Estimating After-Tax Incremental Cash Flows
Cash Flows and Other Topics in
Capital BudgetingIncremental Cash Flows Incremental Cash Flows
Cash (not accounting income) flowss
Operating (not fnancing) flowss
After-tax flowss
Incremental flowss
Cash (not accounting income) flowss
Operating (not fnancing) flowss
After-tax flowss
Incremental flowss
Basic characteristics of
relevant project flowss
Incremental Cash Flows
Incremental Cash FlowsPrinciples that must be adhered to in the estimation
Ignore Ignore sunk costs sunk costs
Include Include opportunity costs opportunity costs
Include project-driven changes in Include project-driven changes in wsorking capital wsorking capital net of net of spontaneous changes in current spontaneous changes in current liabilities liabilities
Include efects of inflation Include efects of inflation and Depreciation
Depreciation represents the systematic allocation of the cost of a capital asset over a period of time for financial reporting purposes, tax purposes, or both.
use an accelerated method for tax
reporting purposes (MACRS).
Generally, proftable frms prefer to
MACRS Method
depreciation charges, the lowser the
taxes paid by the frm. Depreciation is a noncash expense.Everything else equal, the greater the
Assets are depreciated (MACRS) on
one of eight diferent property classes. Generally, the half-year convention is
used for MACRS.
MACRS Sample Schedule
5
4.46
8
8.93
7
8.92
5.76
6
8.93
11.52
Recovery Property Class Year 3-Year 5-Year 7-Year 1 33.33% 20.00% 14.29%
2
11.52
7.41
4
17.49
19.20
14.81
3
24.49
32.00
44.45
12.49
Depreciable Basis
In tax accounting, the fully installed cost
of an asset. This is the amount that, by
laws, may be wsritten of over time for tax
purposes.
Depreciable Basis =
Cost of Asset + Capitalized Expenditures
Capitalized Expenditures
Capitalized Expenditures are
expenditures that may provide
benefts into the future and
therefore are treated as capital
outlays and not as expenses of the
period in wshich they wsere incurred.
Examples: Shipping and installation a Depreciable Asset
Generally, the sale of a “capital asset” (as
defined by the IRS) generates a capital
gain (asset sells for more than book value) or capital loss (asset sells for less than book value). income has received more favorable U.S. tax treatment than operating income.
Often historically, capital gains for purchases of long-term assets.
For 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:
$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
Look at all incremental cash flows occurring as a result of the project
Diferential Cash Flows over
Initial outlay
the life of the project (also referred to as annual cash flows).
1
2
3
4
5 n 6 . . .
1
2
3
4
5 6 . . . n
1
2
3
4
5 6 . . . n Annual Cash Flows
1
2
3
4
5 n 6 . . . Terminal Cash flow
Annual Cash Flows
Initial outlayCapital Budgeting Steps
chapter.
For now, we’ll assume that the
risk of the project is the same as the risk of the overall firm.
firm’s cost of capital as the discount rate for capital
If we do this, we can use the
Capital Budgeting Steps
a) Initial Outlay: What is the cash
flow at “ttime 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
a) Initial Outlay: What is the cash
flow at “ttime 0?� (127,000)+ (shipping and installation costs)
(Depreciable asset)+ (Investment in working capital)
+ After-tax proceeds from sale of
old asset Net Initial Outlay
a) Initial Outlay: What is the cash
flow at “ttime 0?� (127,000) + ( 20,000) (Depreciable asset)+ (Investment in working capital)
+ After-tax proceeds from sale of
old asset Net Initial Outlay
a) Initial Outlay: What is the cash
flow at “ttime 0?� (127,000) + ( 20,000) (147,000)+ (Investment in working capital)
+ After-tax proceeds from sale of
old asset Net Initial Outlay
a) Initial Outlay: What is the cash
flow at “ttime 0?� (127,000) + (20,000) (147,000) + (4,000)+ After-tax proceeds from sale of
old asset Net Initial Outlay
a) Initial Outlay: What is the cash
flow at “ttime 0?� (127,000) + (20,000) (147,000) + (4,000) + 0 Net Initial Outlay flow at “ttime 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
Flows
+ 0 Proceeds from sale of
old asset
Flows
Incremental revenue - Incremental costs - Depreciation on project Incremental earnings before taxes - Tax on incremental EBT Incremental earnings after taxes
Incremental revenue - Incremental costs - Depreciation on project Incremental earnings before taxes - Tax on incremental EBT Incremental earnings after taxes
85,000
- - Incremental costs - Depreciation on project Incremental earnings before taxes - Tax on incremental EBT Incremental earnings after taxes
85,000 (29,750)
- - Depreciation on project Incremental earnings before taxes - Tax on incremental EBT Incremental earnings after taxes
85,000 (29,750) (29,400)
Incremental earnings before taxes - Tax on incremental EBT Incremental earnings after taxes + Depreciation reversal
85,000 (29,750) (29,400) 25,850
- - Tax on incremental EBT Incremental earnings after taxes + Depreciation reversal Annual Cash Flow
85,000 (29,750) (29,400) 25,850 (8,789)
Incremental earnings after taxes + Depreciation reversal Annual Cash Flow
85,000 (29,750)
(29,400)
25,850 (8,789) 17,061- + Depreciation reversal Annual Cash Flow
85,000 (29,750)
(29,400)
25,850 (8,789) 17,061 29,400Annual Cash Flow
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
Flows
c) Terminal Cash Flow: What is the
cash flow at the end of the project’s life? Salvage value +/- Tax efects of capital gain/loss + Recapture of net working capital Terminal Cash FlowFlows
c) Terminal Cash Flow: What is the
cash flow at the end of the project’s life? 50,000 Salvage value +/- Tax efects of capital gain/loss + Recapture of net working capital Terminal Cash FlowTax 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.
