Chapter 7
Net Present Value & Capital Budgeting
Chapter 7
Net Present Value and Capital Budgeting
– In this chapter we will describe how to actually do
a net present value and discounted cash flows
analysis for capital budgeting.
– The primary aim of this part is to describe how to
identify a project’s incremental cash flows,
– In this part we also discusses how to handle such
as sunk costs,opportunity costs,financing costs,
net working capital,and erosion.
Chapter 7
Net Present Value and Capital Budgeting
7.1 Project cash flows,a first look
7.1.1 Relevant cash flows
A relevant cash flows for a project is a change in the
firm’s overall future cash flow that comes about as a
direct consequence of the decision to take that project.
The relevant cash flow also called the incremental cash
flows associated with the project.
Incremental cash flows is the difference between a
firm’s future cash flows with a project or without the
project.
Chapter 7
Net Present Value and Capital Budgeting
The concept of incremental cash flow is central to our
analysis,so we will state a general definition and refer
back to it,
The incremental cash flows for project evaluation consist
of any and all changes in the firm’s future cash flows that
are a direct consequence of taking the project.
7.1.2 The stand-alone principle
Once we identify the effect of undertaking the proposed
project on the firm’s cash flows,we need only focus on
the project’s resulting incremental cash flows.this is
called the stand—alone principle.
The Stand—alone principle refers to the rule that
evaluation of a project based on the project’s
incremental cash flows.
Chapter 7
Net Present Value and Capital Budgeting
What the stand—alone principle says is that,once we
have determined the incremental cash flows from
undertaking a project,we can view that project as a
kind of ―minifirm‖with its own future revenues and
costs,its own assets,and of course,its own cash flows,
We will then be primarily interested in comparing the
cash flows from this minifirm to the cost of acquiring it.
An important consequence of this approach is that we will
be evaluating the proposed project purely on its own
merits,in isolation from any other activities or projects.
Chapter 7
Net Present Value and Capital Budgeting
7.2 Incremental cash flows
7.2.1 Sunk costs
A cost that has already been incurred and and can
not be removed and therefore should not be
considered in an investment decision.
7.2.2 Opportunity cost
The most valuable alternative that is given up if a
particular investment is undertaken.
7.2.3 Side effects
Erosion is the cash flows of a new project that
come at the expense of all firm’s existing projects.
Chapter 7
Net Present Value and Capital Budgeting
7.2.4 Net working capital
7.2.5 Financing costs
Some conclusions of incremental cash flows
When we estimate cash flows on an incremental
basis,we should learn by heart that
Do not confuse average with incremental payoffs.
Include all incidental effects
Do not forget working capital requirements,
Include opportunity costs.
Forget sunk costs
Beware of allocated overhead costs.
Chapter 7
Net Present Value and Capital Budgeting
7.3 Pro forma financial statements and project
cash flows
The first thing we need when we begin evaluating a
proposed investment is a set of pro forma or
projected financial statements.
7.3.1 Getting started,pro forma financial
statements
Pro forma financial statements are those
financial statements projecting future years’
operations.
Chapter 7
Net Present Value and Capital Budgeting
To prepare these statements,we will need estimates
of quantities such as unit sales,the selling price per
unit,the variable cost per unit,and total fixed costs,
We also need to know the total investment
required,including any investment in net working
capital.
Suppose we think we can sell something 50000cans
per year at a price of $4.00per unit,It costs us
about $2.50per can,and a new product such as this
one has only a three-year life,We require a 20%
return on new products,The other factors are
given like the next page.
Chapter 7
Net Present Value and Capital Budgeting
Projected income statements of special firm
Sales $200000
Variables costs 125000
75000
Fixed costs 12000
Depreciation 30000
EBIT 33000
Taxes (34%) 11220
Net income 21780
Chapter 7
Net Present Value and Capital Budgeting
Projected capital requirements of special project
Year
0 1 2 3
Net
working
capital
$20000 20000 20000 20000
Net fixed
assets
90000 60000 30000 0
Total
investment
110000 80000 50000 20000
Chapter 7
Net Present Value and Capital Budgeting
7.3.2 Project cash flows
Project cash flow =project operating cash flow –project
additions to net working capital – project capital
spending
Project Operating Cash Flow (51780)
Operating cash flow = EBIT+ Depreciation – Taxes
Projected Net Working Capital and Capital Spending
Chapter 7
Net Present Value and Capital Budgeting
Project total cash flows
Year
0 1 2 3
Operating cash
flows
51780 51780 51780
Addition to
NWC
-20000 20000
Capital
spending
-90000
Total cash
flows
-110000 51780 51780 71780
Chapter 7
Net Present Value and Capital Budgeting
7.3.3 Projected total cash flow and value
NPV=project cash flows (P/F,i,n)
NPV=10648
The return of this project will exceeds 20%
because the NPV which computed with
20% is over $1000,The project not only
could be acceptable,but also exceed which
we want,If we could calculated,we would
find that the IRR will near 26%.
Chapter 7
Net Present Value and Capital Budgeting
7.4 More on project cash flow
7.4.1 A closer look at net working capital
In this section we will ignore the no depreciation,no taxes,
no fixed assets investments.
Sales $500
Costs 310
Net income $190
Depreciation and taxes are zero,No fixed assets are
purchased during the year,So we will only talk about the
NWC (accounting receivable and payable).
Chapter 7
Net Present Value and Capital Budgeting
Beginning of year End of year Change
Accounts receivable $880 $910 +$30
Accounts payable 550 605 +55
Net working capital 330 305 -25
Total cash flow = $215[190-(-25)]
Now we could ask a question,what were cash flow
revenues for the year? Also what were cash costs?
Sales are 500,but accounting receivable rose by 30 over
the year,so our cash flows is only 500-30=470.
Chapter 7
Net Present Value and Capital Budgeting
Cash flows out can be similarly determined,cost is 310,
but accounts payable increased by 55,this means that
we have not yet paid 55of the 310,so cash costs for the
period are just 310-55=255.
Putting this information together,cash inflows less cash
outflows is 470-255=215,just we had before,Now we
could notice that:
Cash flow =cash inflow- cash outflow=operating cash
flow –change in net working capital
Chapter 7
Net Present Value and Capital Budgeting
Example for cash collections and costs
For the year just completed,corporation CWT reports sales of
998 and costs of 734,You have collected the following
beginning and ending balance sheet information:
Beginning Ending
Accounts receivable 100 110
Inventory 100 80
Accounts payable 100 70
Net Working Capital 100 120
Chapter 7
Net Present Value and Capital Budgeting
Cash inflows:
998-10=988
Cash outflows
734-20+30=744
Net cash flows
988-744=244
Cash flows
(998-734)-(120-100)=244
Chapter 7
Net Present Value and Capital Budgeting
7.4.2 Depreciation
Accounting depreciation is a noncash deduction,As a
result,depreciation has cash flow consequences
only because it influences the tax bill.
Accelerated cost recovery system(ACRS) is a
depreciation method under U.S,tax law allowing
for the accelerated write-off of property under
various classifications,
Modified ACRS depreciation
Calculating depreciation is normally very mechanical,
Once an asset’s tax life is determined the
depreciation for each year is computed by
Chapter 7
Net Present Value and Capital Budgeting
Modified ACRS property classes
Class Examples
3—year Equipment used in research
5—year Autos,computers
7—year Most industrial equipment
Chapter 7
Net Present Value and Capital Budgeting
Modified ACRS depreciation allowances
Year Property class
3—year 5—year 7—year
1 33.33 20.00 14.29
2 44.44 32.00 24.49
3 14.82 19.20 17.49
4 7.41 11.52 12.49
5 11.52 8.93
6 5.76 8.93
7 8.93
8 4.45
Chapter 7
Net Present Value and Capital Budgeting
Year ACRS percentage Depreciation
1 20.00,2000× 12000＝ 2400.00
2 32.00,3200× 12000＝ 3840.00
3 19.20,1920× 12000＝ 2304.00
4 11.52,1152× 12000＝ 1382.40
5 11.52,1152× 12000＝ 1382.40
6 5.76,05.76× 12000＝ 691.20
100.00 12000
Chapter 7
Net Present Value and Capital Budgeting
multiplying the cost of the asset by a fixed percentage,
The expected salvage value(what we think the asset
will be worth when we dispose of it) and the actual
expected economic life(how long we expect the asset
to be in service) are not explicitly considered in the
calculation of depreciation.
Book value versus market value
In calculating depreciation under current tax,the
economic life and future market value of the asset
are not an issue,As a result,the book value of an
asset can differ substantially from its actual market
value.
Chapter 7
Net Present Value and Capital Budgeting
ACRS book values
Year Beginning BV Depreciation Ending BV
1 12000.00 2400.00 9600.00
2 9600.00 3840.00 5760.00
3 5760.00 2304.00 3456.00
4 3456.00 1382.40 2073.60
5 2073.60 1382.40 691.20
6 691.20 691.20 0.00
Chapter 7
Net Present Value and Capital Budgeting
Because the tax rate is different from capital gain rate,
As a general rule,a capital gain only occurs if the
market price exceeds the original cost.
7.5 Alternative definitions of operating cash flow
The analysis we have been through in the previous section
is quite general and can be adapted to just about any
capital investment problem,In the next we illustrate
some particularly useful variations.
First we should to discuss the fact that there are different
definitions of project operating cash flow that are
commonly used,Both in practice and in financial texts.
Chapter 7
Net Present Value and Capital Budgeting
Some basic information:
Sales = $1500,Costs = 700,Depreciation = 600,Tax
rate = 34%,
OCF = $732.
7.5.1 The Bottom-UP approach
Since we are ignoring any financial expenses such
as interest,then project net income will be
EBIT- taxes =132
If we simply add the depreciation to both sides,we
arrive at a slightly different and very common
expression for OCF:
OCF=net income + depreciation
Chapter 7
Net Present Value and Capital Budgeting
This is the bottom-up approach,Here we start with the
accountant’s bottom line(net income) and add back any
noncash deductions(depreciation).
It is crucial to remember that this definition of OCF as
net income plus depreciation is correct only if there is no
interest expense subtracted in the calculation of net
income.
