Chapter 10: Cash Flows and Other Topics in
Capital Budgeting
2002, Prentice Hall, Inc.
Capital Budgeting: the process of planning for purchases of long-term assets.
• example:
Our firm must decide whether to purchase a new plastic molding machine for $127,000. How do we decide?
• Will the machine be profitable?
• Will our firm earn a high rate of return on the investment?
• The relevant project information follows:
• The cost of the new machine is $127,000.
• Installation will cost $20,000.
• $4,000 in net working capital will be needed at the time of installation.
• The project will increase revenues by $85,000 per year, but operating costs will increase by 35% of the revenue increase.
• Simplified straight line depreciation is used.
• Class life is 5 years, and the firm is planning to keep the project for 5 years.
• Salvage value at the end of year 5 will be $50,000.
• 14% cost of capital; 34% marginal tax rate.
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
Capital Budgeting Steps
1) Evaluate Cash Flows
0 1 2 3 4 5 n6 . . .
Capital Budgeting Steps
1) Evaluate Cash Flows
0 1 2 3 4 5 n6 . . .
Initialoutlay
Capital Budgeting Steps
1) Evaluate Cash Flows
0 1 2 3 4 5 n6 . . .
Annual Cash Flows
Initialoutlay
Capital Budgeting Steps
1) Evaluate Cash Flows
0 1 2 3 4 5 n6 . . .
TerminalCash flow
Annual Cash Flows
Initialoutlay
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.
Capital Budgeting Steps
3) Accept or Reject the Project.
Capital Budgeting Steps
Step 1: Evaluate Cash Flows
• a) Initial Outlay: What is the cash flow at “time 0?”
(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
Step 1: Evaluate Cash Flows
• a) Initial Outlay: What is the cash flow at “time 0?”
(127,000)
+ (shipping and installation costs)
(Depreciable asset)
+ (Investment in working capital)
+ After-tax proceeds from sale of old asset
Net Initial Outlay
Step 1: Evaluate Cash Flows
• a) Initial Outlay: What is the cash flow at “time 0?”
(127,000)
+ ( 20,000)
(Depreciable asset)
+ (Investment in working capital)
+ After-tax proceeds from sale of old asset
Net Initial Outlay
Step 1: Evaluate Cash Flows
• a) Initial Outlay: What is the cash flow at “time 0?”
(127,000)
+ ( 20,000)
(147,000)
+ (Investment in working capital)
+ After-tax proceeds from sale of old asset
Net Initial Outlay
Step 1: Evaluate Cash Flows
• a) Initial Outlay: What is the cash flow at “time 0?”
(127,000)
+ ( 20,000)
(147,000)
+ ( 4,000)
+ After-tax proceeds from sale of old asset
Net Initial Outlay
Step 1: Evaluate Cash Flows
• a) Initial Outlay: What is the cash flow at “time 0?”
(127,000)
+ ( 20,000)
(147,000)
+ ( 4,000)
+ 0
Net Initial Outlay
Step 1: Evaluate Cash Flows
• a) Initial Outlay: What is the cash flow at “time 0?”
(127,000) Purchase price of asset
+ ( 20,000) shipping and installation
(147,000) depreciable asset
+ ( 4,000) net working capital
+ 0 proceeds from sale of old asset
($151,000) net initial outlay
Step 1: Evaluate Cash Flows
• a) Initial Outlay: What is the cash flow at “time 0?”
(127,000) Purchase price of asset
+ ( 20,000) shipping and installation
(147,000) depreciable asset
+ ( 4,000) net working capital
+ 0 proceeds from sale of old asset
($151,000) net initial outlay
Step 1: Evaluate Cash Flows
• b) Annual Cash Flows: What incremental cash flows occur over the life of the project?