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
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
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 FlowProject 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
evaluated five capital
investment projects for
your company. Suppose that the VP ofSuppose that you have
Finance has given you a
limited capital budget. How do you decide which projects to select?
by IRR:
You could rank the projects
by IRR:
You could rank the projects
IRR
25% 20% 15% 10% 5%
1
by IRR:
You could rank the projects
IRR
25% 20% 15% 10% 5%
2
1
by IRR:
You could rank the projects
IRR
25% 20% 15% 10% 5%
2
3
1
by IRR:
You could rank the projects
IRR
25% 20% 15% 10% 4 5%
2
3
1
by IRR:
You could rank the projects
IRR
25% 20% 15% 10%
5
4 5%
2
3
1
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.
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.
not always the best way to deal with a limited capital budget. It’s better to pick the
Ranking projects by IRR is
largest NPVs. Let’s try ranking projects by
NPV. Capital Rationing Capital Rationing occurs wshen a constraint (or budget ceiling) is placed on the total size of capital expenditures during a particular period.
Example: Julie Miller must determine
wshat investment opportunities toundertake for Basket Wonders (BW) .
She is limited to a maximum expenditure of $32,500 only for this
Available Projects for BW
Project ICO IRR NPV PI
A $ 500 18% $ 50
1.10 B 5,000 25 6,500 2.30 C 5,000 37 5,500 2.10 D 7,500 20 5,000 1.67 E 12,500 26 500 1.04
F 15,000 28 21,000 2.40 G 17,500 19 7,500 1.43
Choosing by IRRs for BW Project ICO IRR NPV PI
C $ 5,000 37% $ 5,500
2.10 F 15,000 28 21,000
2.40 E 12,500 26 500
1.04 B 5,000 25 6,500 2.30 Projects C, F, and E have the three largest IRRs . Choosing by NPVs for BW
Project ICO IRR NPV
PI F $15,000 28% $21,0001.43 B 5,000 25 6,500 2.30 Projects F and G have the twso
largest NPVs .
The resulting increase in shareholder Choosing by PIs for BW Project ICO IRR NPV PI F $15,000 28% $21,000
2.40 B 5,000 25 6,500
2.30 C 5,000 37 5,500
2.10 D 7,500 20 5,000
1.67 G 17,500 19 7,500 1.43
Projects F, B, C, and D have the four largest
PIs .
The resulting increase in shareholder wsealth is
Summary of Comparison Method Projects Accepted Value Added PI F, B, C, and D $38,000 NPV F and G $28,500
IRR
PI generates the greatest increase in
shareholder wealth wshen a limited capital
Ranking
1) Mutually exclusive projects of
unequal size (the size disparity problem) The NPV decision may not agree with IRR or PI.
the largest NPV .
Solution: select the project with
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
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
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
Cash Flow Disparity Cash Flow Disparity
Let us compare a decreasing cash-flows (D)
project and an increasing cash-flows (I)
project.
END OF YEAR Project D Project I 0 -$1,200 -$1,200 1 1,000 100 2 500 600 3 100 1,080
Cash Flow Disparity Cash Flow Disparity
Calculate the IRR, NPV@10%,
and PI@10%.
Which project is preferred?