7.5.2 The Top-Down approach
OCF= sales – costs – taxes,That is the top-down approach,
Here we start at the top of the income statement
Chapter 7
Net Present Value and Capital Budgeting
with sales and work our way down to net cash flow
by subtracting costs,taxes,and other expenses,
Along the way we simply leave out any strictly
noncash items(depreciation).
7.5.3 The Taxes Shield approach
This approach will be very useful for some problems
we consider in the next section,The taxes shield
definition of OCF is
OCF = (sales - costs)× (1-taxes rate)+ depreciation×
taxes rate
This approach views OCF as having tow
components
Chapter 7
Net Present Value and Capital Budgeting
The first part is what the project’s cash flow would
be if there were no depreciation expense,In this
case this would be have been cash flow is ---.
The second part in this case is the depreciation
deduction multiplied by the tax rate,This is called
the depreciation tax shield,
Depreciation tax shield Tax saving that results from
the depreciation deduction,calculated as
depreciation multiplied by the corporate tax rate.
Because the depreciation is a noncash expense,The
only cash flow effect from deducting depreciation is
to reduce our taxes,a benefit to us.
Chapter 7
Net Present Value and Capital Budgeting
7.6 Some special cases of discounted cash flow
analysis
7.6.1 Evaluating Cost-Cutting proposals
Cost is the important factor that every factories must
be pay attention to,
Suppose we are considering automating some part of
any existing production process,The necessary
equipment costs $80000 to buy and install,It will save
22000per year,For simplicity assume that the
equipment has a five-year life and is depreciated to
zero on a straight-line basis over that period.
Should we do it? The tax rate is 34% and the discount
rate is 10%,
Chapter 7
Net Present Value and Capital Budgeting
The first step in making this decision is to identify
the relevant incremental cash flows,First is
determining the relevant capital spending,the
initial cost is $80000,the aftertax salvage value is
20000(1-,34)=13200,Second there are no working
capital so we do not need to think about additions
to net working capital,OCF is the third component,
Buying new equipment affect OCF in tow ways,
First we save 22000 per year,that is the firm’s
operating income increases by 22000,so this is the
relevant incremental project operating income,
Second we have an additional depreciation
deduction,The depreciation is 16000.
Chapter 7
Net Present Value and Capital Budgeting
Since the project has an operating income of $22000 and a
depreciation deduction of $16000,taking the project will
increase the firm’s EBIT by 22000-16000=6000,so this
is the project’s EBIT.
Finally since EBIT is rising for the firm,taxes will increase
and this increase in taxes will be $6000× 0.34=2040,
then OCF=EBIT+depreciation –taxes=19960
It might be somewhat more enlightening to calculate
operating cash flow using a different approach,What is
actually going on here is very simple.
Chapter 7
Net Present Value and Capital Budgeting
First of all,the cost savings increase our pretax income by
22000,We have to pay taxes on this amount,so our tax
bill increases by 0.34× 22000=7480,In other words,the
22000 pretax saving amounts to 14520.
Second,the extra 16000 in depreciation is not really a
cash outflow,but it dose reduce our taxes by
16000× 0.34=5400,the sum of these tow components is
14520+5440 = 19960,just as we had before,Notice that
5440 is the depreciation tax shield we discussed above,
and we have effectively used the tax shield approach
here.
Chapter 7
Net Present Value and Capital Budgeting
At 10 percent of discounted rate,it’s straightforward to
verify that the NPV here is 3860.
– An example to determine ―to buy or not to buy‖?
A firm want to buy a 200000 computer—based inventory
management system,It will be depreciated straight—line to
zero over its four—year life,It will be worth 30000 at that
time,The system would save 60000 pretaxes costs.
0 1 2 3 4 5
OCF 19960 19960 19960 19960 19960
C.P,-80000 13200
TCF -80000 19960 19960 19960 19960 33160
Chapter 7
Net Present Value and Capital Budgeting
The relevant tax rate is 39%,And this system will free up
45000 in net working capital,
What is the NPV at 16 percent?(-12768) What is the DCF
return on this investment?(11.5%)
First we can calculate the OCF,OCF =36600+19500=56100
Secondly is the capital spending.
0 1 2 3 4
OCF 56100 56100 56100 56100
ANWC 45000 -45000
C.S -200000 18300
TCF -155000 56100 56100 56100 29400
Chapter 7
Net Present Value and Capital Budgeting
7.6.2 Setting the bid price
In some market economic behavior,we should employ
competitive bid to win a job,and the winner is whoever
submit the lowest bid.
There is an old saw concerning this process,the low
bidder is whoever makes the bigger mistake,This is
called the winner’s curse,In other words,if you win,
there is a good chance that you underbid,
Suppose you want to sell five trucks each year for the next
four years by bid,Each truck platform could expend
$10000,The facilities you need can be leased for
$24000per year,the labor and material cost to do
Chapter 7
Net Present Value and Capital Budgeting
the works out to be about $4000 per truck,
Then the total cost per year will thus be
$24000+(10000+4000)× 5=94000
You will need to invest $60000 in new equipment and this
equipment will be depreciated straight-line to a zero
salvage value over the four years,It will be worth about
$5000 at that time,We also need to invest $40000 in raw
materials inventory and other working capital items,
The relevant tax rate is 39%,
What price per truck should we bid if you require a 20%
return on this investment?
Chapter 7
Net Present Value and Capital Budgeting
The computed years
0 1 2 3 4
Operating
cash flow
OCF OCF OCF OCF
Additions to
NWC
-40,000 +40,000
Capital
spending
-60,000 3050
Total cash
flow
-100,000 OCF OCF OCF OCF
+43,050
Chapter 7
Net Present Value and Capital Budgeting
The aftertax salvage value is $5000× (1-,39)=3050.
With this in mind,there is the key observation,The
lowest possible price you can profitably charge will
result in a zero NPV at 20%,So you should to
determine what the OCF must be for the NPV to
be equal to zero.
100000-43050(P/F,i,n)=79239,the the pro forma
changed like this:
Total cash flow,-79239,OCF(1~4)
NPV= -79239+OCF(P/A,i,n)=0
OCF= 30609
Chapter 7
Net Present Value and Capital Budgeting
OCF= Net income + Depreciation
Net income = 30609-15000 =15609
Net income = (sales – costs -depreciation)× (1-T)
= (sale – 94000-15000)× 0.61
Sales = 134589
The sales price has to be $26918 per unit.
So if you round this up a bit,it could to bid about exceed
$27000 per unit.
7.6.3 Evaluating equipment with different lives
In this section,our goal is to choose the most cost-effective,
The approach we consider here is only necessary when
tow special circumstances exist,
Chapter 7
Net Present Value and Capital Budgeting
First is the possibilities under evaluation have different
economic lives,Second and just as important,we need
whatever we buy more or less indefinitely,
We can illustrate this problem with a simple example,
Machine A costs $100 to buy and $10 per year to operate,It
wears out and must be replaced every two years.
Machine B costs $140 to buy and $8 per year to operate,It
last for the three years and must be replaced,Ignoring
taxes,which one should we go with if we use a 10%
discount rate?
Chapter 7
Net Present Value and Capital Budgeting
MAPV= -100+[ -10(P/F,i,n)]+[ -10(P/F,i,n)]= -117.36
MBPV= -140+[-8(P/F,i,n)] + [-8(P/F,i,n)] = -159.89
We could not determine which on is better because that
only computed the cost with different service periods,
And we need to work out a cost per year for these tow
alternatives,We should use the equivalent annual
cost(EAC),
The equivalent annual cost is the present value of a
project’s costs calculated on an annual basis.
Calculating the EAC involves finding an unknown
payment amount.
Chapter 7
Net Present Value and Capital Budgeting
For Machine A,we need to find a tow-year ordinary
annuity with a PV of –117.36 at 10%,
PV of costs A = -117.36 = EAC× (P/A,0.1,2)
EAC= -117.36/1.7355= -67.62
For Machine B,we need to find a three-year
ordinary annuity with a PV of –159.89 at 10%.
PV of costs A = -159.89 = EAC× (P/A,0.1,3)
EAC= -159.89/2.4869 = -64.29
Chapter 7
Net Present Value and Capital Budgeting
Example for evaluating with different lives
A filtration system will cost 1100000,and 60000
pretax annually to operate,It will have 5 years,An
other precipitation system will cost 1900000,but
only 10000 per year to operate,the precipitation
has 8 years life.
They all have no salvages,Which method should we
select if we use 12% discounted rate? The tax rate
is 34%.
Chapter 7
Net Present Value and Capital Budgeting
Filtration system Precipitation
system
Aftertax operating
cost
-39600 -6600
Depreciation tax
shield
74800 80750
OCF 35200 74150
Economic life 5 8
Annuity factor12% 3.6048 4.9676
PV of OCF 126.88 369350
Capital spending -1100000 -1900000
Total CF -973112 -1531650
Chapter 7
Net Present Value and Capital Budgeting
Filtration system’s EAC
-973112=EAC × 3.6048
EAC=-269949 per year
Precipitation system’s EAC
-1531650=EAC × 4.9676
EAC= -308328 per year
Chapter 7
Net Present Value and Capital Budgeting
7.7 Inflation and capital budgeting
7.7.1 Interest rate and inflation
– Real interest rate and nominal interest rate
Real interest rate =Nominal interest rate – inflation rate
7.7.2 Cash flow and inflation
7.7.3 Discounting,nominal or real?
1a t ei n f l a t i o n r1 r a t ei n t e r e s t n o m i n a l 1 r a t ei n t e r e s t r e a l
Chapter 7
Net Present Value and Capital Budgeting
Summary and conclusions
– The identification of relevant cash flows,
– Preparing and using pro forma or financial statements,
From these we could calculating the project cash flows and
operating cash flows.
– The role of net working capital and depreciation in project
cash flows,
– Some special cases in using discounted cash flow analysis.
Chapter 8
Strategy and analysis in using NPV
Chapter 8
Strategy and analysis in using NPV
8.1 Introductions
In previous parts,we discussed how to identify and
organize the relevant cash flows for capital investment
decisions,In these part we focus on assessing the
reliability of such an estimate and on some additional
considerations in project analysis.