Incremental revenue
- Incremental costs
- Depreciation on project
Incremental earnings before taxes
- Tax on incremental EBT
Incremental earnings after taxes
+ Depreciation reversal
Annual Cash Flow
For Each Year, Calculate:
Incremental revenue
- Incremental costs
- Depreciation on project
Incremental earnings before taxes
- Tax on incremental EBT
Incremental earnings after taxes
+ Depreciation reversal
Annual Cash Flow
For Years 1 - 5:
85,000
- Incremental costs
- Depreciation on project
Incremental earnings before taxes
- Tax on incremental EBT
Incremental earnings after taxes
+ Depreciation reversal
Annual Cash Flow
For Years 1 - 5:
85,000
(29,750)
- Depreciation on project
Incremental earnings before taxes
- Tax on incremental EBT
Incremental earnings after taxes
+ Depreciation reversal
Annual Cash Flow
For Years 1 - 5:
85,000
(29,750)
(29,400)
Incremental earnings before taxes
- Tax on incremental EBT
Incremental earnings after taxes
+ Depreciation reversal
Annual Cash Flow
For Years 1 - 5:
85,000
(29,750)
(29,400)
25,850
- Tax on incremental EBT
Incremental earnings after taxes
+ Depreciation reversal
Annual Cash Flow
For Years 1 - 5:
85,000
(29,750)
(29,400)
25,850
(8,789)
Incremental earnings after taxes
+ Depreciation reversal
Annual Cash Flow
For Years 1 - 5:
85,000
(29,750)
(29,400)
25,850
(8,789)
17,061
+ Depreciation reversal
Annual Cash Flow
For Years 1 - 5:
85,000
(29,750)
(29,400)
25,850
(8,789)
17,061
29,400
Annual Cash Flow
For Years 1 - 5:
85,000 Revenue
(29,750) Costs
(29,400) Depreciation
25,850 EBT
(8,789) Taxes
17,061 EAT
29,400 Depreciation reversal
46,461 = Annual Cash Flow
For Years 1 - 5:
Step 1: Evaluate Cash Flows
• c) Terminal Cash Flow: What is the cash flow at the end of the project’s life?
Salvage value
+/- Tax effects of capital gain/loss
+ Recapture of net working capital
Terminal Cash Flow
Step 1: Evaluate Cash Flows
• c) Terminal Cash Flow: What is the cash flow at the end of the project’s life?
50,000 Salvage value
+/- Tax effects of capital gain/loss
+ Recapture of net working capital
Terminal Cash Flow
Tax Effects of Sale of Asset:
• Salvage value = $50,000
• Book value = depreciable asset - total amount depreciated.
• Book value = $147,000 - $147,000
= $0.
• Capital gain = SV - BV
= 50,000 - 0 = $50,000
• Tax payment = 50,000 x .34 = ($17,000)
Step 1: Evaluate Cash Flows
• c) Terminal Cash Flow: What is the cash flow at the end of the project’s life?
50,000 Salvage value
(17,000) Tax on capital gain
Recapture of NWC
Terminal Cash Flow
Step 1: Evaluate Cash Flows
• c) Terminal Cash Flow: What is the cash flow at the end of the project’s life?
50,000 Salvage value
(17,000) Tax on capital gain
4,000 Recapture of NWC
Terminal Cash Flow
Step 1: Evaluate Cash Flows
• c) Terminal Cash Flow: What is the cash flow at the end of the project’s life?
50,000 Salvage value
(17,000) Tax on capital gain
4,000 Recapture of NWC
37,000 Terminal Cash Flow
Project NPV:
• CF(0) = -151,000
• CF(1 - 4) = 46,461
• CF(5) = 46,461 + 37,000 = 83,461
• Discount rate = 14%
• NPV = $27,721
• We would accept the project.
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?
Capital Rationing
• You could rank the projects by IRR:
Capital Rationing
IRR
5%
10%
15%
20%
25%
$
11
• You could rank the projects by IRR:
Capital Rationing
• You could rank the projects by IRR:IRR
5%
10%
15%
20%
25%
$
11 22
Capital Rationing
• You could rank the projects by IRR:IRR
5%
10%
15%
20%
25%
$
11 22 33
Capital Rationing
• You could rank the projects by IRR:IRR
5%
10%
15%
20%
25%
$
11 22 33 44
Capital Rationing
• You could rank the projects by IRR:IRR
5%
10%
15%
20%
25%
$
11 22 33 44 55
Capital Rationing
• You could rank the projects by IRR:IRR
5%
10%
15%
20%
25%
$
11 22 33 44 55
$X
Our budget is limitedso we accept only projects 1, 2, and 3.
Capital Rationing
• You could rank the projects by IRR:IRR
5%
10%
15%
20%
25%
$
11 22 33
$X
Our budget is limitedso we accept only projects 1, 2, and 3.
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.
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.
Size Disparity example
Project A
year cash flow
0 (135,000)
1 60,000
2 60,000
3 60,000
required return = 12%
IRR = 15.89%
NPV = $9,110
PI = 1.07
Size Disparity example
Project B
year cash flow
0 (30,000)
1 15,000
2 15,000
3 15,000
required return = 12%
IRR = 23.38%
NPV = $6,027
PI = 1.20
Project A
year cash flow
0 (135,000)
1 60,000
2 60,000
3 60,000
required return = 12%
IRR = 15.89%
NPV = $9,110
PI = 1.07
Size Disparity example
Project B
year cash flow
0 (30,000)
1 15,000
2 15,000
3 15,000
required return = 12%
IRR = 23.38%
NPV = $6,027
PI = 1.20
Project A
year cash flow
0 (135,000)
1 60,000
2 60,000
3 60,000
required return = 12%
IRR = 15.89%
NPV = $9,110
PI = 1.07
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.