Project IRR NPV PI
? D 23% D
23% $198 1.17 $198 1.17
I 17%
I 17%Examine NPV Profiles
Examine NPV Profiles
Plot NPV for each
00 )
6 project at various
$ ( discount rates.
Project I ue al
NPV@10% nt
IRR se
00
2 re P t
Project D e N
00 0 5 10 15 20 25
- 2
Discount Rate (%)
Fisher’s Rate of Intersection
Fisher’s Rate of Intersection
)
60 $ (
At k<10%, I is best! Fisher’s Rate of ue
Intersection al
00
4 V nt se
2 re P t e N
00 0 5 10 15 20 25
- 2
Discount Rate ($) Mutually Exclusive Investments with Unequal
Lives
expand and we have to select one
of two machines.Suppose our firm is planning to
They difer in terms of economic life and capacity . How do we decide which machine to
select?
are:
Year Machine 1 Machine 2
0 (45,000) (45,000) 1 20,000 12,000 2 20,000 12,000 3 20,000 Step 1: Calculate NPV
1
NPV = $1,433
2 NPV = $1,664 So, does this mean #2 is
better?
No! The two NPVs can’t
be compared!
Step 2: Equivalent Annual Annuity (EAA) method
will be replaced an infinite number of times in the future, we can convert each NPV to an annuity. The projects’ EAAs can be
If we assume that each project
compared to determine which is
the best project! EAA: Simply annuitize the NPV over the project’s life.
EAA with your calculator:
Simply “tspread 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,
EAA = $617 EAA
2 = $428 This tells us that:
2 NPV = annuity of $428 per year. So, we’ve reduced a problem
with diferent time horizons
to a couple of annuities.
Step 3: Convert back to
¥NPV
Step 3: Convert back to
¥NPV
the EAAs are actually perpetuities. Get the PV by dividing the EAA by the required rate of return.
Assuming infinite replacement,
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 1
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 1 ¥
NPV = 428/.14 = $3,057 2
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 1 ¥
NPV = 428/.14 = $3,057 2 This doesn’t change the answer,
of course; it just converts EAA Cash Flows & Other Topics
in Capital Budgeting
Shipping & installation will be $20,000 .
Cost of equipment = $400,000 .
$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
Problem 1a Initial Outlay:
(400,000) Cost of asset + ( 20,000)Shipping & installation (420,000) Depreciable asset + ( 25,000)Investment in NWC
- 3:
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
Terminal Cash Flow:
Salvage value +/- Tax efects of capital gain/loss + Recapture of net working capital
Terminal Cash Flow
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 =
Terminal Cash Flow:
200,000 Salvage value (10,880) Tax on capital gain 25,000 Recapture of NWC
214,120 Terminal Cash
FlowProblem 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%
Project Information:
suppose we can only get $100,000 for the old equipment after year 3, due to rapidly changing technology.
For the same project,
for the project. Is it still acceptable?
Calculate the IRR and NPV
Terminal Cash Flow:
Salvage value +/- Tax efects of capital gain/loss + Recapture of net working capital
Terminal Cash Flow
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 =
Terminal Cash Flow:
100,000 Salvage value 23,120 Tax on capital gain 25,000 Recapture of NWC
148,120 Terminal Cash
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% .
Shipping & installation will be $25,000 .
Cost of equipment = $550,000 .
$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.
analysis.
Already paid consultant $25,000 for
Problem
2 Initial Outlay:
(550,000) Cost of new machine + (25,000) Shipping & installation (575,000) Depreciable asset + (15,000) NWC For Years 1 - 5:
240,000 Cost decrease (115,000) Depreciation increase 125,000 EBIT (42,500) Taxes (34%) 82,500 EAT 115,000 Depreciation reversal
For Years 6 - 8:
240,000 Cost decrease ( 0) Depreciation increase 240,000 EBIT (81,600) Taxes (34%) 158,400 EAT
Terminal Cash Flow:
40,000 Salvage value (13,600) Tax on capital gain 15,000 Recapture of NWC
41,400 Terminal
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
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.
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
Asset
.
Salvage value = $400,000 Book value = depreciable
asset - total amount depreciated.
Book value = $1,125,000 - $562,500 = $562,500.
= 400,000 - 562,500 =
Capital gain = SV - BV
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 For Years 1 - 5:
385,000 Increased sales & cost savings (248,700) Extra depreciation 136,300 EBT (47,705) Taxes (35%) 88,595 EAT 248,700 Depreciation reversal
Terminal Cash Flow:
500,000 Salvage value (175,000) Tax on capital gain 68,000 Recapture of NWC
393,000 Terminal
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!