We begin by discussing the need for an evaluation of cash
flow and NPV estimates,We go on to develop some
tools that are useful for doing so,We also examine some
additional complications and concerns that can arise in
project evaluation.
Chapter 8
Strategy and analysis in using NPV
8.2 Corporate strategy and positive NPV
8.2.1 The basic problems
A significant part of corporate strategy analysis is seeking
investment opportunities that can produce positive NPV.
But there two circumstances under which a discounted
cash flow analysis could lead us to conclude that a
project has a positive NPV,The first possibility is that
the project really does have a positive NPV,The second
possibility is a project may appear to have a positive
NPV because our estimate is inaccurate,
If we conclude that a project has a negative NPV when the
true NPV is positive,we lose a valuable opportunity.
Chapter 8
Strategy and analysis in using NPV
8.2.2 How to create positive NPV
Be the first to introduce a new product.
Further develop a core competency to produce goods or
services at lower cost than competitors.
Create a barrier that makes it difficult for other firms to
compete effectively.
Introduce variations on existing products to take
advantage of unsatisfied demand.
Create product differentiation by aggressive advertising
and marketing networks
Use innovation in organizational processes to do all of
the above.
Chapter 8
Strategy and analysis in using NPV
8.2.3 corporate strategy and the stock market
There should be a connection between the stock market
and capital budgeting,If a firm invests in a project that
is worth more than its costs,the project will produce
positive NPV,and the firm’s stock price should go up,
8.2.4 Forecasting risk
The key inputs into a DCF analysis are projected future
cash flows,If these projections are seriously in error,
then we have a classic GIGO(garbage-in,garbage-out)
system,
The possibility that we make a bad decision because of
errors in the projected cash flows is called forecasting
risk(or estimation risk),
Forecasting risk is the possibility that errors in projected
cash flows lead to incorrect decisions.
Chapter 8
Strategy and analysis in using NPV
Because of forecasting risk,there is the danger that
we think a project has a positive NPV when it really
does not,
8.3 Scenario and other ―what if‖ analysis
Our basic approach to evaluating cash flow and NPV
estimates involves asking ―what if‖ questions,
Accordingly,we discuss some organized ways of going
about a what-if analysis,Our goal in doing so is to
assess the degree of forecasting risk and to identify
those components that are the most critical to the
success or failure of an investment.
Chapter 8
Strategy and analysis in using NPV
8.3.1 Getting started
We are investigating a new project,Naturally,the
first thing we do is estimate NPV based on our
projected cash flows,We will called this the basic
case,
One way to organize this investigation is to put an
upper and lower bound on the various components
of the project,For example,suppose we forecast
sale at 100 units per year,We know this estimate
may be high or low,but we are relatively certain
that it is not off by more than 10 units in either
direction,
Chapter 8
Strategy and analysis in using NPV
We would thus pick a lower bound of 90 and an upper
bound of 110,
With this basic cases,we can calculate the example which
we have had the last text.
8.3.2 Scenario analysis
The basic form of what-if analysis is called scenario
analysis,Scenario analysis is the determination of what
happens to NPV estimates when we ask what-if questions.
What we do is investigate the changes in our NPV
estimates that result from asking questions like this.
Chapter 8
Strategy and analysis in using NPV
There are a number of possible scenarios we could consider,
A good place to start is the worst-case scenario,This will
tell us the minimum NPV of the project,If this were
positive,we would be in good shape,While we are at it,we
will go ahead and determine the other extreme,the best
case,This puts an upper bound on our NPV.
To get the worst case,we assign the least favorable value to
each item,This means low values for items like units sold
and price per unit and high values for costs.we do the
reverse for the best case.
Chapter 8
Strategy and analysis in using NPV
As we have mentioned,there is an unlimited number of
different scenarios that we could examine,At a minimum,
we might want to investigate two intermediate cases by
going halfway between the base amounts and the extreme
amounts,This would give us five scenarios in all,including
the base case.
Beyond this point,it is hard to know when to stop,As we
generate more and more possibilities,we run the risk of
―paralysis of analysis.‖ The difficulty is that no matter
how many scenarios we run,all we can learn are
possibilities,some good and some bad.
Chapter 8
Strategy and analysis in using NPV
A example for base case and scenario analysis
The project under consideration costs 200,000,has five—year
life,and no salvage value,Depreciation is straight—line to
zero,The required return is 12 percent,and the tax rate is
34 percentage,In addition,we have have compiled the
following information.
Base case Lower case Upper case
Unit sales 6,000 5500 6500
Price per unit 80 75 85
Variable costs
per unit
60 58 62
Fixed costs per
year
50,000 45,000 55,000
Chapter 8
Strategy and analysis in using NPV
So we can calculate the base—case NPV by these:
So the base—case NPV= -200000+59800(P/A,12%,5) =15567
Sales 480000
Variable costs 360000
Fixed costs 50000
Depreciation 40000
EBIT 30000
Taxes 10200
Net income 19800
Chapter 8
Strategy and analysis in using NPV
Worst case Best case
Unit sales 5500 6500
Price per unit 75 85
Variable costs
per unit
62 58
Fixed costs 55000 45000
Chapter 8
Strategy and analysis in using NPV
Scenario Net income Cash flow Net
present
value
IRR
Base case 19800 59800 25567 15.1
Worst case -15510 24490 -11719 -14.4
Best case 59730 99730 159504 40.9
At the worst case a tax credit is created,Otherwise the EBIT
will be -23500
Chapter 8
Strategy and analysis in using NPV
Scenario analysis is thus useful in telling us what can
happen and in helping us gauge the potential for
disaster,but it does not tell us whether or not to take the
project.
8.3.3 Sensitivity analysis
Sensitivity analysis is a variation on scenario analysis that
is useful in pinpointing the areas where forecasting risk
is especially severe,
The sensitivity analysis is the investigation of what
happens to NPV when only one variable is changed.
Chapter 8
Strategy and analysis in using NPV
The basic idea with a sensitivity analysis is to freeze all of the
variables expect one and then see how sensitive our
estimate of NPV is to changes in that one variable,If our
NPV estimate turns out to be very sensitive to relatively
small changes in the projected value of some component of
project cash flow,then the forecasting risk associated with
that variable is high.
Because sensitivity analysis is a form of scenario analysis,it
suffers from the same drawbacks,Sensitivity analysis is
useful for pointing out where forecasting errors will do the
most damage,but it does not tell us what to do about
possible errors.
Chapter 8
Strategy and analysis in using NPV
8.3.4 Simulation analysis
Simulation analysis is a combination of scenario and
sensitivity analysis,
If we want to let all the items vary at the same time,we
have to consider a very large number of scenarios,and
computer assistance is almost certainly needed,
Since simulation analysis is an extended form of scenario
analysis,it has the same problems,
8.4 Break-even analysis
Break-even analysis is a popular and commonly used tool for
analyzing the relationship between sales volume and
profitability,There are a variety of different break-even
measures,All break-even measures have a similar goal,
Chapter 8
Strategy and analysis in using NPV
8.4.1 Fixed costs and variable costs
Variable costs,are the costs that change when the
quantity of output changes,They would be zero when
production is zero,We will assume that variable costs
are a constant amount per unit of output.
The relationship between total variable costs(VC),cost
per unit of output(v),and total quantity of output(Q)
can be written as:
VC=v× Q
Fixed costs,are the costs that not change when the
quantity of output changes during a particular time
period.
Chapter 8
Strategy and analysis in using NPV
Naturally,fixed costs are not fixed forever,They are only
fixed during some particular time,beyond that time,
leases can be terminated and executives ―retired.‖
Total costs,total costs(TC) for a given level of output
are the sum of variable costs(VC) and fixed costs(FC):
TC=VC+FC
TC= v× Q+FC
Marginal or incremental cost is the change in costs that
occurs when there is a small change in output.
Marginal or incremental revenue is the change in revenue
that occurs when there is a small change in output.
Chapter 8
Strategy and analysis in using NPV
Total costs
Variable costs
Fixed costs
Quantity
of output
Chapter 8
Strategy and analysis in using NPV
8.4.2 Accounting break-even
Accounting break-even is the most widely used measures
of break-even,The accounting break-even point is
simply the sales level that results in a zero project net
income.
To determine a project’s accounting break-even point,we
start off with some common sense,Suppose we retail
something for $5 per unit,we can buy this from a
wholesale supplier for $3 per unit,We have accounting
expenses of $600 in fixed costs and $300 in depreciation,
How many the break-even point?
Chapter 8
Strategy and analysis in using NPV
5-3=2
Total accounting expenses is 300+600=900
So we can sell 900/2=450 units production.
Then the income statement will be
Sales 2250
Variable costs 1350
Fixed costs 600
Depreciation 300
EBIT 0
Taxes 0
Net income 0
Chapter 8
Strategy and analysis in using NPV
Remember,since we discussing a proposed new project,we
do not consider any interest expense in calculating net
income or cash flow from the project,
Also,notice that we conclude depreciation in calculating
expenses here,even though depreciation is not a cash
outflow,That is why we call it accounting break-even,
Finally,notice that when net income is zero,so are pretax
income and taxes,In accounting terms,our revenues are
equal to our costs,so there is no profit to tax.
Chapter 8
Strategy and analysis in using NPV
Sales and costs
Revenues
Total costs
BEP
Q Quantity of output
Chapter 8
Strategy and analysis in using NPV
8.4.3 Accounting break-even,a closer look
Some basic variables,
P =selling price per unit
v = variable cost per unit
Q =total unit sold
FC =fixed costs
D = depreciation
T =tax rate
Project net income is given by:
Net income =(sales-variable costs-fixed costs-depreciation)
× (1-T)
Chapter 8
Strategy and analysis in using NPV
(S-VC-FC-D)× (1-T)=0
Divided both sides by (1-T) to get:
S-VC-FC-D=0
S=PQ and VC= vQ,then we can rearrange this to solve for
the break-even level,
S-VC=FC+D
PQ-vQ =FC +D
(p-v)Q =FC+D
Q=(FC+D)/(p-v)
Chapter 8
Strategy and analysis in using NPV
8.4.4 Using for the accounting break-even
To illustrate how accounting break-even can be used,
suppose that we are a small specialty manufacturer with
a strictly local distribution,We are thinking about
expanding into new market,Based on the estimated cash
flows,we find that the expansion has a positive NPV.