Time Disparity example
Project A year cash flow
0 (48,000)
1 1,200
2 2,400
3 39,000
4 42,000
required return = 12%
IRR = 18.10%
NPV = $9,436
PI = 1.20
Time Disparity example
Project B year cash flow
0 (46,500)
1 36,500
2 24,000
3 2,400
4 2,400
required return = 12%
IRR = 25.51%
NPV = $8,455
PI = 1.18
Project A year cash flow
0 (48,000)
1 1,200
2 2,400
3 39,000
4 42,000
required return = 12%
IRR = 18.10%
NPV = $9,436
PI = 1.20
Time Disparity example
Project B year cash flow
0 (46,500)
1 36,500
2 24,000
3 2,400
4 2,400
required return = 12%
IRR = 25.51%
NPV = $8,455
PI = 1.18
Project A year cash flow
0 (48,000)
1 1,200
2 2,400
3 39,000
4 42,000
required return = 12%
IRR = 18.10%
NPV = $9,436
PI = 1.20
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?
• The after-tax cash flows are:
Year Machine 1 Machine 2
0 (45,000) (45,000)
1 20,000 12,000
2 20,000 12,000
3 20,000 12,000
4 12,000
5 12,000
6 12,000
• Assume a required return of 14%.
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!
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.
EAA with your calculator:
• Simply “spread the NPV over the life of the project”
• Machine 1: PV = 1433, N = 3, I = 14,
solve: PMT = -617.24.
• Machine 2: PV = 1664, N = 6, I = 14,
solve: PMT = -427.91.
• 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.
Step 3: Convert back to NPV
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.
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 1 = 617/.14 = $4,407
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 1 = 617/.14 = $4,407
• NPV 2 = 428/.14 = $3,057
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 1 = 617/.14 = $4,407
• NPV 2 = 428/.14 = $3,057
• This doesn’t change the answer, of course; it just converts EAA to a NPV that can be compared.
Practice Problems:Cash Flows & Other Topics
in Capital Budgeting
Project Information:• Cost of equipment = $400,000
• Shipping & installation will be $20,000
• $25,000 in net working capital required at setup
• 3-year project life, 5-year class life
• Simplified straight line depreciation
• Revenues will increase by $220,000 per year
• Defects costs will fall by $10,000 per year
• Operating costs will rise by $30,000 per year
• Salvage value after year 3 is $200,000
• Cost of capital = 12%, marginal tax rate = 34%
Problem 1a
Problem 1a• Initial Outlay:
(400,000)Cost of asset
+ ( 20,000)Shipping & installation
(420,000)Depreciable asset
+ ( 25,000)Investment in NWC
($445,000) Net Initial Outlay
220,000 Increased revenue
10,000 Decreased defects
(30,000) Increased operating costs
(84,000) Increased depreciation
116,000 EBT
(39,440) Taxes (34%)
76,560 EAT
84,000 Depreciation reversal
160,560 = Annual Cash Flow
For Years 1 - 3: Problem 1aProblem 1a
• Terminal Cash Flow:
Salvage value
+/- Tax effects of capital gain/loss
+ Recapture of net working capital
Terminal Cash Flow
Problem 1aProblem 1a
• Terminal Cash Flow:
• Salvage value = $200,000
• Book value = depreciable asset - total amount depreciated.
• Book value = $168,000.
• Capital gain = SV - BV = $32,000
• Tax payment = 32,000 x .34 = ($10,880)
Problem 1aProblem 1a
• Terminal Cash Flow:
200,000 Salvage value
(10,880) Tax on capital gain
25,000 Recapture of NWC
214,120 Terminal Cash Flow
Problem 1aProblem 1a
Problem 1a Solution:
• NPV and IRR:
• CF(0) = -445,000
• CF(1 ), (2), = 160,560
• CF(3 ) = 160,560 + 214,120 = 374,680
• Discount rate = 12%
• IRR = 22.1%
• NPV = $93,044. Accept the project!
Project Information:
• For the same project, suppose we can only get $100,000 for the old equipment after year 3, due to rapidly changing technology.
• Calculate the IRR and NPV for the project.
• Is it still acceptable?
