NPV and Capital Budgeting

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Lecture 7

• NPV and Capital Budgeting

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Cash flows calculations
NPV analysis is based on cash flows not
accounting earnings. Capital investments are
treated as current expenses in cash flow
analysis, but are depreciated in earnings
calculation. Depreciation nevertheless affect
taxes, and thus cash flows NPV.
Only cash flows incremental to a project should
be used. Sunk costs are irrelevant to the NPV of
going ahead. Lost opportunities to sell assets
affect NPV of a project. Erosion of sales from
existing product lines also affect NPV.
Changes in net working capital represent cash
flows. Changes in inventories of raw materials
and goods in process Changes in accounts
receivable and accounts payable Changes in cash
on hand needed for unexpected expenses
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Cash flows calculations (continued)
Investment in net working capital represents cash
outflow
Income needs to be calculated to calculate tax
payments.
Example Baldwin company
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Inflation and Capital budgeting
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Inflation and Capital budgeting (continued)
Nominal cash flows discounted with nominal
interest rate gives the same NPV as real cash
flows discounted with real interest rate.
More convenient to use nominal cash flows for the
depreciation tax deduction Depreciation
allowances are based on historical costs
(nominal!)
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Example
real cash flow at date 4, since it is expressed
in terms of date 0 purchasing power
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Example Baldwin Company
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Example Baldwin Company (continued)
Derive the operating revenues and costs as in
Table 2.
For this project, IRS depreciation allowances
would be 20,000 in year1, 32,000 in year2,
19,200 in year3, 11,520 in year4, and 11,520
in year5 leaving an adjusted basis of 5,760.
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Example Baldwin Company (continued)
We then calculate income taxes as in Table 3.
Assuming capital gains are also taxed at 34
percent, the capital gains tax 0.34 (30,000 -
5,760) 0.34 24,240 8,240 and the net of tax
gain in year5 will be 30,000 - 8,240 21, 760.
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Example Baldwin Company (continued)
Finally, we get the incremental cash flows
presented in Table 4.
Table 4 Incremental Cash Flows for the Project
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Example Baldwin Company (continued)
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Investments of Unequal Lives
Choice between two mutually exclusive projects
that have different lives. The projects do the
same job, bring same revenues, but decisions lead
to different operation costs. Simple NPV rule may
lead to a wrong decision.
The projects must be evaluated on an equal-life
basis, taking into account all future replacement
decisions.
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Investments of Unequal Lives (continued)
The PV of the cost of A is lower than that of B,
but A needs to be replaced more frequently.
We may adjust for the difference in useful life
in comparing the two machines by the methods of
matching cycles or equivalent annual cost (EAC).
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Investments of Unequal Lives (continued)
Matching Cycles of Replacement
B is thus preferred to A. This method is simple
but may require excessive calculations if the
cycle is too high.
The methods based on replacement chains assume
that the time horizon is a multiple of 12. Thus
the method may not work for unknown time horizon
or for short time horizon.
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Investments of Unequal Lives (continued)
Equivalent Annual Cost
To use this method, calculate the PV of each
machine at date 0, and express the calculated PV
as annuity equivalent for the machines life time.
EAC is the PV of a single cycle converted to an
annuity equivalent. Again B is preferred to A.
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General decision to replace
Calculate specific NPVs and compare.
Example Suppose both A and B will be worthless
when the projects end at date 5.
Now A is preferred to B, without repeating cycles.
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General decision to replace (continued)
Replacement of old machine An old machine
should be replaced right before its cost exceeds
the EAC for new equipment.
The cost of keeping the old machine one more year
includes the opportunity cost of not selling it
for 4,000 additional maintenance of 1,000 assumed
to be paid at year end a return of -2,500 from
selling it at year end
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General decision to replace (continued)
Similarly, the one year carrying costs at the end
of year1 is 3375, year2 is 3725, and year3 is
5150.
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General decision to replace (continued)
New equipment thus costs 2859.95 each year
starting a year hence. But the old machine costs
3100 (gt 2859.95) for year1 and increases after
that. Better to replace old machine now.
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Example EAC, Problem 7.19
A machine costs 12000, has annual year end
operating costs of 6000, and lasts 4 years. It
has 2000 salvage value. What is the PV of
operating a series of such machines in
perpetuity, if the appropriate discount rate is
6 ?
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Example EAC (continued)
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Example Problem 7.17
MMC wants to know the maximum price (Pm) it
should be willing to pay for a new piece of
equipment. I.e., the price that will give NPV0.
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Example Problem 7.17 (continued)
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Example Problem 7.17 (continued)
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Example Problem 7.17 (continued)
Book value of old equipment
40 - 5(40/10) 20 Capital gain market value -
book value 20 -20 0 No tax
After tax cost savings in years 18 10(1-0.34)
6.6 each year Total saving for 8 years
6.6 A80.08
Net cost for new equipment
Pm - 20 Net depreciation tax shield for years
15 0.34(Pm/5-4) each year
In year 8, book value of new equipment is 0 ,
Net revenue
(5 - 0)(1 - 0.34) 3.3