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FINS5514-无代写
时间：2024-03-09
UNSW Business School
School of Banking and Finance
FINS5514: Capital Budgeting and Financial
Decisions
Lecture 4: The Investment Decision III
Project Cash Flows II and Estimating Risk in
Capital Budgeting
1
• Pro-forma financial statements
• Depreciation
‒ Straight-line deprecation
‒ Modified accelerated cost recovery system
• Examples of capital budgeting decisions in
practice
• Break-even analysis
• Operating leverage
Outline
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2
• So far, it has been assumed that project cash
flows are known with certainty.
• What if this is not true?
– In reality it is often difficult to know what cash flows a
project will produce.
– So the cash flows must be estimated.
• Pro-forma statements are projected financial
statements
– They are used to produce projected cash flows from
the project which are then used for capital budgeting
decisions.
Pro-forma Financial Statements
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3
• Pro-forma statements require information on:
– Net capital spending
– Net working capital
– Variable costs per unit
– Fixed costs
– Unit sales
– Selling price per unit
Pro-forma Financial Statements
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4
• Thus we can estimate project income:
ITEM DEFINITION
Sales Units sold x price per unit
Variable costs Units sold x variable costs per unit
Gross Profit Sales – Variable costs
Fixed costs Given information
Depreciation Given information
EBIT Gross Profit – (Fixed costs + Depreciation)
Taxes EBIT x tax rate
Net income EBIT – Taxes
Pro-forma Financial Statements
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5
• Using this information, we can also estimate
project capital requirements:
ITEM DEFINITION
Change in net working
capital
ΔNet working capital
Net capital spending ΔNet fixed assets + Depreciation
Total investment Change in NWC+ Net capital spending
Pro-forma Financial Statements
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6
• Why do we have to consider changes in NWC
separately?
₋ Sales may not translate immediately into cash inflows,
if customers buy on credit
₋ Expenses may not translate immediately into cash
outflows, if suppliers provide credit
₋ Finally, we have to increase inventory to support
sales; inventory will eventually turn into cash
• Changes in NWC adjust for the discrepancy
between the accounting of sales and costs, and
their actual cash receipts and payments
Net working capital
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7
• Project cash flow is calculated as:
Project Cash Flow = Project Operating Cash Flow
– Project Change in Net Working Capital
– Project Net Capital Spending
• Where
Operating Cash Flow = EBIT + Depreciation −Taxes
• In addition, recall that net working capital will be
repaid at the end of the project, altering the final
year cash inflows
Project Cash Flows
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8
• Now we can estimate the project cash flows
Year 0 Year 1 Year 2 Year 3
Operating
Cash Flow
Nothing in
year 0
Project cash
flows
Project cash
flows
Project cash
flows
Changes in
Net Working
Capital
Outflows for
project
creation
Inflow at end
of project
Net Capital
Spending
Outflows for
project
creation
Inflow at end
of project
Total project
cash flow
Sum of the
above
Sum of the
above
Sum of the
above
Sum of the
above
Pro-forma Financial Statements
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9
Sales (50,000 units at $4.00/unit) $200,000
Variable Costs ($2.50/unit) 125,000
Gross profit $ 75,000
Fixed costs 12,000
Depreciation ($90,000 / 3) 30,000
EBIT $ 33,000
Taxes (34%) 11,220
Net Income $ 21,780
Pro-forma Income Statement
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10
Year
0 1 2 3
NWC $20,000 $20,000 $20,000 $20,000
NFA 90,000 60,000 30,000 0
Total $110,000 $80,000 $50,000 $20,000
Projected Capital Requirements
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11
Year
0 1 2 3
OCF $51,780 $51,780 $51,780
Change in
NWC
-$20,000 20,000
NCS -$90,000
Project CF -$110,00 $51,780 $51,780 $71,780
Year 0 CF = cost of machinery and working capital investment
Year 1 OCF = EBIT + dep – tax = $33000 + 30000-11220 = $51780
Year 3 – recoup working capital investment
Projected Total Cash Flows
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12
$ -110,000
1 2 3
CF1 =
51,780
CF2 =
51,780
CF3 =
71,780
R = 20%
NPV=-110,000+51,780/(1+0.2)+51,780/(1+ 0.2)2+ 71,780/(1+ 0.2)3
=10,647.69
IRR = ?
25.8%
Making The Decision
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13
• Depreciation is a non-cash item
– Non-cash items track things such as changes to the value
of investments that have not been sold, and wear and tear
on valuable items
– Depreciation appears in as an income statement item
• Depreciation impacts the firm’s tax bill and, as
a result, has an impact on cash flows
– It must be considered in capital budgeting decisions
– The tax shield on depreciation is
Depreciation tax shield = T × Depreciation
Depreciation
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14
• Straight line depreciation works by multiplying
the original asset cost by the depreciation rate
every year in which it is owned.
– This is the depreciation that can be claimed that year.
Depreciation = (Initial cost − Salvage)/ number of years
– Salvage here is book value of an asset at the end of useful
life
• Depreciation can be claimed each year, to the
end of its useful life, assuming the asset is owned
until it is fully depreciated
– A fully depreciated asset is one whose accumulated
depreciation equals its original cost.
Straight Line Depreciation
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15
• Consider an asset worth $25,000 that has
5-year economic life.
