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 n 6,,,
Capital Budgeting Steps
1) Evaluate Cash Flows
0 1 2 3 4 5 n 6,,,
Initial
outlay
Capital Budgeting Steps
1) Evaluate Cash Flows
0 1 2 3 4 5 n 6,,,
Annual Cash Flows
Initial
outlay
Capital Budgeting Steps
1) Evaluate Cash Flows
0 1 2 3 4 5 n 6,,,
Terminal
Cash flow
Annual Cash Flows
Initial
outlay
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%
$
1
? You could rank the projects by IRR,
Capital Rationing
? You could rank the projects by IRR,
IRR
5%
10%
15%
20%
25%
$
1 2
Capital Rationing
? You could rank the projects by IRR,
IRR
5%
10%
15%
20%
25%
$
1 2 3
Capital Rationing
? You could rank the projects by IRR,
IRR
5%
10%
15%
20%
25%
$
1 2 3 4
Capital Rationing
? You could rank the projects by IRR,
IRR
5%
10%
15%
20%
25%
$
1 2 3 4 5
Capital Rationing
? You could rank the projects by IRR,
IRR
5%
10%
15%
20%
25%
$
1 2 3 4 5
$X
Our budget is limited
so we accept only
projects 1,2,and 3,
Capital Rationing
? You could rank the projects by IRR,
IRR
5%
10%
15%
20%
25%
$
1 2 3
$X
Our budget is limited
so 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 1a
? Terminal Cash Flow,
Salvage value
+/- Tax effects of capital gain/loss
+ Recapture of net working capital
Terminal Cash Flow
Problem 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 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 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 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 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 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!
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 n 6,,,
Capital Budgeting Steps
1) Evaluate Cash Flows
0 1 2 3 4 5 n 6,,,
Initial
outlay
Capital Budgeting Steps
1) Evaluate Cash Flows
0 1 2 3 4 5 n 6,,,
Annual Cash Flows
Initial
outlay
Capital Budgeting Steps
1) Evaluate Cash Flows
0 1 2 3 4 5 n 6,,,
Terminal
Cash flow
Annual Cash Flows
Initial
outlay
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%
$
1
? You could rank the projects by IRR,
Capital Rationing
? You could rank the projects by IRR,
IRR
5%
10%
15%
20%
25%
$
1 2
Capital Rationing
? You could rank the projects by IRR,
IRR
5%
10%
15%
20%
25%
$
1 2 3
Capital Rationing
? You could rank the projects by IRR,
IRR
5%
10%
15%
20%
25%
$
1 2 3 4
Capital Rationing
? You could rank the projects by IRR,
IRR
5%
10%
15%
20%
25%
$
1 2 3 4 5
Capital Rationing
? You could rank the projects by IRR,
IRR
5%
10%
15%
20%
25%
$
1 2 3 4 5
$X
Our budget is limited
so we accept only
projects 1,2,and 3,
Capital Rationing
? You could rank the projects by IRR,
IRR
5%
10%
15%
20%
25%
$
1 2 3
$X
Our budget is limited
so 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 1a
? Terminal Cash Flow,
Salvage value
+/- Tax effects of capital gain/loss
+ Recapture of net working capital
Terminal Cash Flow
Problem 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 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 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 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 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 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!