Going back to our discussion of forecasting risk,it is
likely that what will make or break our expansion is
sales volume,Because we probably have a fairly good
idea of what we can charge for the production,
Chapter 8
Strategy and analysis in using NPV
Given the costs and selling price,we can immediately
calculate the break-even point,
There are several other reasons why knowing the accounting
break-even can be useful,First,as we discuss in more detail
below,accounting break-even and payback period are very
similar measures,They all easy to calculate and explain.
Second,managers are often concerned with the contribution
a project will make to firm’s total accounting earnings,A
project that does not break even in an accounting sense
actually reduces total earnings.
Third,a project that just break even on an accounting basis
loses money in a financial or opportunity cost sense,This is
true because we could have earned more by investing
elsewhere,
Chapter 8
Strategy and analysis in using NPV
8.5 Operating cash flow,sales volume,and break-even
We need to know more about the relationship between sales
volume and cash flow than just the accounting break-even,
In this section we will to illustrate the relationship between
operating cash flow and sales volume,We also discuss some
other break-even measures,And we will ignore taxes,
8.5.1 Accounting break-even and cash flow
The basic case
A corporation want to determined whether or not to
launch its new production,The selling price will be
$40000 per unit,The variable costs will be about half
that,and fixed costs will be $500000 per year.
Chapter 8
Strategy and analysis in using NPV
The total investment is $3500000 and have five years life,
The salvage value is zero,and there are no working
capital consequences,The company has a 20% required
return on this project.
Based on market surveys and historical experience,the
project total sales for the five years at 425 unit,or about 85
per year,Ignoring taxes,should this project be launched?
OCF=EBIT + depreciation – taxes=(S-VC-FC-D)+D-0
= $1,200,000
NPV= -3500000+1200000(P/A,0.2,5)= 88720
Calculating the break-even level
Q=(FC+D)/(P-v)=(500000+700000)/(40000-20000)
=60 units per year to break-even on an accounting basis.
Chapter 8
Strategy and analysis in using NPV
Payback and break-even
Whenever a project breaks even on an accounting basis,
the cash flow for that period will be equal to the
depreciation and internal rate of return exactly zero,
And this example shows that a project’s payback period is
exactly equal to its life if the project breaks even every
period,Similarly,that a project that does better than
break-even has a payback that is shorter than the life of
the project and has a positive rate of return.
The bad news is that a project that just breaks even on an
accounting basis has a negative NPV and a zero return.
Chapter 8
Strategy and analysis in using NPV
8.5.2 Sales volume and operating cash flow
At this point,we can generalize our example and
introduce some other break-even measures,From our
discussion just above,we know that,ignore taxes,a
project’s OCF can be written simply as EBIT plus
depreciation.
OCF=[(P-v)× Q-FC-D]+ D
=(P-v)× Q –FC
For the example,the general relationship between OCF
and sales volume is that:
OCF=(40000-20000)Q-500000= -500000+20000Q
Chapter 8
Strategy and analysis in using NPV
8.5.3 Cash flow,accounting,and financial break-
even points
Because OCF= (P-v)× Q –FC,if we rearrange this and
solve it for Q,we could get:
Q=(FC+OCF)/(P-v)
This tell us what sales volume(Q) is necessary to achieve
any given OCF,so this result is more general than the
accounting break-even,We use it to find the various
break-even point.
Chapter 8
Strategy and analysis in using NPV
OCF
Quantity sold
Cash
break-even AccountingBreak-even Financial Break-even
Chapter 8
Strategy and analysis in using NPV
Accounting break-even revisited
Looking the figure,suppose OCF was equal to
depreciation(D),Recall that this corresponds to our
break-even point on an accounting basis,To find the
sales volume,we substitute the 700000depreciation
amount for OCF in our general expression.
Q=(FC+OCF)/(P-v) =60,
That is the same quantity we had before.
Cash break-even
Cash break-even is the sales level that results in a zero
OCF.
Chapter 8
Strategy and analysis in using NPV
Q=(FC+0)/(P-v) =25
That is the corporation must sell 25 units to cover the
fixed costs,As we show in the figure,this point occurs
right where the OCF line crosses the horizontal axis.
Notice that a project that just breaks even on a cash flow
basis can cover its own fixed costs,but that is all,It
never pays back anything so the original investment is a
complete loss.
Financial break-even
Financial break-even is the sales level that result in a zero
NPV.
Chapter 8
Strategy and analysis in using NPV
To the financial manager,this is the most interesting case,
What we do is first determine what OCF has to be for
the NPV to be zero,We then use this amount to
determine the sales volume.
To illustrate,recall that the company required a 20%
required return on its 3500000 investment,How many
productions does the company have to sell to breaks
even once we account for the 20% per year opportunity
costs?
3500000=OCF(P/A,0.2,5)
OCF=3500000/2.9906=1170000
Chapter 8
Strategy and analysis in using NPV
The company need an OCF of 1170000 each year to break
even,We can mow plug this OCF for sales volume:
Q=83.5,This is not a good news.
Conclusion
How much confidence do we have in our project?
How important is the project to the future of the company?
How badly will the company be hurt if sales do turn out to
be low? What options are available to the company this
case?
Chapter 8
Strategy and analysis in using NPV
8.6 Operating leverage
8.6.1 The basic idea
Operating leverage is the degree to which a project or
firm is committed to fixed production costs,A firm with
low operating leverage will have low fixed costs
compared to a form with high operating leverage,
Generally speaking,projects with relatively heavy
investment in plant and equipment will have a relatively
high degree of operating leverage,Such projects are said
to be capital intensive.
Chapter 8
Strategy and analysis in using NPV
8.6.2 Implication of operating leverage
Regardless of how it is measured,operating leverage has
important implications for project evaluation,Fixed
costs act like a lever in the sense that a small percentage
change in operating leverage can be magnified into a
large percentage change in OCF and NPV,This explains
why we call it operating ―leverage.‖
The higher the degree of operating leverage,the greater is
the potential danger from forecasting risk,The reason is
that relatively small errors in forecasting sales volume
can get magnified or ―levered up‖ into large errors in
cash flow projections.
Chapter 8
Strategy and analysis in using NPV
From a managerial perspective,one way of coping with
highly uncertain projects is to keep the degree of
operating leverage as low as possible,This will
generally have the effect of keeping the break-even
point (however measured) at its minimum level,We will
illustrate this point below,but first we need to discuss
how to measure operating leverage.
8.6.3 Measuring operating leverage
The degree of operating leverage(DOL) is one way of
measuring operating leverage,Degree of operating
leverage is the percentage change in OCF relative to
the percentage change in quantity sold,The DOL is
defined such that
Percentage change in OCF=DOL × percentage change in
Q
Chapter 8
Strategy and analysis in using NPV
Because if Q goes up by 1 unit,OCF will go up by (P-v),
So the percentage change in Q is 1/Q,and the
percentage change in OCF is (P-v)/OCF,Given this we
have:
Percentage change in OCF = DOL × percentage change in
Q
(P-v)/OCF = DOL × (1/Q),
DOL =(P-v) × Q/OCF,
and OFC+FC=(P-v) × Q
so DOL=1+ FC/OCF
Chapter 8
Strategy and analysis in using NPV
The ratio FC/OCF simply measures fixed costs as a
percentage of total OCF,Notice that zero fixed costs
would result in a DOL of 1,implying that percentage
changes in would show up one for one in OCF,That is
no magnification or leverage effect would exist.
Our formulation of DOL depends on the current output level,
Q,However,it can handle changes from the current level
of any size,not just one unit,
The reason DOL declines is that fixed costs,considered as a
percentage of OCF,get smaller and smaller,so that the
leverage effect diminishes,
8.6.4 Operating leverage and break-even
Chapter 8
Strategy and analysis in using NPV
8.7 Additional considerations in capital budgeting
8.7.1 Managerial options and capital budgeting
In our capital budgeting analysis thus far,we have more
or less ignored the possibility of future managerial
actions.
Implicitly,we assumed that once a project is launched,its
basic feature can not be changed,For this reason,we say
that our analysis is static(as opposed to dynamic).
In reality,depending on what actually happens in the future,
there will always be ways to modify a project,We will call
these opportunities managerial options.
Chapter 8
Strategy and analysis in using NPV
Managerial options is the opportunities that managers can
exploit if certain things happens in the future.
Contingency planning
– The option to expand
– The option to abandon
– The option to wait
Strategic options
8.7.2 Capital rationing
Capital rationing is said to exist when we have profitable
investment available but we can not get the need funds
to undertake them,
Capital rationing is the situation that exists if a firm has
positive NPV projects but can not find the necessary
financing.
Chapter 8
Strategy and analysis in using NPV
– Soft rationing
Soft rationing is the situation that occurs when units in
a business are allocated a certain amount of financing for
capital budgeting.
Hard rationing
Hard rationing is the situation that occurs when a
business cannot raise financing for a project under any
circumstances,
8.8 Decision trees
Expected payoff = (probability of success × payoff if
successful) + （ probability of failure × payoff if failure ）
Chapter 8
Strategy and analysis in using NPV
8.10 Summary and conclusions
– NPV estimates depend on projected future cash flows,
– Scenario and sensitivity analysis are useful tools for
identifying which variables are critical to a project and
where forecasting problems can do the most damage.
– Break-even analysis in its various forms is a particularly
common type of scenario analysis that is useful for
identifying critical levels of sales.
– Operating leverage is a key determinant of break-even
levels,It reflects the degree to which a project or a firm is
committed to fixed costs,The degree of operating leverage
tells us the sensitivity of OCF to changes in sales volume.
Chapter 8
Strategy and analysis in using NPV
– Project usually have future managerial options associated
with them,These options may be very important,but
standard discounted cash flow analysis tends to ignore
them.
– Capital rationing occurs when apparently profitable
projects cannot be funded,Standard discounted cash flow
analysis is troublesome in this case,Because NPV is not
necessarily the appropriate criterion anymore.
