000 to research and design the Ping Kings.
Ping will need to buy $4,000,000 in new manufacturing equipment plus $500,000 in shipping and installation costs, which would be depreciated over 5 years using the simplified straight-line depreciation.
At the end of the project’s 3-year life, Ping estimates they can sell this equipment for $800,000.

52. Ping cash flow information (cont)
Ping will also need $700,000 in additional working capital at the beginning of the project.
Ping estimates they can sell 10,000 sets of Ping Kings in year 1, 15,000 sets in year 2, and 9,000 in year 3. They also estimate they can sell the Ping Kings for $640 a set in years 1 & 2, but they will only be able to sell them for $540 a set in year 3. Variable costs will be $350 a set for all three years and Ping also expects to have $300,000 in fixed manufacturing costs annually for this project.

53. Ping cash flow information (cont)
Ping’s marginal tax rate is 40%.
Ping’s required rate of return is 18%.
What are the free cash flows for this Ping King project?
Should Ping go ahead with the Ping Kings?

54. Step 1: Evaluate Cash Flows
a) Initial Outlay: What is the cash flow at “time 0?”
General Steps
(Purchase price of the asset)
+ (shipping and installation costs)
(Depreciable asset)
+ (Investment in working capital)
Net Initial Outlay

55. Initial Outlay for Ping Kings
Cost of Equipment $4,000,000
Shipping&Installation ,000
Depreciable Asset $4,500,000
Increase in WC ,000
Initial Outlay $5,200,000

56. Step 1: Evaluate Cash Flows
b) Annual Cash Flows: What incremental cash flows occur over the life of the project?

57. For Each Year, Calculate:
Incremental revenue
- Incremental costs
- Depreciation increase on project
Incremental earnings before taxes
- Tax on incremental EBT
Incremental earnings after taxes
+ Depreciation increase reversal
- annual increase in net working capital(none here)
Annual Cash Flow

58. Ping King Annual Depreciation
Depreciable Asset = $4,500,000
5-year simplified straight-line depreciation.
Annual Depreciation = $4,500,000/5 = $900,000
Book Value at the end of year 3:
$4,500,000 – 3($900,000) = $1,800,000

59. Annual CFs for Ping Kings
Year
Unit Sales 10,000 15,000 9,000
$/Unit $640 $640 $540
VC/Unit $350 $350 $350
Revenue($000) 6,400 9,600 4,860
-Variable Costs 3,500 5,250 3,150
-Fixed Costs
-Depreciation
EBIT 1,700 3,
Tax(40%) ,
Earnings After Tax 1,020 1,
+Depreciation
Cash Flow 1,920 2,790 1,206

60. Step 1: Evaluate Cash Flows
c) Termination Cash Flow: What is the cash flow at the end of the project’s life?
New Salvage value
-/+ Tax effects of new capital gain/loss
+ Recapture of all increase in net working capital
Terminal Cash Flow

61. Ping King Termination CF
Salvage Value(SV) $800,000
Taxes on Salvage Value
-T(SV-BV) = -.4(800k-1800k) 400,000
Recovery of Working Capital 700,000
Termination CF at end of 3 $1,900,000

62. Coronate Ping Kings? Year Cash Flow 0 ($5,200,000) 1 $1,740,000
0 ($5,200,000)
1 $1,740,000
2 $2,610,000
3 1,206k+1,900k = $3,106,000
NPV at 18% = $321,261
IRR = 21.5%

63. What about this?
Ping’s current line of irons is the Ping i3, which have an estimated product life of 1 year remaining. Should Ping go ahead with the Ping Kings project if they thought next year’s Ping i3 sales and variable costs would decrease by $1,000,000 and $500,000 respectively on a BEFORE-TAX basis.

64. This would affect the year 1 CF: cannibalization!
Year Orig 1 Change New 1
Revenue($000) 6,400 (1,000) 5,400
-Variable Costs 3,500 (500) 3,000
-Fixed Costs
-Depreciation
EBIT 1,700 (500) 1,200
Tax(40%) (200)
Earnings After Tax 1,020 (300)
+Depreciation
Cash Flow 1,920 (300) 1,620

65. New CFs with cannibalization
Year Cash Flow
0 ($5,200,000)
1 $1,620,000
2 $2,790,000
3 1,206k+1,900k = $3,106,000
NPV at 18% = $67,023
IRR = 18.7%