– Depreciation is at 20% per annum, straight line
– The asset has $0 salvage value
• At the end of the first year, the depreciation is:
Depreciation = Cost ×Depreciation rate
Depreciation = 25,000×20% = $5000
Straight Line Depreciation Example
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16
• If the asset were purchased part way through
the year so there were only 9 months until the
end of the fiscal year, the deprecation would
be:
Depreciation = (Cost ×Depreciation rate)× Months owned
12
Depreciation = ($25,000×20%)× 9 = $3750
12
Straight Line Depreciation Example
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17
• An alternative method of calculating
depreciation, MACRS allocates every asset to a
particular depreciation class for tax purposes
• Each class specifies a sequence of percentages
which alter each year.
– To calculate depreciation, the initial cost of the asset is
multiplied by the relevant percentage for that year
– The asset is depreciated to zero
Modified Accelerated Cost Recovery System (MACRS)
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18
• MACRS depreciation allowances :
Property Class
Year 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
Modified Accelerated Cost Recovery System (MACRS)
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19
• Consider a $12,000 asset in the 5-year class
Year 5-Year
(%)
Depreciation Starting Book
Value
Ending Book
Value
1 20.00 0.20 x $12,000= $2,400.00 $12,000 $9,600.00
2 32.00 0.32 x $12,000 = $3,840 $9,600.00 $5,760.00
3 19.20 0.1920 x $12,000 = $2,304.00 $5,760.00 $3,456.00
4 11.52 0.1152 x $12,000 = $1,382.40 $3,456.00 $2,073.60
5 11.52 0.1152 x $12,000 = $1,382.40 $2,073.60 $691.20
6 5.76 0.0576 x $12,000 = $691.20 $691.20 0
100.00 $12,000.00
Modified Accelerated Cost Recovery System Example
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20
• If the salvage value of an asset is different
from the book value, then there is a tax effect
Book value = Initial cost - accumulated depreciation
After - tax salvage = salvage value - T(salvage value - book
value)
• Salvage value here is the market price that the
asset is sold.
After-tax Salvage
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21
• Some equipment is purchased for $100,000 and it
costs $10,000 to have it delivered and installed.
• Based on past information, you believe that you
can sell the equipment for $17,000 when you
are done with it in 6 years
• The marginal tax rate is 40%.
• What is the depreciation expense each year and
the after-tax salvage in year 6 for each of the
following situations?
– Straight line depreciation
– 3-years MACRS
After-tax Salvage and Depreciation Example
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22
• With Straight-line depreciation
Depreciation = (Initial cost − Salvage)/ number of years
Depreciation = (110,000 −17,000)/ 6 = 15,500 eachyear
Book value in year 6 = 110,000 − (6×15,500)= 17,000
After - tax salvage = salvage value - T(salvage - book value)
After - tax salvage = 17,000 - 0.40(17,000 - 17,000)= 17,000
After-tax Salvage and Depreciation Example
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23
• With 3-Year MACRS
BV in year 6 = 110,000 − (36,663+ 48,884 + 16,302 + 8,151)= 0
After - tax salvage = salvage value - T(salvage - book value)
After - tax salvage = 17,000 - 0.4(17,000 - 0)= $10,200
Year 3-Year
(%)
Depreciation Starting Book
Value
Ending Book
Value
1 33.33 0.3333 x $110,000= $36,663 $110,000 $73,337.00
2 44.44 0.4444 x $110,000 = $48,884 $73,337.00 $24,452.00
3 14.82 0.1482 x $110000 = $16,302 $24,452.00 $8,151.00
4 7.41 0.0741 x $110,000 = $8,151 $8,151.00 $0.00
After-tax Salvage and Depreciation Example
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24
• Sometimes facilities need to be upgraded to
remain efficient.
– The issue here is whether the savings are worth the costs
of the upgrade
• What to do here:
– What are the relevant cash flows?
– Are there working capital impacts? Usually not in this type
of project
– Depreciation will change – there is new equipment to
consider
– Taxes will also alter (due to changes in EBIT and
depreciation)
Capital Budgeting Decisions in Practice - Cost Cutting Projects
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25
• Walmart is considering a new system that will initially
cost $1 million.
• It will save $300,000 a year in inventory and
receivables management costs.
• The system is expected to last for five years and will be
depreciated using 3-year MACRS.
• There is no impact on net working capital.
• The marginal tax rate is 40% and the required return is 8%.
• The system is expected to have a salvage value of
$50,000 at the end of year 5.
– The after-tax salvage = salvage value – T( salvage – book value)
– Thus, the after-tax salvage value is 50,000 – 0.4(50,000 – 0) = $30,000
• Should Walmart install the new system?
Cost Cutting Example
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26
27
Year 1 2 3 4
Percentage 33.33% 44.44% 14.82% 7.41%
Depreciation 333.3 444.4 148.2 74.1
MACRS Depreciation Schedule
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Create a pro-forma income statement
Here the cost savings are the incremental project operating income
Year 1 2 3 4 5
Cost savings 300,000 300,000 300,000 300,000 300,000
Depreciation 333,300 444,400 148,200 74,100 0
EBIT -33,300 -144,400 151,800 225,900 300,000
Taxes (@ 40%) -13,320 -57,760 60,720 90,360 120,000
OCF (EBIT +
Depreciation – tax)
313,320 357,760 239,280 209,640 180,000
Cost Cutting Example
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28
Cash flow from assets:
NPV = $83,795
The cost cutting project should be accepted.
