11 - 1
Lecture Fourteen
Cash Flow Estimation and Other
Topics in Capital Budgeting
Relevant cash flows
Working capital in capital budgeting
Unequal project lives
Inflation
11 - 2
Proposed Project
Cost: $200,000 + $10,000 shipping
+ $30,000 installation. Depreciable
cost: $240,000.
Inventories will rise by $25,000 and
payables by $5,000.
Economic life = 4 years.
Salvage value = $25,000.
MACRS 3-year class.
11 - 3
Sales: 100,000 units/yr @ $2.
Variable cost = 60% of sales.
Tax rate = 40%.
WACC = 10%.
11 - 4
Set up, without numbers, a time line
for the project’s cash flows.
0
1
2
3
4
Initial
Costs
(CF0)
OCF1
OCF2
OCF3
OCF4
NCF0
NCF1
+
Terminal
CF
NCF2
NCF3
NCF4
11 - 5
Investment at t = 0:
Equipment
-$200
Installation & Shipping
-40
Increase in inventories
-25
Increase in A/P
Net CF0
DNWC = $25 - $5 = $20.
5
-$260
11 - 6
Modified Accelerated Cost Recovery System
(MACRS)
Major Classes and Asset Lives for MACRS
Class
Type of Property
3-year
Certain special manufacturing tools
5-year
Automobiles, light-duty trucks, computers, and
certain special manufacturing equipment
7-year
Most industrial equipment, office furniture, and
fixtures
10-year
Certain longer-lived types of equipment
27.5-year
Residential rental real property such as apartment
buildings
39-year
All non-residential real property, including
commercial and industrial buildings
11 - 7
Recovery Allowance Percentage for
Personal Property (MACRS)
Ownership
Year
1
2
3
4
5
6
7
8
9
10
11
3-Year
Class of Investment
5-Year
7-Year
33%
45
15
7
20%
32
19
12
11
6
14%
25
17
13
9
9
9
4
100%
100%
100%
10-Year
10%
18
14
12
9
7
7
7
7
6
3
100%
11 - 8
What’s the annual depreciation?
Year
Rate
1
2
3
4
0.33
0.45
0.15
0.07
1.00
x
Basis Depreciation
$240
240
240
240
$ 79
108
36
17
$240
Due to 1/2-year convention, a 3-year
asset is depreciated over 4 years.
11 - 9
Computing the Cash Inflow from Operations
REV
-
TAX
+
TAX ADV.
of DEPR.
27,000 - 27,000 (0.40) +
27,000 10,800
+
+
16,200
REV - DEPR.
27,000 - 16,500
10,500
10,500
REV 27,000
DEP 16,500
NIBT 10,500
Tax
4,200
NIAT
6,300
+ DEP 16,500
CASH
$ 22,800
FLOW
16,500 (0.4)
6,600
6,600
= $22,800
TAX
TAX
- 10,500 (0.40)
4,200
+
+
+
+
DEPR.
16,500
16,500
16,500 = $22,800
REV
Tax
10,800
4,200
6,600
27,000
10,800
REV
after Tax,
16,200
but bef.
DEPR Ad.
6,600 (1)
CASH
$22,800
FLOW
(1) 16,500 (0.40) = 6,600
1.
Net investment at t=0:
Cost of new machine
Net investment outlay (CF 0)
2.
Year
1
2
3
4
5
6
7
8
After-tax
Earnings
$16,200
16,200
16,200
16,200
16,200
16,200
16,200
16,200
TDDep
$6,600
10,560
6,270
3,960
3,630
1,980
0
0
11 - 10
$82,500
$82,500
Annual CFt
$22,800
26,760
22,470
20,160
19,830
18,180
16,200
16,200
Notes:
a.
The after-tax earnings is $27,000 (1 - T) = $27,000 (0.6) = $16,200
b.
Find DDep over Years 1 - 8:
The old machine was fully depreciated; therefore,
DDep = depreciation on the new machine.
(1)
Year
1
2
3
4
5
6
7-8
(2)
Dep Rate
0.20
0.32
0.19
0.12
0.11
0.06
0.00
(3)
Dep Basis
$82,500
82,500
82,500
82,500
82,500
82,500
82,500
(4)
Depreciation
$16,500
26,400
15,675
9,900
9,075
4,950
0
Tax Rate
0.40
0.40
0.40
-
TDDep or Tax
advantage of Depr.
= (4) x Tax Rate
$6,600
10,560
-
11 - 11
3.
Now find the NPV of the replacement machine:
Year
CFt
PVIF (12%)
1
2
3
4
5
6
7
8
$22,800
26,760
22,470
20,160
19,830
18,180
16,200
16,200
Product
0.8929
0.7972
0.7118
0.6355
0.5674
0.5066
0.4523
0.4039
$20,358
21,333
15,994
12,812
11,252
9,210
7,327
6,543
Sum = PV inflows = $104,829
Less: Cost = CF0
82,500
NPV = $22,329
Alternatively, place the cash flows on a time line:
0
1
2
3
4
5
6
7
8
12%
-82,500
22,800 26,760 22,470 20,160 19,830 18,180 16,200 16,200
With a financial calculator, input the appropriate cash flows into the
cash flow register, input I = 12, and then solve for NPV = $22,329.
