Chapter 10
Cash Flows and Other Issues in
Capital Budgeting
Overview



Capital Rationing
Cash Flow Estimation
Comparing Projects with Unequal Lives
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

You could rank the projects by IRR:
IRR
25%
20%
15%
10%
5%
1
2
3
4
5
$
Capital Rationing

You could rank the projects by IRR:
IRR
Our budget is limited
so we accept only
projects 1, 2, and 3.
25%
20%
15%
10%
5%
1
2
3
4
$X
5
$
Capital Rationing

You could rank the projects by IRR:
IRR
Our budget is limited
so we accept only
projects 1, 2, and 3.
25%
20%
15%
10%
5%
1
2
3
$X
$
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
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
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
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
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%
Project B
year
cash flow
0
(46,500)
1
36,500
2
24,000
3
2,400
4
2,400
required return = 12%
IRR = 18.10%
NPV = $9,436
PI = 1.20
IRR = 25.51%
NPV = $8,455
PI = 1.18
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%
Project B
year
cash flow
0
(46,500)
1
36,500
2
24,000
3
2,400
4
2,400
required return = 12%
IRR = 18.10%
NPV = $9,436
PI = 1.20
IRR = 25.51%
NPV = $8,455
PI = 1.18
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
6
...
n
Capital Budgeting
Steps
1) Evaluate Cash Flows
Initial
outlay
0
1
2
3
4
5
6
...
n
Capital Budgeting
Steps
1) Evaluate Cash Flows
Initial
outlay
0
1
2
3
4
5
6
Annual Cash Flows
...
n
Capital Budgeting
Steps
1) Evaluate Cash Flows
Terminal
Cash flow
Initial
outlay
0
1
2
3
4
5
6
Annual Cash Flows
...
n
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.
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.
Capital Budgeting Steps
3)

Accept or Reject the Project.
Calculate Project’s NPV and IRR
to make this decision.
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.
IDC Death Star Replacement
Project Info(cont.)


The new Death Star is estimated to have a 4year 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
$5 billion salvage value at the end of its
Death Star Replacement
Project Tasks


Estimate the cash flows of the
replacement project assuming a
marginal tax rate of 40%.
Should the old Death Star be replaced if
Imperial Defense Co.’s cost of capital is
10%.
Replacement Project CF
Analysis



Assume old project is sold today and
replaced be the new one.
Receive inflow from the sale of old
project today, but give up any future
expected inflows (opportunity costs).
General form: Increase in Net Income +
(Depreciation on New - Depreciation on
Old) – Increase in Net Working Capital
Step 1: Evaluate Cash Flows
a) Initial Outlay: What is the cash flow at
“time 0?”
General Steps
(Purchase price of the asset)
+ (shipping and installation costs)
(Depreciable asset)
+ (Investment in working capital)
+ After-tax proceeds from sale of old asset
Net Initial Outlay
After-tax Proceeds from sale of Old
Death Star($billion). Tax Rate = 40%
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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 = $28
Initial Outlay of Death Star
Replacement ($billion)
($160)
($15)
+ $28
($147)
Cost of New Depreciable Asset
Increase in Net Working Capital
After-tax Proceeds from sale of
replaced asset
Initial Outlay
Step 1: Evaluate Cash Flows

b) Annual Cash Flows: What
incremental cash flows occur over the
life of the project?
For Each Year, Calculate:
Incremental revenue
- Incremental costs
- Depreciation increase on project
Incremental earnings before taxes
- Tax on incremental EBT
Incremental earnings after taxes
+ Depreciation increase reversal
- annual increase in net working capital(none here)
Annual Cash Flow
Death Star Replacement Project
Depreciation($billion)



Annual Depreciation on Old = $100/10 =
$10
Annual Depreciation on New = $160/4 =
$40
Annual Increase in Depreciation due to
Replacement = $40 - $10 = $30 for years 1
through 4.
Death Star Replacement Project
Annual Free Cash Flows($billion)
Year
Inc in Rev
-Inc in Exp
-Inc in Dep
EBT
-Tax(40%)
EAT
+Inc in Dep
Cash Flow
1
50
10
30
10
4
6
30
36
2
90
20
30
40
16
24
30
54
3
90
30
30
30
12
18
30
48
4
90
40
30
20
8
12
30
42
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
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 - 0 = $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 = $3
Death Star Replacement
Terminal Cash Flows ($billion)
at t=4
New Salvage Value
-Taxes on New SV = .4(30-0)
-Old Net Salvage Value
+Recovery of Net Working Capital
Total Terminal CF (t = 4)

$30
$12
$3
$15
$30
Death Star Replacement Project
Decision Time ($billion)
Year
Cash Flow
0
(147)
CF0
1
36
C01
2
54
C02
3
48
C03
4
42 + 30 =
72
C04
 NPV at 10% = $15.59 Billion, PI = 1.11
 IRR = 14.3%, MIRR = 12.8%
Other Incremental Cash Flow
Issues
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

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.
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.
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
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
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,
CPT: PMT = -617.24.
Machine 2: PV = 1664, N = 6, I = 14,
CPT: PMT = -427.91.
Decision Time
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


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
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.
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 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%.
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 1
0
(45,000)
1
20,000
2
20,000
3
20,000 – 45,000 = (25,000)
4
20,000
5
20,000
6
20,000
Assume a required return of 14%.
Machine 2
(45,000)
12,000
12,000
12,000
12,000
12,000
12,000
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 + 20,000/(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 = 1443 +
1443/(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.
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
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.
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.
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?
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
Initial Outlay for Ping Kings





Cost of Equipment
Shipping&Installation
Depreciable Asset
Increase in WC
Initial Outlay
$4,000,000
500,000
$4,500,000
700,000
$5,200,000
Step 1: Evaluate Cash Flows

b) Annual Cash Flows: What
incremental cash flows occur over the
life of the project?
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
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

Annual CFs for Ping Kings
Year
Unit Sales
$/Unit
VC/Unit
Revenue($000)
-Variable Costs
-Fixed Costs
-Depreciation
EBIT
Tax(40%)
Earnings After Tax
+Depreciation
Cash Flow
1
10,000
$640
$350
6,400
3,500
300
900
1,700
680
1,020
900
1,920
2
15,000
$640
$350
9,600
5,250
300
900
3,150
1,260
1,890
900
2,790
3
9,000
$540
$350
4,860
3,150
300
900
510
204
306
900
1,206
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
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
Coronate Ping Kings?
Year
Cash Flow
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%
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.
This would affect the year 1
CF: cannibalization!
Year
Revenue($000)
-Variable Costs
-Fixed Costs
-Depreciation
EBIT
Tax(40%)
Earnings After Tax
+Depreciation
Cash Flow
Orig 1
6,400
3,500
300
900
1,700
680
1,020
900
1,920
Change
(1,000)
(500)
(500)
(200)
(300)
(300)
New 1
5,400
3,000
300
900
1,200
480
720
900
1,620
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%