Year 0 1 2 3 4 5
OCF 313,320 357,760 239,280 209,640 180,000
Net
Capital
Spend
-1,000,000 30,000
Change
in NWC
CF -1,000,000 313,320 357,760 239,280 209,640 210,000
Cost Cutting Example
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29
13
• Ford considers replacing an old machine with a new
machine. If Ford buys the new machine today, the
old machine will be sold.
• The original machine:
• Initial cost = 100,000
• Annual depreciation = 9000
• Purchased 5 years ago
• Book value = 55,000
• Salvage today = 65,000
• Salvage in 5 years = 10,000
The Replacement Problem Example
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30
• The new machine:
• Initial cost = 150,000
• 5-year life and salvage in 5 years = 0
• Cost savings = 50,000 pa
• 3-year MACRS depreciation
• Required return = 10% and tax rate = 40%
• Should Ford replace the old machine with the new
machine?
14
The Replacement Problem Example
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31
32
• Remember that we are interested in incremental
cash flows
• If we buy the new machine, then we will sell the
old machine
• What are the cash flow consequences of selling
the old machine today instead of in 5 years?
The Replacement Problem Example
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Create a pro-forma income statement
Year 1 2 3 4 5
Cost savings 50,000 50,000 50,000 50,000 50,000
Depreciation
New asset 49,995 66,660 22,230 11,115 0
Old asset 9,000 9,000 9,000 9,000 9,000
Incremental CF 40,995 57,660 13,230 2,115 -9,000
EBIT (Saving –Incremental) 9,005 -7,660 36,770 47,885 59,000
Taxes (@ 40%) 3,602 -3,064 14,708 19,154 23,600
Net income (EBIT – tax) 5,403 -4,596 22,062 28,731 35,400
The Replacement Problem Example
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33
• Consider the incremental capital spending
• Year 0
– Cost of new asset = 150,000 (outflow)
– After-tax salvage on old asset = 65,000 – 0.4(65,000 –
55,000) = 61,000 (inflow)
– Incremental new capital spending = 150,000 – 61,000 =
89,000 (outflow)
• And, Year 5
– After-tax salvage on old asset = 10,000 – 0.4(10,000-
10,000) = 10,000 (outflow as this is no longer received by
the firm)
The Replacement Problem Example
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34
Cash flow from assets:
Year 0 1 2 3 4 5
OCF (EBIT +
Depreciation-Taxes)
46,398 53,064 35,292 30,846 26,400
New Capital Spending -89,000 -10,000
Change in NWC 0 0
Cash flows for analysis -89,000 46,398 53,064 35,292 30,846 16,400
The Replacement Problem Example
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35
• Now analyse the cash flows, recalling the
required rate of return is 10%
• NPV = 54,801
• IRR = 23.89%
• Therefore, the machine should be replaced.
The Replacement Problem Example
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36
• There are several different definitions of operating
cash flow
– All of these definitions should give the same answer
– However, sometimes one definition is more effective than
the others, depending on the information given
• The bottom-up approach starts from net income and
adds in non-cash deductions
‒ Works only when there is no interest expense
Project Net Income = EBIT −Taxes
OCF = Net Income + Depreciation
Alternative Definitions of Operating Cash Flow
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37
• The top-down approach starts with
subtracts costs, taxes etc.
– Non-cash items are left out in this case
OCF = Sales- Costs -Taxes
sales
• The tax shield approach splits OCF into two
elements:
1. Cash flow without depreciation
2. The depreciation tax shield
OCF = (Sales - Costs )×(1- T )+ Depreciation×T
Alternative Definitions of Operating Cash Flow
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38
• Sometimes there are several different options
for equipment / manufacturing procedures
etc.
– The firm must choose the most cost effective option
– Often the options have different life spans which makes
comparisons more difficult
– With unequal lives, NPV rule can lead to the wrong
decision
• What to do here:
– To compare multiple projects, estimate the
equivalent annual cost (EAC)
– The EAC is the present value of a project’s costs,
calculated on an annual basis
Equivalent Annual Cost Analysis
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39
• The project with the lowest EAC is the best one to
choose
• The EAC is estimated as:
EAC = PVcosts
At,r
• Where
r
(1+ r)t At,r = Annuity factor =
1− 1
Equivalent Annual Cost Analysis
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41
• Consider a factory that must have an air cleaner. The
equipment is mandated by law, so there is no “doing
without”
• There are two choices:
– The “Cadillac cleaner” costs $4,000 today, has annual
operating costs of $100 and lasts for 10 years
– The “cheaper cleaner” costs $1,000 today, has annual
operating costs of $500 and lasts for 5 years
• The discount rate is 10%
• Which one should we choose?
Investments of unequal lives
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42
-$4,000 –100 -100 -100 -100 -100 -100 -100 -100 -100 -100
0 1 2 3 4 5 6 7 8 9 10
10
=
t=1 (1.10)
$4,000+∑ $100 t = 4,614.46CostsPV
EAC = -4614.46/[(1-1/1.110)/0.1] = 750.98
Equivalent Annual Cost
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44
– The EAC for the Cadillac air cleaner is $750.98
Cheaper air cleaner:
– EAC = 2,895.39 /[(1-1/1.15)/0.1] = 763.80
– The EAC for the cheaper air cleaner is $763.80
– When we incorporate the fact that the Cadillac cleaner
lasts twice as long as the cheaper air cleaner, the Cadillac
cleaner is actually cheaper
Equivalent Annual Cost
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45
costs
t=1 (1.10)
5
PV = $1,000∑ $500 t = 2,895.39
• There can be issues with using NPV based on
estimates
• Using projectedcash flows – what if the projections
are inaccurate?