Net Present Value & Capital Budgeting
Chapter 7
Net Present Value and Capital Budgeting
– In this chapter we will describe how to actually do
a net present value and discounted cash flows
analysis for capital budgeting.
– The primary aim of this part is to describe how to
identify a project’s incremental cash flows,
– In this part we also discusses how to handle such
as sunk costs,opportunity costs,financing costs,
net working capital,and erosion.
Chapter 7
Net Present Value and Capital Budgeting
7.1 Project cash flows,a first look
7.1.1 Relevant cash flows
A relevant cash flows for a project is a change in the
firm’s overall future cash flow that comes about as a
direct consequence of the decision to take that project.
The relevant cash flow also called the incremental cash
flows associated with the project.
Incremental cash flows is the difference between a
firm’s future cash flows with a project or without the
project.
Chapter 7
Net Present Value and Capital Budgeting
The concept of incremental cash flow is central to our
analysis,so we will state a general definition and refer
back to it,
The incremental cash flows for project evaluation consist
of any and all changes in the firm’s future cash flows that
are a direct consequence of taking the project.
7.1.2 The stand-alone principle
Once we identify the effect of undertaking the proposed
project on the firm’s cash flows,we need only focus on
the project’s resulting incremental cash flows.this is
called the stand—alone principle.
The Stand—alone principle refers to the rule that
evaluation of a project based on the project’s
incremental cash flows.
Chapter 7
Net Present Value and Capital Budgeting
What the stand—alone principle says is that,once we
have determined the incremental cash flows from
undertaking a project,we can view that project as a
kind of ―minifirm‖with its own future revenues and
costs,its own assets,and of course,its own cash flows,
We will then be primarily interested in comparing the
cash flows from this minifirm to the cost of acquiring it.
An important consequence of this approach is that we will
be evaluating the proposed project purely on its own
merits,in isolation from any other activities or projects.
Chapter 7
Net Present Value and Capital Budgeting
7.2 Incremental cash flows
7.2.1 Sunk costs
A cost that has already been incurred and and can
not be removed and therefore should not be
considered in an investment decision.
7.2.2 Opportunity cost
The most valuable alternative that is given up if a
particular investment is undertaken.
7.2.3 Side effects
Erosion is the cash flows of a new project that
come at the expense of all firm’s existing projects.
Chapter 7
Net Present Value and Capital Budgeting
7.2.4 Net working capital
7.2.5 Financing costs
Some conclusions of incremental cash flows
When we estimate cash flows on an incremental
basis,we should learn by heart that
Do not confuse average with incremental payoffs.
Include all incidental effects
Do not forget working capital requirements,
Include opportunity costs.
Forget sunk costs
Beware of allocated overhead costs.
Chapter 7
Net Present Value and Capital Budgeting
7.3 Pro forma financial statements and project
cash flows
The first thing we need when we begin evaluating a
proposed investment is a set of pro forma or
projected financial statements.
7.3.1 Getting started,pro forma financial
statements
Pro forma financial statements are those
financial statements projecting future years’
operations.
Chapter 7
Net Present Value and Capital Budgeting
To prepare these statements,we will need estimates
of quantities such as unit sales,the selling price per
unit,the variable cost per unit,and total fixed costs,
We also need to know the total investment
required,including any investment in net working
capital.
Suppose we think we can sell something 50000cans
per year at a price of $4.00per unit,It costs us
about $2.50per can,and a new product such as this
one has only a three-year life,We require a 20%
return on new products,The other factors are
given like the next page.
Chapter 7
Net Present Value and Capital Budgeting
Projected income statements of special firm
Sales $200000
Variables costs 125000
75000
Fixed costs 12000
Depreciation 30000
EBIT 33000
Taxes (34%) 11220
Net income 21780
Chapter 7
Net Present Value and Capital Budgeting
Projected capital requirements of special project
Year
0 1 2 3
Net
working
capital
$20000 20000 20000 20000
Net fixed
assets
90000 60000 30000 0
Total
investment
110000 80000 50000 20000
Chapter 7
Net Present Value and Capital Budgeting
7.3.2 Project cash flows
Project cash flow =project operating cash flow –project
additions to net working capital – project capital
spending
Project Operating Cash Flow (51780)
Operating cash flow = EBIT+ Depreciation – Taxes
Projected Net Working Capital and Capital Spending
Chapter 7
Net Present Value and Capital Budgeting
Project total cash flows
Year
0 1 2 3
Operating cash
flows
51780 51780 51780
Addition to
NWC
-20000 20000
Capital
spending
-90000
Total cash
flows
-110000 51780 51780 71780
Chapter 7
Net Present Value and Capital Budgeting
7.3.3 Projected total cash flow and value
NPV=project cash flows (P/F,i,n)
NPV=10648
The return of this project will exceeds 20%
because the NPV which computed with
20% is over $1000,The project not only
could be acceptable,but also exceed which
we want,If we could calculated,we would
find that the IRR will near 26%.
Chapter 7
Net Present Value and Capital Budgeting
7.4 More on project cash flow
7.4.1 A closer look at net working capital
In this section we will ignore the no depreciation,no taxes,
no fixed assets investments.
Sales $500
Costs 310
Net income $190
Depreciation and taxes are zero,No fixed assets are
purchased during the year,So we will only talk about the
NWC (accounting receivable and payable).
Chapter 7
Net Present Value and Capital Budgeting
Beginning of year End of year Change
Accounts receivable $880 $910 +$30
Accounts payable 550 605 +55
Net working capital 330 305 -25
Total cash flow = $215[190-(-25)]
Now we could ask a question,what were cash flow
revenues for the year? Also what were cash costs?
Sales are 500,but accounting receivable rose by 30 over
the year,so our cash flows is only 500-30=470.
Chapter 7
Net Present Value and Capital Budgeting
Cash flows out can be similarly determined,cost is 310,
but accounts payable increased by 55,this means that
we have not yet paid 55of the 310,so cash costs for the
period are just 310-55=255.
Putting this information together,cash inflows less cash
outflows is 470-255=215,just we had before,Now we
could notice that:
Cash flow =cash inflow- cash outflow=operating cash
flow –change in net working capital
Chapter 7
Net Present Value and Capital Budgeting
Example for cash collections and costs
For the year just completed,corporation CWT reports sales of
998 and costs of 734,You have collected the following
beginning and ending balance sheet information:
Beginning Ending
Accounts receivable 100 110
Inventory 100 80
Accounts payable 100 70
Net Working Capital 100 120
Chapter 7
Net Present Value and Capital Budgeting
Cash inflows:
998-10=988
Cash outflows
734-20+30=744
Net cash flows
988-744=244
Cash flows
(998-734)-(120-100)=244
Chapter 7
Net Present Value and Capital Budgeting
7.4.2 Depreciation
Accounting depreciation is a noncash deduction,As a
result,depreciation has cash flow consequences
only because it influences the tax bill.
Accelerated cost recovery system(ACRS) is a
depreciation method under U.S,tax law allowing
for the accelerated write-off of property under
various classifications,
Modified ACRS depreciation
Calculating depreciation is normally very mechanical,
Once an asset’s tax life is determined the
depreciation for each year is computed by
Chapter 7
Net Present Value and Capital Budgeting
Modified ACRS property classes
Class Examples
3—year Equipment used in research
5—year Autos,computers
7—year Most industrial equipment
Chapter 7
Net Present Value and Capital Budgeting
Modified ACRS depreciation allowances
Year Property class
3—year 5—year 7—year
1 33.33 20.00 14.29
2 44.44 32.00 24.49
3 14.82 19.20 17.49
4 7.41 11.52 12.49
5 11.52 8.93
6 5.76 8.93
7 8.93
8 4.45
Chapter 7
Net Present Value and Capital Budgeting
Year ACRS percentage Depreciation
1 20.00,2000× 12000＝ 2400.00
2 32.00,3200× 12000＝ 3840.00
3 19.20,1920× 12000＝ 2304.00
4 11.52,1152× 12000＝ 1382.40
5 11.52,1152× 12000＝ 1382.40
6 5.76,05.76× 12000＝ 691.20
100.00 12000
Chapter 7
Net Present Value and Capital Budgeting
multiplying the cost of the asset by a fixed percentage,
The expected salvage value(what we think the asset
will be worth when we dispose of it) and the actual
expected economic life(how long we expect the asset
to be in service) are not explicitly considered in the
calculation of depreciation.
Book value versus market value
In calculating depreciation under current tax,the
economic life and future market value of the asset
are not an issue,As a result,the book value of an
asset can differ substantially from its actual market
value.
Chapter 7
Net Present Value and Capital Budgeting
ACRS book values
Year Beginning BV Depreciation Ending BV
1 12000.00 2400.00 9600.00
2 9600.00 3840.00 5760.00
3 5760.00 2304.00 3456.00
4 3456.00 1382.40 2073.60
5 2073.60 1382.40 691.20
6 691.20 691.20 0.00
Chapter 7
Net Present Value and Capital Budgeting
Because the tax rate is different from capital gain rate,
As a general rule,a capital gain only occurs if the
market price exceeds the original cost.
7.5 Alternative definitions of operating cash flow
The analysis we have been through in the previous section
is quite general and can be adapted to just about any
capital investment problem,In the next we illustrate
some particularly useful variations.
First we should to discuss the fact that there are different
definitions of project operating cash flow that are
commonly used,Both in practice and in financial texts.
Chapter 7
Net Present Value and Capital Budgeting
Some basic information:
Sales = $1500,Costs = 700,Depreciation = 600,Tax
rate = 34%,
OCF = $732.
7.5.1 The Bottom-UP approach
Since we are ignoring any financial expenses such
as interest,then project net income will be
EBIT- taxes =132
If we simply add the depreciation to both sides,we
arrive at a slightly different and very common
expression for OCF:
OCF=net income + depreciation
Chapter 7
Net Present Value and Capital Budgeting
This is the bottom-up approach,Here we start with the
accountant’s bottom line(net income) and add back any
noncash deductions(depreciation).
It is crucial to remember that this definition of OCF as
net income plus depreciation is correct only if there is no
interest expense subtracted in the calculation of net
income.