The NPV of the investment is positive; therefore, the new machine
should be bought.
11
11 -- 12
7
Operating cash flows:
1
2
3
4
Revenues
$200 $200 $200 $200
Op. Cost, 60% -120 -120 -120 -120
Depreciation
-79 -108
-36
-17
Oper. inc. (BT)
1
-28
44
63
Tax, 40%
--11
18
25
1
-17
26
38
Oper. inc. (AT)
Add. Depr’n
79
108
36
17
Op. CF
80
91
62
55
11
11 -- 13
8
Net Terminal CF at t = 4:
Recovery of NWC
Salvage Value
Tax on SV (40%)
Net termination CF
Q.
Q.
$20
25
-10
$35
Always a tax on SV? Ever a
positive tax number?
How is NWC recovered?
11
11 -- 14
9
Should CFs include interest expense?
Dividends?
No. The cost of capital is
accounted for by discounting at
the 10% WACC, so deducting
interest and dividends would be
“double counting” financing
costs.
11 - 10
15
Suppose $50,000 had been spent last
year to improve the building. Should
this cost be included in the analysis?
No. This is a sunk cost.
Analyze incremental investment.
11 - 16
11
Suppose the plant could be leased out
for $25,000 a year. Would this affect
the analysis?
Yes. Accepting the project means
foregoing the $25,000. This is an
opportunity cost, and it should be
charged to the project.
A.T. opportunity cost = $25,000(1 - T)
= $25,000(0.6) = $15,000 annual cost.
11 - 12
17
If the new product line would decrease
sales of the firm’s other lines, would
this affect the analysis?
Yes. The effect on other projects’ CFs
is an “externality.”
Net CF loss per year on other lines
would be a cost to this project.
Externalities can be positive or
negative, i.e., complements or
substitutes.
18
11 - 13
Here are all the project’s net CFs (in
thousands) on a time line:
0
k = 10%
-260
1
79.7
2
3
91.2
62.4
Terminal CF
4
54.7
35.0
89.7
Enter CFs in CF register, and I = 10%.
NPV = -$4.03
IRR = 9.3%
19
11 - 14
What’s the project’s MIRR?
0
1
2
3
4
-260
79.7
91.2
62.4
89.7
68.6
110.4
106.1
374.8
10%
10%
-260
10%
MIRR = ?
Can we solve using a calculator?
20
11 - 15
Yes.
CF0
CF1
CF2
CF3
CF4
I
=
=
=
=
=
=
0
79.7
91.2
62.4
89.7
10
NPV = 255.97
INPUTS
OUTPUT
4
10
-255.97
0
N
I/YR
PV
PMT
FV
TV = FV = 374.8
21
11 - 16
Use the FV = TV of inputs to find MIRR
INPUTS
4
N
OUTPUT
-260
I/YR
PV
0
374.8
PMT
FV
9.6
MIRR = 9.6%. Since MIRR < k = 10%,
reject the project.
22
11 - 17
What’s the payback period?
0
1
2
3
4
-260
79.7
91.2
62.4
89.7
-89.1
-26.7
63.0
Cumulative:
-260
-180.3
Payback = 3 + 26.7/89.7 = 3.3 years.
23
11 - 18
If this were a replacement rather than a
new project, would the analysis
change?
Yes. The old equipment would be
sold, and the incremental CFs would
be the changes from the old to the
new situation.
24
11 - 19
The relevant depreciation would be
the change with the new equipment.
Also, if the firm sold the old machine
now, it would not receive the SV at
the end of the machine’s life. This is
an opportunity cost for the
replacement project.
25
11 - 20
Q. If E(INFL) = 5%, is NPV biased?
CFt
Re v t  Cost t

.
A. YES. NPV  
t
t
t  0 1  k 
1  k 
n
k = k* + IP + DRP + LP + MRP.
Inflation is in denominator but not in
numerator, so downward bias to NPV.
Should build inflation into CF forecasts.
26
11 - 21
Consider project with 5% inflation.
Investment remains same, $260.
Terminal CF remains same, $35.
Operating cash flows:
1
Revenues
$210
Op. cost 60%
-126
Depr’n
-79
Oper. inc. (BT)
5
Tax, 40%
2
Oper. inc. (AT)
3
Add Depr’n
79
Op. CF
82
2
$220
-132
-108
-20
-8
-12
108
96
3
$232
-139
-36
57
23
34
36
70
4
$243
-146
-17
80
32
48
17
65
27
11 - 22
Here are all the project’s net CFs (in
thousands) when inflation is
considered.
0
k = 10%
-260
1
82.1
2
3
96.1
70.0
Terminal CF
4
65.0
35.0
100.0
Enter CFs in CF register, and I = 10%.
NPV = $15.0 Project should be accepted.
IRR = 12.6%
28
11 - 23
S and L are mutually exclusive and will
be repeated. k = 10%. Which is better?