– This is forecasting risk
– Projecting over longer periods increases the possibility of
error
– Highly competitive markets decrease the chance of
positive NPV investments. Potential competition cannot be
ignored
46
Evaluating NPV estimates
_______________________________________________________________________________
• Here the firm considers the NPV of an
investment under several different outcomes
– These are the best case, the worst case and the
base case (the most likely outcome)
– Other cases can be considered if required
• This is a way of determining the impact of
forecast errors
• The firm still has to decide whether to take
the project or not
Scenario Analysis
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47
Consider an investment that costs $200,000 and has a 5 year life.
There is no salvage and depreciation is straight line.
The required returns is 12% and the tax rate is 34%
In the base case, the NPV is $15,567 but there are three
scenarios to consider
Year Base Case Worse
Case
Best Case
Unit Sales 6,000 5,500 6,500
Price per unit 80 75 85
VC per unit 60 62 58
FC 50,000 55,000 45,000
Scenario Analysis Example
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48
The pro-forma statements for these scenarios are:
Base case: NI = 19,800; CF = 59,800; NPV = 15,567; IRR = 15.10%
Worse case: NI = -15.510; CF = 24,490; NPV = -111,719; IRR = -14.40%
Best case: NI = 59,730; CF = 99.730; NPV = 159,504; IRR = 40.90%
Year Base Case Worse Case Best Case
Sales 480,000 412,500 552,500
VC 360,000 341,000 377,000
FC 50,000 55,000 45,000
Depreciation 40,000 40,000 40,000
EBIT 30,000 -23,500 90,500
Taxes 10,200 -7,990 30,770
Net income 19,800 -15,510 59,730
Scenario Analysis Example
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49
• This technique measures the impact on NPV
of a change to any one aspect of the project
whilst holding all other aspects the same
• This is a way of highlighting the impact of
forecasting errors on NPV calculations
• As before, the firm still has to determine
whether to accept the project or not
Sensitivity Analysis
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50
• This is the analysis of the level of operations
necessary to cover all operating costs
– It is sometimes called cost-volume-profit analysis
– There will be a certain number of units that the company
must produce in order to cover its costs.
• Breakeven analysis is also used to:
– Evaluate the profitability associated with different levels of
sales
Break-Even Analysis
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51
• Variable costs (VC) are the product of the number
of units produced and the cost per unit
VC = Q×v
• Fixed costs (FC) are set during the investment
• Total costs (TC) are the sum of VC and FC
TC =VC + FC = Q×v + FC
• Sales are the product of price and the number of
units produced
S = P ×Q
Break-Even Analysis
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52
Co
s
t
s
/
R
e
v
e
n
u
e
(
$
)
Fixed operating costs are a constant value
Sales (units)
Break-Even Analysis
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53
Co
s
t
s
/
R
e
v
e
n
u
e
(
$
)
Fixed costs
Sales (units)
Adding variable
costs gives the
total operating
cost
Break-Even Analysis
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54
Co
s
t
s
/
R
e
v
e
n
u
e
(
$
)
Fixed costs
Sales (units)
Adding Sales Revenue
Total Operating Costs
Break-Even Analysis
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55
Co
s
t
s
/
R
e
v
e
n
u
e
(
$
)
Fixed costs
Sales (units)
Adding Sales Revenue
Total Operating Costs
Operating Break-even Point
Break-Even Analysis
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56
Co
s
t
s
/
R
e
v
e
n
u
e
(
$
)
Below the break-even point, the project
makes a loss
Fixed costs
Sales (units)
Adding Sales Revenue
Total Operating Costs
Break-Even Analysis
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57
Co
s
t
s
/
R
e
v
e
n
u
e
(
$
)
Above the break-even point, the project
makes money
Fixed costs
Sales (units)
Adding Sales Revenue
Total Operating Costs
Break-Even Analysis
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58
• Common tool for analyzing the relationship
between sales volume and profitability
• There are three common break-even measures
‒ Accounting break-even: sales volume at which
NI = 0
‒ Cash break-even: sales volume at which OCF = 0
‒ Financial break-even: sales volume at which
NPV = 0
11-58
Break-Even Analysis
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59
• Recall net income:
Net income = (Sales −Variable Costs - Fixed Costs - Depreciation)
×(1- T)
NI = (S -VC - FC - D)×(1−T )= (PQ - vQ - FC - D)×(1−T )
• Accounting break-even is the quantity of sales
that gives net income of zero
Break-Even Analysis
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60
• Rearranging for the quantity of units sold gives
NI = (PQ - vQ - FC - D)×(1−T )= 0
(PQ - vQ - FC - D)= Q(P - v)− FC − D = 0
Q(P - v)= FC + D
(FC + D)
Q = (P −v)
Break-Even Analysis
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61
•Accounting break-even and cash flow
Operating Cash Flow = EBIT + Depreciation - Taxes
OCF = (S −VC − FC − D)+ D - T
• We ignore taxes for simplicity
OCF = (S −VC − FC − D)+ D
OCF = QP − Qv − FC = Q(P − v)− FC
(OCF + FC)
Q = (P − v)
Break-Even Analysis
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62
• Cash break-even is the point at which OCF=0
• Financial break-even is the point at which
NPV=0
– This is found be estimating the level of OCF that
gives NPV=0
– Then work backwards to find the amount of sales
that equate to this level of OCF
Break-Even Analysis
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63
• A new product needs $5 million in initial investment and
depreciates to a salvage value of zero in 5 years
• The price of the new product is $25,000, variable cost