7.5.2 The Top-Down approach
OCF= sales – costs – taxes,That is the top-down approach,
Here we start at the top of the income statement
Chapter 7
Net Present Value and Capital Budgeting
with sales and work our way down to net cash flow
by subtracting costs,taxes,and other expenses,
Along the way we simply leave out any strictly
noncash items(depreciation).
7.5.3 The Taxes Shield approach
This approach will be very useful for some problems
we consider in the next section,The taxes shield
definition of OCF is
OCF = (sales - costs)× (1-taxes rate)+ depreciation×
taxes rate
This approach views OCF as having tow
components
Chapter 7
Net Present Value and Capital Budgeting
The first part is what the project’s cash flow would
be if there were no depreciation expense,In this
case this would be have been cash flow is ---.
The second part in this case is the depreciation
deduction multiplied by the tax rate,This is called
the depreciation tax shield,
Depreciation tax shield Tax saving that results from
the depreciation deduction,calculated as
depreciation multiplied by the corporate tax rate.
Because the depreciation is a noncash expense,The
only cash flow effect from deducting depreciation is
to reduce our taxes,a benefit to us.
Chapter 7
Net Present Value and Capital Budgeting
7.6 Some special cases of discounted cash flow
analysis
7.6.1 Evaluating Cost-Cutting proposals
Cost is the important factor that every factories must
be pay attention to,
Suppose we are considering automating some part of
any existing production process,The necessary
equipment costs $80000 to buy and install,It will save
22000per year,For simplicity assume that the
equipment has a five-year life and is depreciated to
zero on a straight-line basis over that period.
Should we do it? The tax rate is 34% and the discount
rate is 10%,
Chapter 7
Net Present Value and Capital Budgeting
The first step in making this decision is to identify
the relevant incremental cash flows,First is
determining the relevant capital spending,the
initial cost is $80000,the aftertax salvage value is
20000(1-,34)=13200,Second there are no working
capital so we do not need to think about additions
to net working capital,OCF is the third component,
Buying new equipment affect OCF in tow ways,
First we save 22000 per year,that is the firm’s
operating income increases by 22000,so this is the
relevant incremental project operating income,
Second we have an additional depreciation
deduction,The depreciation is 16000.
Chapter 7
Net Present Value and Capital Budgeting
Since the project has an operating income of $22000 and a
depreciation deduction of $16000,taking the project will
increase the firm’s EBIT by 22000-16000=6000,so this
is the project’s EBIT.
Finally since EBIT is rising for the firm,taxes will increase
and this increase in taxes will be $6000× 0.34=2040,
then OCF=EBIT+depreciation –taxes=19960
It might be somewhat more enlightening to calculate
operating cash flow using a different approach,What is
actually going on here is very simple.
Chapter 7
Net Present Value and Capital Budgeting
First of all,the cost savings increase our pretax income by
22000,We have to pay taxes on this amount,so our tax
bill increases by 0.34× 22000=7480,In other words,the
22000 pretax saving amounts to 14520.
Second,the extra 16000 in depreciation is not really a
cash outflow,but it dose reduce our taxes by
16000× 0.34=5400,the sum of these tow components is
14520+5440 = 19960,just as we had before,Notice that
5440 is the depreciation tax shield we discussed above,
and we have effectively used the tax shield approach
here.
Chapter 7
Net Present Value and Capital Budgeting
At 10 percent of discounted rate,it’s straightforward to
verify that the NPV here is 3860.
– An example to determine ―to buy or not to buy‖?
A firm want to buy a 200000 computer—based inventory
management system,It will be depreciated straight—line to
zero over its four—year life,It will be worth 30000 at that
time,The system would save 60000 pretaxes costs.
0 1 2 3 4 5
OCF 19960 19960 19960 19960 19960
C.P,-80000 13200
TCF -80000 19960 19960 19960 19960 33160
Chapter 7
Net Present Value and Capital Budgeting
The relevant tax rate is 39%,And this system will free up
45000 in net working capital,
What is the NPV at 16 percent?(-12768) What is the DCF
return on this investment?(11.5%)
First we can calculate the OCF,OCF =36600+19500=56100
Secondly is the capital spending.
0 1 2 3 4
OCF 56100 56100 56100 56100
ANWC 45000 -45000
C.S -200000 18300
TCF -155000 56100 56100 56100 29400
Chapter 7
Net Present Value and Capital Budgeting
7.6.2 Setting the bid price
In some market economic behavior,we should employ
competitive bid to win a job,and the winner is whoever
submit the lowest bid.
There is an old saw concerning this process,the low
bidder is whoever makes the bigger mistake,This is
called the winner’s curse,In other words,if you win,
there is a good chance that you underbid,
Suppose you want to sell five trucks each year for the next
four years by bid,Each truck platform could expend
$10000,The facilities you need can be leased for
$24000per year,the labor and material cost to do
Chapter 7
Net Present Value and Capital Budgeting
the works out to be about $4000 per truck,
Then the total cost per year will thus be
$24000+(10000+4000)× 5=94000
You will need to invest $60000 in new equipment and this
equipment will be depreciated straight-line to a zero
salvage value over the four years,It will be worth about
$5000 at that time,We also need to invest $40000 in raw
materials inventory and other working capital items,
The relevant tax rate is 39%,
What price per truck should we bid if you require a 20%
return on this investment?
Chapter 7
Net Present Value and Capital Budgeting
The computed years
0 1 2 3 4
Operating
cash flow
OCF OCF OCF OCF
Additions to
NWC
-40,000 +40,000
Capital
spending
-60,000 3050
Total cash
flow
-100,000 OCF OCF OCF OCF
+43,050
Chapter 7
Net Present Value and Capital Budgeting
The aftertax salvage value is $5000× (1-,39)=3050.
With this in mind,there is the key observation,The
lowest possible price you can profitably charge will
result in a zero NPV at 20%,So you should to
determine what the OCF must be for the NPV to
be equal to zero.
100000-43050(P/F,i,n)=79239,the the pro forma
changed like this:
Total cash flow,-79239,OCF(1~4)
NPV= -79239+OCF(P/A,i,n)=0
OCF= 30609
Chapter 7
Net Present Value and Capital Budgeting
OCF= Net income + Depreciation
Net income = 30609-15000 =15609
Net income = (sales – costs -depreciation)× (1-T)
= (sale – 94000-15000)× 0.61
Sales = 134589
The sales price has to be $26918 per unit.
So if you round this up a bit,it could to bid about exceed
$27000 per unit.
7.6.3 Evaluating equipment with different lives
In this section,our goal is to choose the most cost-effective,
The approach we consider here is only necessary when
tow special circumstances exist,
Chapter 7
Net Present Value and Capital Budgeting
First is the possibilities under evaluation have different
economic lives,Second and just as important,we need
whatever we buy more or less indefinitely,
We can illustrate this problem with a simple example,
Machine A costs $100 to buy and $10 per year to operate,It
wears out and must be replaced every two years.
Machine B costs $140 to buy and $8 per year to operate,It
last for the three years and must be replaced,Ignoring
taxes,which one should we go with if we use a 10%
discount rate?
Chapter 7
Net Present Value and Capital Budgeting
MAPV= -100+[ -10(P/F,i,n)]+[ -10(P/F,i,n)]= -117.36
MBPV= -140+[-8(P/F,i,n)] + [-8(P/F,i,n)] = -159.89
We could not determine which on is better because that
only computed the cost with different service periods,
And we need to work out a cost per year for these tow
alternatives,We should use the equivalent annual
cost(EAC),
The equivalent annual cost is the present value of a
project’s costs calculated on an annual basis.
Calculating the EAC involves finding an unknown
payment amount.
Chapter 7
Net Present Value and Capital Budgeting
For Machine A,we need to find a tow-year ordinary
annuity with a PV of –117.36 at 10%,
PV of costs A = -117.36 = EAC× (P/A,0.1,2)
EAC= -117.36/1.7355= -67.62
For Machine B,we need to find a three-year
ordinary annuity with a PV of –159.89 at 10%.
PV of costs A = -159.89 = EAC× (P/A,0.1,3)
EAC= -159.89/2.4869 = -64.29
Chapter 7
Net Present Value and Capital Budgeting
Example for evaluating with different lives
A filtration system will cost 1100000,and 60000
pretax annually to operate,It will have 5 years,An
other precipitation system will cost 1900000,but
only 10000 per year to operate,the precipitation
has 8 years life.
They all have no salvages,Which method should we
select if we use 12% discounted rate? The tax rate
is 34%.
Chapter 7
Net Present Value and Capital Budgeting
Filtration system Precipitation
system
Aftertax operating
cost
-39600 -6600
Depreciation tax
shield
74800 80750
OCF 35200 74150
Economic life 5 8
Annuity factor12% 3.6048 4.9676
PV of OCF 126.88 369350
Capital spending -1100000 -1900000
Total CF -973112 -1531650
Chapter 7
Net Present Value and Capital Budgeting
Filtration system’s EAC
-973112=EAC × 3.6048
EAC=-269949 per year
Precipitation system’s EAC
-1531650=EAC × 4.9676
EAC= -308328 per year
Chapter 7
Net Present Value and Capital Budgeting
7.7 Inflation and capital budgeting
7.7.1 Interest rate and inflation
– Real interest rate and nominal interest rate
Real interest rate =Nominal interest rate – inflation rate
7.7.2 Cash flow and inflation
7.7.3 Discounting,nominal or real?
1a t ei n f l a t i o n r1 r a t ei n t e r e s t n o m i n a l 1 r a t ei n t e r e s t r e a l
Chapter 7
Net Present Value and Capital Budgeting
Summary and conclusions
– The identification of relevant cash flows,
– Preparing and using pro forma or financial statements,
From these we could calculating the project cash flows and
operating cash flows.
– The role of net working capital and depreciation in project
cash flows,
– Some special cases in using discounted cash flow analysis.
Chapter 8
Strategy and analysis in using NPV
Chapter 8
Strategy and analysis in using NPV
8.1 Introductions
In previous parts,we discussed how to identify and
organize the relevant cash flows for capital investment
decisions,In these part we focus on assessing the
reliability of such an estimate and on some additional
considerations in project analysis.
