Lecture Fourteen Cash Flow Estimation and Other Topics in Capital Budgeting

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Lecture FourteenCash Flow Estimation and Other
Topics in Capital Budgeting

• Relevant cash flows
• Working capital in capital budgeting
• Unequal project lives
• Inflation

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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.

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• Sales 100,000 units/yr _at_ 2.
• Variable cost 60 of sales.
• Tax rate 40.
• WACC 10.

4
Set up, without numbers, a time line for the
projects cash flows.
0
1
2
3
4
OCF1
OCF2
OCF3
OCF4
Initial Costs

(CF0)
Terminal CF
NCF0
NCF1
NCF2
NCF3
NCF4
5
Investment at t 0
Equipment
-200
Installation Shipping
-40
Increase in inventories
-25
Increase in A/P
5
Net CF0
-260
DNWC 25 - 5 20.
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Modified Accelerated Cost Recovery System
(MACRS)Major Classes and Asset Lives for MACRS
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Recovery Allowance Percentage for Personal
Property (MACRS)
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Whats the annual depreciation?
Year
Rate
x
Basis
Depreciation
1
0.33
240
79
2
0.45
240
108
3
0.15
240
36
4
0.07
240
17
1.00
240
Due to 1/2-year convention, a 3-year asset is
depreciated over 4 years.
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Computing the Cash Inflow from Operations
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11 - 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. Deprn
79
108
36
17
Op. CF
80
91
62
55
13
Net Terminal CF at t 4
11 - 8
Recovery of NWC
20
Salvage Value
25
Tax on SV (40)
-10
Net termination CF
35
Q. Always a tax on SV? Ever a positive tax
number? Q. How is NWC recovered?
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Should CFs include interest expense? Dividends?
11 - 9

• 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.

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Suppose 50,000 had been spent last year to
improve the building. Should this cost be
included in the analysis?
11 - 10

• No. This is a sunk cost.Analyze incremental
  investment.

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Suppose the plant could be leased out for 25,000
a year. Would this affect the analysis?
11 - 11

• 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.

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If the new product line would decrease sales of
the firms other lines, would this affect the
analysis?
11 - 12

• 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.

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11 - 13
Here are all the projects net CFs (in thousands)
on a time line
0
1
2
3
4
k 10
79.7
91.2
62.4
54.7
-260
Terminal CF
35.0 89.7
Enter CFs in CF register, and I 10.
NPV -4.03 IRR 9.3
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Whats the projects MIRR?
11 - 14
0
1
2
3
4
79.7
91.2
62.4
89.7
-260
10
68.6
10
110.4
10
106.1
MIRR ?
374.8
-260
Can we solve using a calculator?
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11 - 15
Yes.
CF0 0 CF1 79.7 CF2 91.2 CF3
62.4 CF4 89.7 I 10
NPV 255.97
INPUTS
4 10 -255.97 0
TV FV 374.8
OUTPUT
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Use the FV TV of inputs to find MIRR
11 - 16
INPUTS
4 -260 0 374.8
9.6
OUTPUT
MIRR 9.6. Since MIRR lt k 10, reject the
project.
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Whats the payback period?
11 - 17
0
1
2
3
4
79.7
91.2
62.4
89.7
-260
Cumulative
-26.7
-260
-89.1
-180.3
63.0
Payback 3 26.7/89.7 3.3 years.
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If this were a replacement rather than a new
project, would the analysis change?
11 - 18
Yes. The old equipment would be sold, and the
incremental CFs would be the changes from the old
to the new situation.
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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
  machines life. This is an opportunity cost for
  the replacement project.

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11 - 20
Q. If E(INFL) 5, is NPV biased?
A. YES.
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.
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11 - 21
Consider project with 5 inflation. Investment
remains same, 260. Terminal CF remains same,
35.
Operating cash flows 1 2 3 4
Revenues 210 220 232 243 Op. cost
60 -126 -132 -139 -146 Deprn -79 -108
-36 -17 Oper. inc. (BT) 5 -20 57 80 Tax, 40
2 -8 23 32 Oper. inc.
(AT) 3 -12 34 48 Add Deprn 79 108 36
17 Op. CF 82 96 70 65
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Here are all the projects net CFs (in thousands)
when inflation is considered.
0
1
2
3
4
k 10
82.1
96.1
70.0
65.0
-260
Terminal CF
35.0 100.0
Enter CFs in CF register, and I 10.
Project should be accepted.
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S and L are mutually exclusive and will be
repeated. k 10. Which is better?
11 - 23
Expected Net CFs
Year
Project S
Project L
(100,000)
0
(100,000)
60,000
1
33,500
60,000
2
33,500
--
3
33,500
--
4
33,500
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11 - 24
S
L
CF
-100,000
-100,000
0
CF
60,000
33,500
1
N
2
4
j
I
10
10
NPV
4,132
6,190
Q. NPVL gt NPVS. Is L better? A. Cant say. Need
replacement chain analysis.
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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.

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L
0
1
2
3
4
10
33,500
33,500
33,500
33,500
-100,000
NPVL 6,190 (already to Year 4)
S
0
1
2
3
4
10
60,000
60,000
60,000
60,000
-100,000
-100,000
-40,000
NPVS 7,547 (on extended basis)
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Equivalent Annual Annuity (EAA)
That annuity PMT whose PV equals the projects
NPV.
S
2
0
10
10
EAAS
EAAS
PV1 PV2
4,132 Previously determined NPVS.
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11 - 28
Project S (EAA)
INPUTS
2 10 -4132 0
EAAS 2380.82
OUTPUT
Project L (EAA)
INPUTS
4 10 -6190 0 EAAL
1952.76
OUTPUT
The higher annuity is better.
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• The project, in effect, provides an annuity of
  EAA.
• EAAS gt EAAL , so pick S.
• Replacement chains and EAA always lead to the
  same decision.

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If the cost to repeat S in two years rises to
105,000, which would be best?
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4
0
1
10
60,000
-100,000
60,000
60,000
NPVS 3,415 lt NPVL 6,190.
Now choose L.
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11-11
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 firms 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?
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