per unit is $15,000. Fixed costs are $1 million. The
required return is 18%
• Find:
– The accounting break-even point
– The operating cash flow at the accounting break-even point
(ignoring taxes)
– The cash break-even quantity and
– The financial break-even point
Break-Even Analysis Example
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64
• Start with the depreciation:
Depreciation = (Initial cost − Salvage)/ number of years
Depreciation = (5,000,000 − 0)/5 = 1,000,000
• Hence, the accounting break-even point is:
(FC + D) (1,000,000+ 1,000,000)
(25,000 −15,000) = 200 unitsQ = (P −v) =
Break-Even Analysis Example
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65
• Now the operating cash flow at the accounting
break-even point (ignoring tax):
Operating Cash Flow = EBIT + Depreciation
OCF = (S −VC − FC − D)+ D
OCF = ([200× 25,000]− [200×15,000]− 1,000,000)
OCF = 1,000,000
Break-Even Analysis Example
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66
• Next, the cash break-even quantity
• Recall that this is the point at which OCF=0
OCF = (S −VC − FC − D)+ D = S −VC − FC
OCF = PQ − Qv − FC = Q(P − v)− FC
(OCF + FC) (0 + 1,000,000)
Q = (P − v) = (25,000 −15,000) = 100 units
Break-Even Analysis Example
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67
• Finally, the financial break-even
• We know:
– Accounting break-even is 200 units
– Cash break-even is 100 units
• Financial break-even occurs when NPV=0
– We also know: n = 5, PV = 5,000,000, r = 18%.
– We need to know what OCF makes NPV = 0?
Break-Even Analysis Example
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68
• This question can be treated as an annuity
where C is the OCF:
1
r r(1+ r)
1
t
PVAt = C −
0.18(1.18) 5,000,000 = C −
5
1 1
0.18
C = 1,598,889
Break-Even Analysis Example
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69
• Now, using the formula:
• Since this is the level of OCF that gives NPV =0, the
question becomes can we sell more than 260 units
per year?
– If we can, then the project will make money.
(OCF + FC)
(P − v) =
(1,598,889 + 1,000,000)
(25,000 −15,000) = 260 unitsQ =
Break-Even Analysis Example
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70
• This example gives the following:
– The accounting break-even point is 200 units
– Cash break-even is 100 units
– Financial break-even point 260 units
• This illustrates an important point:
Cash BE < Accounting BE < Financial BE
Break-Even Analysis Example
_______________________________________________________________________________
71
• Operating leverage measures the degree to
which a project relies on fixed costs
• It is also the relationship between the firm’s
sales revenue and EBIT
• A firm with a high proportion of fixed costs has
a high degree of operating leverage (DOL).
– This means that, if all other factors are held
constant, a small change in sales will bring about a
large change in ROE for a firm with a high DOL.
Operating Leverage
_______________________________________________________________________________
72
• Can a firm control the DOL?
– Operating leverage is strongly influenced by
technology. Some firms need a lot of fixed assets
and this increases operating leverage.
– By carefully selecting investments, a firm can exert
some control over its operating leverage by trying
to limit fixed costs as much as possible.
• The DOL will have an impact on business risk.
– If all other things are held constant, a firm with
high DOL will have high business risk
Operating Leverage
_______________________________________________________________________________
73
Operating leverage is measured using the
degree of operating leverage (DOL). This is the
percentage change in OCF relative to the
percentage change in quantity sold.
DOL = %∆OCF
%∆Q
• An alternative equation is:
DOL = 1 + FC
OCF
Operating Leverage
_______________________________________________________________________________
74
• Extending on the previous example.
• Suppose sales are 300 units which exceeds all
three break-even measures
• What is the DOL at this sales level?
• Recall, in the absence of taxes
OCF = Q(P − v)− FC
OCF = 300(25,000 − 15,000)− 1,000,000 = 2,000,000
Operating Leverage Example
_______________________________________________________________________________
75
• The DOL is:
DOL = 1 + FC = 1 + 1,000,000 = 1.5
OCF 2,000,000
• What happens to the OCF if unit sales increase
by 20%?
• Recall,
DOL = %∆OCF
%∆Q
Operating Leverage Example
_______________________________________________________________________________
76
• Rearranging the equation gives:
%∆OCF = DOL(%∆Q)
• Therefore,
%∆OCF = DOL(%∆Q)= 1.5(0.20) = 0.30 = 30%
• And the OCF would increase to:
2,000,000(1.3) = 2,600,000
Operating Leverage Example
_______________________________________________________________________________
77
77
• Pro-forma statements
• Depreciation
‒ Straight-line deprecation
‒ Modified accelerated cost recovery system
• Cost cutting and Replacement problem
• When a firm must choose between two machines
of unequal lives:
– the equivalent annual cost approach
• Break-even analysis
– Cash BE, accounting BE, financial BE
• Operating leverage
Summary
_______________________________________________________________________________
78
School of Banking and Finance
FINS5514: Capital Budgeting and Financial
Decisions
Lecture 4: The Investment Decision III
Project Cash Flows II and Estimating Risk in
Capital Budgeting
1
• Pro-forma financial statements
• Depreciation
‒ Straight-line deprecation
‒ Modified accelerated cost recovery system
• Examples of capital budgeting decisions in
practice
• Break-even analysis
• Operating leverage
Outline
_______________________________________________________________________________
2
• So far, it has been assumed that project cash
flows are known with certainty.