Expected Net CFs
Year
Project S
0
($100,000)
60,000
1
Project L
($100,000)
33,500
2
60,000
33,500
3
--
33,500
4
--
33,500
29
11 - 24
S
L
CF0
-100,000
-100,000
CF1
60,000
33,500
2
4
10
10
4,132
6,190
Nj
I
NPV
Q. NPVL > NPVS. Is L better?
A. Can’t say. Need replacement chain
analysis.
30
11 - 25
Note that Project S could be
repeated after 2 years to generate
additional profits.
Use replacement chain to calculate
extended NPVS to a common life.
Since S has a 2-year life and L has
a 4-year life, the common life is 4
years.
31
11 - 26
L:
0
1
2
3
4
33,500
33,500
33,500
33,500
10%
-100,000
NPVL = $6,190 (already to Year 4)
S:
0
10%
-100,000
1
60,000
2
60,000
-100,000
-40,000
3
60,000
4
60,000
NPVS = $7,547 (on extended basis)
32
11 - 27
Equivalent Annual Annuity (EAA)
That annuity PMT whose PV equals the
project’s NPV.
S:
0
10%
1
EAAS
10%
2
EAAS
PV1
PV2
4,132 = Previously determined NPVS.
33
11 - 28
Project S (EAA):
INPUTS
OUTPUT
2
10
N
I/YR
-4132
PV
0
PMT
FV
EAAS = 2380.82
Project L (EAA):
INPUTS
OUTPUT
4
10
N
I/YR
-6190
PV
0
PMT
FV
EAAL = 1952.76
The higher annuity is better.
34
11 - 29
The project, in effect, provides an
annuity of EAA.
EAAS > EAAL , so pick S.
Replacement chains and EAA
always lead to the same decision.
35
11 - 30
If the cost to repeat S in two years
rises to $105,000, which would be
best?
0
10%
-100,000
1
60,000
2
60,000
-105,000
-45,000
3
60,000
NPVS = 3,415 < NPVL = 6,190.
Now choose L.
4
60,000
11-11
11 - 36
The Erley Equipment Company purchased a machine 5 years ago at a cost of $100,000.
The machine had an expected life of 10 years at the time of purchase, and an expected
salvage value of $10,000 at the end of 10 years. It is being depreciated by the straight
line method toward a salvage value of $10,000, or by $9,000 per year.
A new machine can be purchased for $150,000, including installation costs. During its
5-year life, it will reduce cash operating expenses by $50,000 per year. Sales are not
expected to change. At the end of its useful life, the machine is estimated to be
worthless. MACRS depreciation will be used, and the machine will be depreciated over
its 3-year class life rather than its 5-year economic life. (See Table 11A-2 for MACRS
recovery allowance percentages.)
The old machine can be sold today for $65,000. The firm’s tax rate is 35 percent. The
appropriate discount rate is 16 percent.
a) If the machine is purchased, what is the amount of the initial cash flow at Year 0?
b) What incremental operating cash flows will occur at the end of Years 1 through 5 as a
result of replacing the old machine?
c) What incremental terminal cash flow will occur at the end of Year 5 if the new
machine is purchased?
d) What is the NPV of this project? Should Erley replace the old machine?
11 - 37
a. Old depreciation = $9,000 per year
Book value = $100,000 - 5 ($9,000) = $55,000
Gain = $65,000 - $55,000 = $10,000
Tax on book gain = $10,000 (0.35) = $3,500
Price
SV (old machine)
Tax effect
Initial outlay
b.
Year
1
2
3
4
5
Recovery
Percentage
33%
45%
15%
7%
($150,000)
$65,000
($3,500)
($88,500)
Depreciation
Basis
$150,000
150,000
150,000
150,000
Depreciation
Allowance, New
$49,500
67,500
22,500
10,500
Depreciation
Allowance, Old
$9,000
9,000
9,000
9,000
9,000
Annual cash flows = CFt = (DOperating expenses) (1 - T) + (DDepreciation) (T)
CF1 = ($50,000) (0.65) + ($40,500) (0.35) = $32,500 + $14,175 = $46,675
CF2 = ($50,000) (0.65) + ($58,500) (0.35) = $32,500 + $20,475 = $52,975
CF3 = ($50,000) (0.65) + ($13,500) (0.35) = $32,500 + $ 4,725 = $37,225
CF4 = ($50,000) (0.65) + ($ 1,500) (0.35) = $32,500 + $ 525 = $33,025
CF5 = ($50,000) (0.65) + (-$9,000) (0.35) = $32,500 - $ 3,150 = $29,350
Change in
Depreciation
$40,500
58,500
13,500
1,500
(9,000)
11 - 38
c. Salvage value on new machine
Salvage value on old machine
(opportunity cost)
Terminal CF
$
$
0
(10,000)
(10,000)
d.
0
1
2
3
4
5
16%
(88,500)
46,675
52,975
37,225
NPV = $42,407
Therefore, the firm should replace the old machine.
33,025
29,350
(10,000)
19,350