Problem 1b
• Terminal Cash Flow:
Salvage value
+/- Tax effects of capital gain/loss
+ Recapture of net working capital
Terminal Cash Flow
Problem 1bProblem 1b
• Terminal Cash Flow:
• Salvage value = $100,000
• Book value = depreciable asset - total amount depreciated.
• Book value = $168,000.
• Capital loss = SV - BV = ($68,000)
• Tax refund = 68,000 x .34 = $23,120
Problem 1bProblem 1b
• Terminal Cash Flow:
100,000 Salvage value
23,120 Tax on capital gain
25,000 Recapture of NWC
148,120 Terminal Cash Flow
Problem 1bProblem 1b
Problem 1b Solution
• NPV and IRR:
• CF(0) = -445,000
• CF(1 ), (2), = 160,560
• CF(3 ) = 160,560 + 148,120 = 308,680
• Discount rate = 12%
• IRR = 17.3%
• NPV = $46,067. Accept the project!
Automation Project:
• Cost of equipment = $550,000
• Shipping & installation will be $25,000
• $15,000 in net working capital required at setup
• 8-year project life, 5-year class life
• Simplified straight line depreciation
• Current operating expenses are $640,000 per yr.
• New operating expenses will be $400,000 per yr.
• Already paid consultant $25,000 for analysis.
• Salvage value after year 8 is $40,000
• Cost of capital = 14%, marginal tax rate = 34%
Problem 2
Problem 2 • Initial Outlay:
(550,000) Cost of new machine
+ (25,000) Shipping & installation
(575,000) Depreciable asset
+ ( 15,000) NWC investment
(590,000) Net Initial Outlay
240,000 Cost decrease
(115,000) Depreciation increase
125,000 EBIT
(42,500) Taxes (34%)
82,500 EAT
115,000 Depreciation reversal
197,500 = Annual Cash Flow
For Years 1 - 5: Problem 2
240,000 Cost decrease
( 0) Depreciation increase
240,000 EBIT
(81,600) Taxes (34%)
158,400 EAT
0 Depreciation reversal
158,400 = Annual Cash Flow
For Years 6 - 8:Problem 2
• Terminal Cash Flow:
40,000 Salvage value
(13,600) Tax on capital gain
15,000 Recapture of NWC
41,400 Terminal Cash Flow
Problem 2
Problem 2 Solution:
• NPV and IRR:
• CF(0) = -590,000
• CF(1 - 5) = 197,500
• CF(6 - 7) = 158,400
• CF(10) = 158,400 + 41,400 = 199,800
• Discount rate = 14%
• IRR = 28.13% NPV = $293,543
• We would accept the project!
Replacement Project:
Old Asset (5 years old):
• Cost of equipment = $1,125,000
• 10-year project life, 10-year class life
• Simplified straight line depreciation
• Current salvage value is $400,000
• Cost of capital = 14%, marginal tax rate = 35%
Problem 3
Replacement Project:• New Asset:• Cost of equipment = $1,750,000• Shipping & installation will be $56,000• $68,000 investment in net working capital.• 5-year project life, 5-year class life• Simplified straight line depreciation• Will increase sales by $285,000 per year • Operating expenses will fall by $100,000 per year• Already paid $15,000 for training program• Salvage value after year 5 is $500,000• Cost of capital = 14%, marginal tax rate = 34%
Problem 3
Problem 3: Sell the Old Asset:
• Salvage value = $400,000
• Book value = depreciable asset - total amount depreciated.
• Book value = $1,125,000 - $562,500
= $562,500.
• Capital gain = SV - BV
= 400,000 - 562,500 = ($162,500)
• Tax refund = 162,500 x .35 = $56,875
Problem 3• Initial Outlay:
(1,750,000) Cost of new machine
+ ( 56,000) Shipping & installation
(1,806,000) Depreciable asset
+ ( 68,000) NWC investment
+ 456,875 After-tax proceeds (sold old machine)
(1,417,125) Net Initial Outlay
385,000 Increased sales & cost savings
(248,700) Extra depreciation
136,300 EBT
(47,705) Taxes (35%)
88,595 EAT
248,700 Depreciation reversal
337,295 = Differential Cash Flow
For Years 1 - 5:Problem 3
• Terminal Cash Flow:
500,000 Salvage value
(175,000) Tax on capital gain
68,000 Recapture of NWC
393,000 Terminal Cash Flow
Problem 3
Problem 3 Solution:
• NPV and IRR: • CF(0) = -1,417,125• CF(1 - 4) = 337,295• CF(5) = 337,295 + 393,000 = 730,295• Discount rate = 14%• NPV = (55,052.07)• IRR = 12.55%• We would not accept the project!
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