• What if this is not true?
– In reality it is often difficult to know what cash flows a
project will produce.
– So the cash flows must be estimated.
• Pro-forma statements are projected financial
statements
– They are used to produce projected cash flows from
the project which are then used for capital budgeting
decisions.
Pro-forma Financial Statements
_______________________________________________________________________________
3
• Pro-forma statements require information on:
– Net capital spending
– Net working capital
– Variable costs per unit
– Fixed costs
– Unit sales
– Selling price per unit
Pro-forma Financial Statements
_______________________________________________________________________________
4
• Thus we can estimate project income:
ITEM DEFINITION
Sales Units sold x price per unit
Variable costs Units sold x variable costs per unit
Gross Profit Sales – Variable costs
Fixed costs Given information
Depreciation Given information
EBIT Gross Profit – (Fixed costs + Depreciation)
Taxes EBIT x tax rate
Net income EBIT – Taxes
Pro-forma Financial Statements
_______________________________________________________________________________
5
• Using this information, we can also estimate
project capital requirements:
ITEM DEFINITION
Change in net working
capital
ΔNet working capital
Net capital spending ΔNet fixed assets + Depreciation
Total investment Change in NWC+ Net capital spending
Pro-forma Financial Statements
_______________________________________________________________________________
6
• Why do we have to consider changes in NWC
separately?
₋ Sales may not translate immediately into cash inflows,
if customers buy on credit
₋ Expenses may not translate immediately into cash
outflows, if suppliers provide credit
₋ Finally, we have to increase inventory to support
sales; inventory will eventually turn into cash
• Changes in NWC adjust for the discrepancy
between the accounting of sales and costs, and
their actual cash receipts and payments
Net working capital
_______________________________________________________________________________
7
• Project cash flow is calculated as:
Project Cash Flow = Project Operating Cash Flow
– Project Change in Net Working Capital
– Project Net Capital Spending
• Where
Operating Cash Flow = EBIT + Depreciation −Taxes
• In addition, recall that net working capital will be
repaid at the end of the project, altering the final
year cash inflows
Project Cash Flows
_______________________________________________________________________________
8
• Now we can estimate the project cash flows
Year 0 Year 1 Year 2 Year 3
Operating
Cash Flow
Nothing in
year 0
Project cash
flows
Project cash
flows
Project cash
flows
Changes in
Net Working
Capital
Outflows for
project
creation
Inflow at end
of project
Net Capital
Spending
Outflows for
project
creation
Inflow at end
of project
Total project
cash flow
Sum of the
above
Sum of the
above
Sum of the
above
Sum of the
above
Pro-forma Financial Statements
_______________________________________________________________________________
9
Sales (50,000 units at $4.00/unit) $200,000
Variable Costs ($2.50/unit) 125,000
Gross profit $ 75,000
Fixed costs 12,000
Depreciation ($90,000 / 3) 30,000
EBIT $ 33,000
Taxes (34%) 11,220
Net Income $ 21,780
Pro-forma Income Statement
_______________________________________________________________________________
10
Year
0 1 2 3
NWC $20,000 $20,000 $20,000 $20,000
NFA 90,000 60,000 30,000 0
Total $110,000 $80,000 $50,000 $20,000
Projected Capital Requirements
_______________________________________________________________________________
11
Year
0 1 2 3
OCF $51,780 $51,780 $51,780
Change in
NWC
-$20,000 20,000
NCS -$90,000
Project CF -$110,00 $51,780 $51,780 $71,780
Year 0 CF = cost of machinery and working capital investment
Year 1 OCF = EBIT + dep – tax = $33000 + 30000-11220 = $51780
Year 3 – recoup working capital investment
Projected Total Cash Flows
_______________________________________________________________________________
12
$ -110,000
1 2 3
CF1 =
51,780
CF2 =
51,780
CF3 =
71,780
R = 20%
NPV=-110,000+51,780/(1+0.2)+51,780/(1+ 0.2)2+ 71,780/(1+ 0.2)3
=10,647.69
IRR = ?
25.8%
Making The Decision
_______________________________________________________________________________
13
• Depreciation is a non-cash item
– Non-cash items track things such as changes to the value
of investments that have not been sold, and wear and tear
on valuable items
– Depreciation appears in as an income statement item
• Depreciation impacts the firm’s tax bill and, as
a result, has an impact on cash flows
– It must be considered in capital budgeting decisions
– The tax shield on depreciation is
Depreciation tax shield = T × Depreciation
Depreciation
_______________________________________________________________________________
14
• Straight line depreciation works by multiplying
the original asset cost by the depreciation rate
every year in which it is owned.
– This is the depreciation that can be claimed that year.
Depreciation = (Initial cost − Salvage)/ number of years
– Salvage here is book value of an asset at the end of useful
life
• Depreciation can be claimed each year, to the
end of its useful life, assuming the asset is owned
until it is fully depreciated
– A fully depreciated asset is one whose accumulated
depreciation equals its original cost.
Straight Line Depreciation
_______________________________________________________________________________
15
• Consider an asset worth $25,000 that has
5-year economic life.