We begin by discussing the need for an evaluation of cash
flow and NPV estimates,We go on to develop some
tools that are useful for doing so,We also examine some
additional complications and concerns that can arise in
project evaluation.
Chapter 8
Strategy and analysis in using NPV
8.2 Corporate strategy and positive NPV
8.2.1 The basic problems
A significant part of corporate strategy analysis is seeking
investment opportunities that can produce positive NPV.
But there two circumstances under which a discounted
cash flow analysis could lead us to conclude that a
project has a positive NPV,The first possibility is that
the project really does have a positive NPV,The second
possibility is a project may appear to have a positive
NPV because our estimate is inaccurate,
If we conclude that a project has a negative NPV when the
true NPV is positive,we lose a valuable opportunity.
Chapter 8
Strategy and analysis in using NPV
8.2.2 How to create positive NPV
Be the first to introduce a new product.
Further develop a core competency to produce goods or
services at lower cost than competitors.
Create a barrier that makes it difficult for other firms to
compete effectively.
Introduce variations on existing products to take
advantage of unsatisfied demand.
Create product differentiation by aggressive advertising
and marketing networks
Use innovation in organizational processes to do all of
the above.
Chapter 8
Strategy and analysis in using NPV
8.2.3 corporate strategy and the stock market
There should be a connection between the stock market
and capital budgeting,If a firm invests in a project that
is worth more than its costs,the project will produce
positive NPV,and the firm’s stock price should go up,
8.2.4 Forecasting risk
The key inputs into a DCF analysis are projected future
cash flows,If these projections are seriously in error,
then we have a classic GIGO(garbage-in,garbage-out)
system,
The possibility that we make a bad decision because of
errors in the projected cash flows is called forecasting
risk(or estimation risk),
Forecasting risk is the possibility that errors in projected
cash flows lead to incorrect decisions.
Chapter 8
Strategy and analysis in using NPV
Because of forecasting risk,there is the danger that
we think a project has a positive NPV when it really
does not,
8.3 Scenario and other ―what if‖ analysis
Our basic approach to evaluating cash flow and NPV
estimates involves asking ―what if‖ questions,
Accordingly,we discuss some organized ways of going
about a what-if analysis,Our goal in doing so is to
assess the degree of forecasting risk and to identify
those components that are the most critical to the
success or failure of an investment.
Chapter 8
Strategy and analysis in using NPV
8.3.1 Getting started
We are investigating a new project,Naturally,the
first thing we do is estimate NPV based on our
projected cash flows,We will called this the basic
case,
One way to organize this investigation is to put an
upper and lower bound on the various components
of the project,For example,suppose we forecast
sale at 100 units per year,We know this estimate
may be high or low,but we are relatively certain
that it is not off by more than 10 units in either
direction,
Chapter 8
Strategy and analysis in using NPV
We would thus pick a lower bound of 90 and an upper
bound of 110,
With this basic cases,we can calculate the example which
we have had the last text.
8.3.2 Scenario analysis
The basic form of what-if analysis is called scenario
analysis,Scenario analysis is the determination of what
happens to NPV estimates when we ask what-if questions.
What we do is investigate the changes in our NPV
estimates that result from asking questions like this.
Chapter 8
Strategy and analysis in using NPV
There are a number of possible scenarios we could consider,
A good place to start is the worst-case scenario,This will
tell us the minimum NPV of the project,If this were
positive,we would be in good shape,While we are at it,we
will go ahead and determine the other extreme,the best
case,This puts an upper bound on our NPV.
To get the worst case,we assign the least favorable value to
each item,This means low values for items like units sold
and price per unit and high values for costs.we do the
reverse for the best case.
Chapter 8
Strategy and analysis in using NPV
As we have mentioned,there is an unlimited number of
different scenarios that we could examine,At a minimum,
we might want to investigate two intermediate cases by
going halfway between the base amounts and the extreme
amounts,This would give us five scenarios in all,including
the base case.
Beyond this point,it is hard to know when to stop,As we
generate more and more possibilities,we run the risk of
―paralysis of analysis.‖ The difficulty is that no matter
how many scenarios we run,all we can learn are
possibilities,some good and some bad.
Chapter 8
Strategy and analysis in using NPV
A example for base case and scenario analysis
The project under consideration costs 200,000,has five—year
life,and no salvage value,Depreciation is straight—line to
zero,The required return is 12 percent,and the tax rate is
34 percentage,In addition,we have have compiled the
following information.
Base case Lower case Upper case
Unit sales 6,000 5500 6500
Price per unit 80 75 85
Variable costs
per unit
60 58 62
Fixed costs per
year
50,000 45,000 55,000
Chapter 8
Strategy and analysis in using NPV
So we can calculate the base—case NPV by these:
So the base—case NPV= -200000+59800(P/A,12%,5) =15567
Sales 480000
Variable costs 360000
Fixed costs 50000
Depreciation 40000
EBIT 30000
Taxes 10200
Net income 19800
Chapter 8
Strategy and analysis in using NPV
Worst case Best case
Unit sales 5500 6500
Price per unit 75 85
Variable costs
per unit
62 58
Fixed costs 55000 45000
Chapter 8
Strategy and analysis in using NPV
Scenario Net income Cash flow Net
present
value
IRR
Base case 19800 59800 25567 15.1
Worst case -15510 24490 -11719 -14.4
Best case 59730 99730 159504 40.9
At the worst case a tax credit is created,Otherwise the EBIT
will be -23500
Chapter 8
Strategy and analysis in using NPV
Scenario analysis is thus useful in telling us what can
happen and in helping us gauge the potential for
disaster,but it does not tell us whether or not to take the
project.
8.3.3 Sensitivity analysis
Sensitivity analysis is a variation on scenario analysis that
is useful in pinpointing the areas where forecasting risk
is especially severe,
The sensitivity analysis is the investigation of what
happens to NPV when only one variable is changed.
Chapter 8
Strategy and analysis in using NPV
The basic idea with a sensitivity analysis is to freeze all of the
variables expect one and then see how sensitive our
estimate of NPV is to changes in that one variable,If our
NPV estimate turns out to be very sensitive to relatively
small changes in the projected value of some component of
project cash flow,then the forecasting risk associated with
that variable is high.
Because sensitivity analysis is a form of scenario analysis,it
suffers from the same drawbacks,Sensitivity analysis is
useful for pointing out where forecasting errors will do the
most damage,but it does not tell us what to do about
possible errors.
Chapter 8
Strategy and analysis in using NPV
8.3.4 Simulation analysis
Simulation analysis is a combination of scenario and
sensitivity analysis,
If we want to let all the items vary at the same time,we
have to consider a very large number of scenarios,and
computer assistance is almost certainly needed,
Since simulation analysis is an extended form of scenario
analysis,it has the same problems,
8.4 Break-even analysis
Break-even analysis is a popular and commonly used tool for
analyzing the relationship between sales volume and
profitability,There are a variety of different break-even
measures,All break-even measures have a similar goal,
Chapter 8
Strategy and analysis in using NPV
8.4.1 Fixed costs and variable costs
Variable costs,are the costs that change when the
quantity of output changes,They would be zero when
production is zero,We will assume that variable costs
are a constant amount per unit of output.
The relationship between total variable costs(VC),cost
per unit of output(v),and total quantity of output(Q)
can be written as:
VC=v× Q
Fixed costs,are the costs that not change when the
quantity of output changes during a particular time
period.
Chapter 8
Strategy and analysis in using NPV
Naturally,fixed costs are not fixed forever,They are only
fixed during some particular time,beyond that time,
leases can be terminated and executives ―retired.‖
Total costs,total costs(TC) for a given level of output
are the sum of variable costs(VC) and fixed costs(FC):
TC=VC+FC
TC= v× Q+FC
Marginal or incremental cost is the change in costs that
occurs when there is a small change in output.
Marginal or incremental revenue is the change in revenue
that occurs when there is a small change in output.
Chapter 8
Strategy and analysis in using NPV
Total costs
Variable costs
Fixed costs
Quantity
of output
Chapter 8
Strategy and analysis in using NPV
8.4.2 Accounting break-even
Accounting break-even is the most widely used measures
of break-even,The accounting break-even point is
simply the sales level that results in a zero project net
income.
To determine a project’s accounting break-even point,we
start off with some common sense,Suppose we retail
something for $5 per unit,we can buy this from a
wholesale supplier for $3 per unit,We have accounting
expenses of $600 in fixed costs and $300 in depreciation,
How many the break-even point?
Chapter 8
Strategy and analysis in using NPV
5-3=2
Total accounting expenses is 300+600=900
So we can sell 900/2=450 units production.
Then the income statement will be
Sales 2250
Variable costs 1350
Fixed costs 600
Depreciation 300
EBIT 0
Taxes 0
Net income 0
Chapter 8
Strategy and analysis in using NPV
Remember,since we discussing a proposed new project,we
do not consider any interest expense in calculating net
income or cash flow from the project,
Also,notice that we conclude depreciation in calculating
expenses here,even though depreciation is not a cash
outflow,That is why we call it accounting break-even,
Finally,notice that when net income is zero,so are pretax
income and taxes,In accounting terms,our revenues are
equal to our costs,so there is no profit to tax.
Chapter 8
Strategy and analysis in using NPV
Sales and costs
Revenues
Total costs
BEP
Q Quantity of output
Chapter 8
Strategy and analysis in using NPV
8.4.3 Accounting break-even,a closer look
Some basic variables,
P =selling price per unit
v = variable cost per unit
Q =total unit sold
FC =fixed costs
D = depreciation
T =tax rate
Project net income is given by:
Net income =(sales-variable costs-fixed costs-depreciation)
× (1-T)
Chapter 8
Strategy and analysis in using NPV
(S-VC-FC-D)× (1-T)=0
Divided both sides by (1-T) to get:
S-VC-FC-D=0
S=PQ and VC= vQ,then we can rearrange this to solve for
the break-even level,
S-VC=FC+D
PQ-vQ =FC +D
(p-v)Q =FC+D
Q=(FC+D)/(p-v)
Chapter 8
Strategy and analysis in using NPV
8.4.4 Using for the accounting break-even
To illustrate how accounting break-even can be used,
suppose that we are a small specialty manufacturer with
a strictly local distribution,We are thinking about
expanding into new market,Based on the estimated cash
flows,we find that the expansion has a positive NPV.