– Depreciation is at 20% per annum, straight line
– The asset has $0 salvage value
• At the end of the first year, the depreciation is:
Depreciation = Cost ×Depreciation rate
Depreciation = 25,000×20% = $5000
Straight Line Depreciation Example
_______________________________________________________________________________
16
• If the asset were purchased part way through
the year so there were only 9 months until the
end of the fiscal year, the deprecation would
be:
Depreciation = (Cost ×Depreciation rate)× Months owned
12
Depreciation = ($25,000×20%)× 9 = $3750
12
Straight Line Depreciation Example
_______________________________________________________________________________
17
• An alternative method of calculating
depreciation, MACRS allocates every asset to a
particular depreciation class for tax purposes
• Each class specifies a sequence of percentages
which alter each year.
– To calculate depreciation, the initial cost of the asset is
multiplied by the relevant percentage for that year
– The asset is depreciated to zero
Modified Accelerated Cost Recovery System (MACRS)
_______________________________________________________________________________
18
• MACRS depreciation allowances :
Property Class
Year 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
Modified Accelerated Cost Recovery System (MACRS)
_______________________________________________________________________________
19
• Consider a $12,000 asset in the 5-year class
Year 5-Year
(%)
Depreciation Starting Book
Value
Ending Book
Value
1 20.00 0.20 x $12,000= $2,400.00 $12,000 $9,600.00
2 32.00 0.32 x $12,000 = $3,840 $9,600.00 $5,760.00
3 19.20 0.1920 x $12,000 = $2,304.00 $5,760.00 $3,456.00
4 11.52 0.1152 x $12,000 = $1,382.40 $3,456.00 $2,073.60
5 11.52 0.1152 x $12,000 = $1,382.40 $2,073.60 $691.20
6 5.76 0.0576 x $12,000 = $691.20 $691.20 0
100.00 $12,000.00
Modified Accelerated Cost Recovery System Example
_______________________________________________________________________________
20
• If the salvage value of an asset is different
from the book value, then there is a tax effect
Book value = Initial cost - accumulated depreciation
After - tax salvage = salvage value - T(salvage value - book
value)
• Salvage value here is the market price that the
asset is sold.
After-tax Salvage
_______________________________________________________________________________
21
• Some equipment is purchased for $100,000 and it
costs $10,000 to have it delivered and installed.
• Based on past information, you believe that you
can sell the equipment for $17,000 when you
are done with it in 6 years
• The marginal tax rate is 40%.
• What is the depreciation expense each year and
the after-tax salvage in year 6 for each of the
following situations?
– Straight line depreciation
– 3-years MACRS
After-tax Salvage and Depreciation Example
_______________________________________________________________________________
22
• With Straight-line depreciation
Depreciation = (Initial cost − Salvage)/ number of years
Depreciation = (110,000 −17,000)/ 6 = 15,500 eachyear
Book value in year 6 = 110,000 − (6×15,500)= 17,000
After - tax salvage = salvage value - T(salvage - book value)
After - tax salvage = 17,000 - 0.40(17,000 - 17,000)= 17,000
After-tax Salvage and Depreciation Example
_______________________________________________________________________________
23
• With 3-Year MACRS
BV in year 6 = 110,000 − (36,663+ 48,884 + 16,302 + 8,151)= 0
After - tax salvage = salvage value - T(salvage - book value)
After - tax salvage = 17,000 - 0.4(17,000 - 0)= $10,200
Year 3-Year
(%)
Depreciation Starting Book
Value
Ending Book
Value
1 33.33 0.3333 x $110,000= $36,663 $110,000 $73,337.00
2 44.44 0.4444 x $110,000 = $48,884 $73,337.00 $24,452.00
3 14.82 0.1482 x $110000 = $16,302 $24,452.00 $8,151.00
4 7.41 0.0741 x $110,000 = $8,151 $8,151.00 $0.00
After-tax Salvage and Depreciation Example
_______________________________________________________________________________
24
• Sometimes facilities need to be upgraded to
remain efficient.
– The issue here is whether the savings are worth the costs
of the upgrade
• What to do here:
– What are the relevant cash flows?
– Are there working capital impacts? Usually not in this type
of project
– Depreciation will change – there is new equipment to
consider
– Taxes will also alter (due to changes in EBIT and
depreciation)
Capital Budgeting Decisions in Practice - Cost Cutting Projects
_______________________________________________________________________________
25
• Walmart is considering a new system that will initially
cost $1 million.
• It will save $300,000 a year in inventory and
receivables management costs.
• The system is expected to last for five years and will be
depreciated using 3-year MACRS.
• There is no impact on net working capital.
• The marginal tax rate is 40% and the required return is 8%.
• The system is expected to have a salvage value of
$50,000 at the end of year 5.
– The after-tax salvage = salvage value – T( salvage – book value)
– Thus, the after-tax salvage value is 50,000 – 0.4(50,000 – 0) = $30,000
• Should Walmart install the new system?
Cost Cutting Example
_______________________________________________________________________________
26
27
Year 1 2 3 4
Percentage 33.33% 44.44% 14.82% 7.41%
Depreciation 333.3 444.4 148.2 74.1
MACRS Depreciation Schedule
_______________________________________________________________________________
Create a pro-forma income statement
Here the cost savings are the incremental project operating income
Year 1 2 3 4 5
Cost savings 300,000 300,000 300,000 300,000 300,000
Depreciation 333,300 444,400 148,200 74,100 0
EBIT -33,300 -144,400 151,800 225,900 300,000
Taxes (@ 40%) -13,320 -57,760 60,720 90,360 120,000
OCF (EBIT +
Depreciation – tax)
313,320 357,760 239,280 209,640 180,000
Cost Cutting Example
_______________________________________________________________________________
28
Cash flow from assets:
NPV = $83,795
The cost cutting project should be accepted.