Going back to our discussion of forecasting risk,it is
likely that what will make or break our expansion is
sales volume,Because we probably have a fairly good
idea of what we can charge for the production,
Chapter 8
Strategy and analysis in using NPV
Given the costs and selling price,we can immediately
calculate the break-even point,
There are several other reasons why knowing the accounting
break-even can be useful,First,as we discuss in more detail
below,accounting break-even and payback period are very
similar measures,They all easy to calculate and explain.
Second,managers are often concerned with the contribution
a project will make to firm’s total accounting earnings,A
project that does not break even in an accounting sense
actually reduces total earnings.
Third,a project that just break even on an accounting basis
loses money in a financial or opportunity cost sense,This is
true because we could have earned more by investing
elsewhere,
Chapter 8
Strategy and analysis in using NPV
8.5 Operating cash flow,sales volume,and break-even
We need to know more about the relationship between sales
volume and cash flow than just the accounting break-even,
In this section we will to illustrate the relationship between
operating cash flow and sales volume,We also discuss some
other break-even measures,And we will ignore taxes,
8.5.1 Accounting break-even and cash flow
The basic case
A corporation want to determined whether or not to
launch its new production,The selling price will be
$40000 per unit,The variable costs will be about half
that,and fixed costs will be $500000 per year.
Chapter 8
Strategy and analysis in using NPV
The total investment is $3500000 and have five years life,
The salvage value is zero,and there are no working
capital consequences,The company has a 20% required
return on this project.
Based on market surveys and historical experience,the
project total sales for the five years at 425 unit,or about 85
per year,Ignoring taxes,should this project be launched?
OCF=EBIT + depreciation – taxes=(S-VC-FC-D)+D-0
= $1,200,000
NPV= -3500000+1200000(P/A,0.2,5)= 88720
Calculating the break-even level
Q=(FC+D)/(P-v)=(500000+700000)/(40000-20000)
=60 units per year to break-even on an accounting basis.
Chapter 8
Strategy and analysis in using NPV
Payback and break-even
Whenever a project breaks even on an accounting basis,
the cash flow for that period will be equal to the
depreciation and internal rate of return exactly zero,
And this example shows that a project’s payback period is
exactly equal to its life if the project breaks even every
period,Similarly,that a project that does better than
break-even has a payback that is shorter than the life of
the project and has a positive rate of return.
The bad news is that a project that just breaks even on an
accounting basis has a negative NPV and a zero return.
Chapter 8
Strategy and analysis in using NPV
8.5.2 Sales volume and operating cash flow
At this point,we can generalize our example and
introduce some other break-even measures,From our
discussion just above,we know that,ignore taxes,a
project’s OCF can be written simply as EBIT plus
depreciation.
OCF=[(P-v)× Q-FC-D]+ D
=(P-v)× Q –FC
For the example,the general relationship between OCF
and sales volume is that:
OCF=(40000-20000)Q-500000= -500000+20000Q
Chapter 8
Strategy and analysis in using NPV
8.5.3 Cash flow,accounting,and financial break-
even points
Because OCF= (P-v)× Q –FC,if we rearrange this and
solve it for Q,we could get:
Q=(FC+OCF)/(P-v)
This tell us what sales volume(Q) is necessary to achieve
any given OCF,so this result is more general than the
accounting break-even,We use it to find the various
break-even point.
Chapter 8
Strategy and analysis in using NPV
OCF
Quantity sold
Cash
break-even AccountingBreak-even Financial Break-even
Chapter 8
Strategy and analysis in using NPV
Accounting break-even revisited
Looking the figure,suppose OCF was equal to
depreciation(D),Recall that this corresponds to our
break-even point on an accounting basis,To find the
sales volume,we substitute the 700000depreciation
amount for OCF in our general expression.
Q=(FC+OCF)/(P-v) =60,
That is the same quantity we had before.
Cash break-even
Cash break-even is the sales level that results in a zero
OCF.
Chapter 8
Strategy and analysis in using NPV
Q=(FC+0)/(P-v) =25
That is the corporation must sell 25 units to cover the
fixed costs,As we show in the figure,this point occurs
right where the OCF line crosses the horizontal axis.
Notice that a project that just breaks even on a cash flow
basis can cover its own fixed costs,but that is all,It
never pays back anything so the original investment is a
complete loss.
Financial break-even
Financial break-even is the sales level that result in a zero
NPV.
Chapter 8
Strategy and analysis in using NPV
To the financial manager,this is the most interesting case,
What we do is first determine what OCF has to be for
the NPV to be zero,We then use this amount to
determine the sales volume.
To illustrate,recall that the company required a 20%
required return on its 3500000 investment,How many
productions does the company have to sell to breaks
even once we account for the 20% per year opportunity
costs?
3500000=OCF(P/A,0.2,5)
OCF=3500000/2.9906=1170000
Chapter 8
Strategy and analysis in using NPV
The company need an OCF of 1170000 each year to break
even,We can mow plug this OCF for sales volume:
Q=83.5,This is not a good news.
Conclusion
How much confidence do we have in our project?
How important is the project to the future of the company?
How badly will the company be hurt if sales do turn out to
be low? What options are available to the company this
case?
Chapter 8
Strategy and analysis in using NPV
8.6 Operating leverage
8.6.1 The basic idea
Operating leverage is the degree to which a project or
firm is committed to fixed production costs,A firm with
low operating leverage will have low fixed costs
compared to a form with high operating leverage,
Generally speaking,projects with relatively heavy
investment in plant and equipment will have a relatively
high degree of operating leverage,Such projects are said
to be capital intensive.
Chapter 8
Strategy and analysis in using NPV
8.6.2 Implication of operating leverage
Regardless of how it is measured,operating leverage has
important implications for project evaluation,Fixed
costs act like a lever in the sense that a small percentage
change in operating leverage can be magnified into a
large percentage change in OCF and NPV,This explains
why we call it operating ―leverage.‖
The higher the degree of operating leverage,the greater is
the potential danger from forecasting risk,The reason is
that relatively small errors in forecasting sales volume
can get magnified or ―levered up‖ into large errors in
cash flow projections.
Chapter 8
Strategy and analysis in using NPV
From a managerial perspective,one way of coping with
highly uncertain projects is to keep the degree of
operating leverage as low as possible,This will
generally have the effect of keeping the break-even
point (however measured) at its minimum level,We will
illustrate this point below,but first we need to discuss
how to measure operating leverage.
8.6.3 Measuring operating leverage
The degree of operating leverage(DOL) is one way of
measuring operating leverage,Degree of operating
leverage is the percentage change in OCF relative to
the percentage change in quantity sold,The DOL is
defined such that
Percentage change in OCF=DOL × percentage change in
Q
Chapter 8
Strategy and analysis in using NPV
Because if Q goes up by 1 unit,OCF will go up by (P-v),
So the percentage change in Q is 1/Q,and the
percentage change in OCF is (P-v)/OCF,Given this we
have:
Percentage change in OCF = DOL × percentage change in
Q
(P-v)/OCF = DOL × (1/Q),
DOL =(P-v) × Q/OCF,
and OFC+FC=(P-v) × Q
so DOL=1+ FC/OCF
Chapter 8
Strategy and analysis in using NPV
The ratio FC/OCF simply measures fixed costs as a
percentage of total OCF,Notice that zero fixed costs
would result in a DOL of 1,implying that percentage
changes in would show up one for one in OCF,That is
no magnification or leverage effect would exist.
Our formulation of DOL depends on the current output level,
Q,However,it can handle changes from the current level
of any size,not just one unit,
The reason DOL declines is that fixed costs,considered as a
percentage of OCF,get smaller and smaller,so that the
leverage effect diminishes,
8.6.4 Operating leverage and break-even
Chapter 8
Strategy and analysis in using NPV
8.7 Additional considerations in capital budgeting
8.7.1 Managerial options and capital budgeting
In our capital budgeting analysis thus far,we have more
or less ignored the possibility of future managerial
actions.
Implicitly,we assumed that once a project is launched,its
basic feature can not be changed,For this reason,we say
that our analysis is static(as opposed to dynamic).
In reality,depending on what actually happens in the future,
there will always be ways to modify a project,We will call
these opportunities managerial options.
Chapter 8
Strategy and analysis in using NPV
Managerial options is the opportunities that managers can
exploit if certain things happens in the future.
Contingency planning
– The option to expand
– The option to abandon
– The option to wait
Strategic options
8.7.2 Capital rationing
Capital rationing is said to exist when we have profitable
investment available but we can not get the need funds
to undertake them,
Capital rationing is the situation that exists if a firm has
positive NPV projects but can not find the necessary
financing.
Chapter 8
Strategy and analysis in using NPV
– Soft rationing
Soft rationing is the situation that occurs when units in
a business are allocated a certain amount of financing for
capital budgeting.
Hard rationing
Hard rationing is the situation that occurs when a
business cannot raise financing for a project under any
circumstances,
8.8 Decision trees
Expected payoff = (probability of success × payoff if
successful) + （ probability of failure × payoff if failure ）
Chapter 8
Strategy and analysis in using NPV
8.10 Summary and conclusions
– NPV estimates depend on projected future cash flows,
– Scenario and sensitivity analysis are useful tools for
identifying which variables are critical to a project and
where forecasting problems can do the most damage.
– Break-even analysis in its various forms is a particularly
common type of scenario analysis that is useful for
identifying critical levels of sales.
– Operating leverage is a key determinant of break-even
levels,It reflects the degree to which a project or a firm is
committed to fixed costs,The degree of operating leverage
tells us the sensitivity of OCF to changes in sales volume.
Chapter 8
Strategy and analysis in using NPV
– Project usually have future managerial options associated
with them,These options may be very important,but
standard discounted cash flow analysis tends to ignore
them.
– Capital rationing occurs when apparently profitable
projects cannot be funded,Standard discounted cash flow
analysis is troublesome in this case,Because NPV is not
necessarily the appropriate criterion anymore.