Year 0 1 2 3 4 5
OCF 313,320 357,760 239,280 209,640 180,000
Net
Capital
Spend
-1,000,000 30,000
Change
in NWC
CF -1,000,000 313,320 357,760 239,280 209,640 210,000
Cost Cutting Example
_______________________________________________________________________________
29
13
• Ford considers replacing an old machine with a new
machine. If Ford buys the new machine today, the
old machine will be sold.
• The original machine:
• Initial cost = 100,000
• Annual depreciation = 9000
• Purchased 5 years ago
• Book value = 55,000
• Salvage today = 65,000
• Salvage in 5 years = 10,000
The Replacement Problem Example
_______________________________________________________________________________
30
• The new machine:
• Initial cost = 150,000
• 5-year life and salvage in 5 years = 0
• Cost savings = 50,000 pa
• 3-year MACRS depreciation
• Required return = 10% and tax rate = 40%
• Should Ford replace the old machine with the new
machine?
14
The Replacement Problem Example
_______________________________________________________________________________
31
32
• Remember that we are interested in incremental
cash flows
• If we buy the new machine, then we will sell the
old machine
• What are the cash flow consequences of selling
the old machine today instead of in 5 years?
The Replacement Problem Example
_______________________________________________________________________________
Create a pro-forma income statement
Year 1 2 3 4 5
Cost savings 50,000 50,000 50,000 50,000 50,000
Depreciation
New asset 49,995 66,660 22,230 11,115 0
Old asset 9,000 9,000 9,000 9,000 9,000
Incremental CF 40,995 57,660 13,230 2,115 -9,000
EBIT (Saving –Incremental) 9,005 -7,660 36,770 47,885 59,000
Taxes (@ 40%) 3,602 -3,064 14,708 19,154 23,600
Net income (EBIT – tax) 5,403 -4,596 22,062 28,731 35,400
The Replacement Problem Example
_______________________________________________________________________________
33
• Consider the incremental capital spending
• Year 0
– Cost of new asset = 150,000 (outflow)
– After-tax salvage on old asset = 65,000 – 0.4(65,000 –
55,000) = 61,000 (inflow)
– Incremental new capital spending = 150,000 – 61,000 =
89,000 (outflow)
• And, Year 5
– After-tax salvage on old asset = 10,000 – 0.4(10,000-
10,000) = 10,000 (outflow as this is no longer received by
the firm)
The Replacement Problem Example
_______________________________________________________________________________
34
Cash flow from assets:
Year 0 1 2 3 4 5
OCF (EBIT +
Depreciation-Taxes)
46,398 53,064 35,292 30,846 26,400
New Capital Spending -89,000 -10,000
Change in NWC 0 0
Cash flows for analysis -89,000 46,398 53,064 35,292 30,846 16,400
The Replacement Problem Example
_______________________________________________________________________________
35
• Now analyse the cash flows, recalling the
required rate of return is 10%
• NPV = 54,801
• IRR = 23.89%
• Therefore, the machine should be replaced.
The Replacement Problem Example
_______________________________________________________________________________
36
• There are several different definitions of operating
cash flow
– All of these definitions should give the same answer
– However, sometimes one definition is more effective than
the others, depending on the information given
• The bottom-up approach starts from net income and
adds in non-cash deductions
‒ Works only when there is no interest expense
Project Net Income = EBIT −Taxes
OCF = Net Income + Depreciation
Alternative Definitions of Operating Cash Flow
_______________________________________________________________________________
37
• The top-down approach starts with
subtracts costs, taxes etc.
– Non-cash items are left out in this case
OCF = Sales- Costs -Taxes
sales
• The tax shield approach splits OCF into two
elements:
1. Cash flow without depreciation
2. The depreciation tax shield
OCF = (Sales - Costs )×(1- T )+ Depreciation×T
Alternative Definitions of Operating Cash Flow
_______________________________________________________________________________
38
• Sometimes there are several different options
for equipment / manufacturing procedures
etc.
– The firm must choose the most cost effective option
– Often the options have different life spans which makes
comparisons more difficult
– With unequal lives, NPV rule can lead to the wrong
decision
• What to do here:
– To compare multiple projects, estimate the
equivalent annual cost (EAC)
– The EAC is the present value of a project’s costs,
calculated on an annual basis
Equivalent Annual Cost Analysis
_______________________________________________________________________________
39
• The project with the lowest EAC is the best one to
choose
• The EAC is estimated as:
EAC = PVcosts
At,r
• Where
r
(1+ r)t At,r = Annuity factor =
1− 1
Equivalent Annual Cost Analysis
_______________________________________________________________________________
41
• Consider a factory that must have an air cleaner. The
equipment is mandated by law, so there is no “doing
without”
• There are two choices:
– The “Cadillac cleaner” costs $4,000 today, has annual
operating costs of $100 and lasts for 10 years
– The “cheaper cleaner” costs $1,000 today, has annual
operating costs of $500 and lasts for 5 years
• The discount rate is 10%
• Which one should we choose?
Investments of unequal lives
_______________________________________________________________________________
42
-$4,000 –100 -100 -100 -100 -100 -100 -100 -100 -100 -100
0 1 2 3 4 5 6 7 8 9 10
10
=
t=1 (1.10)
$4,000+∑ $100 t = 4,614.46CostsPV
EAC = -4614.46/[(1-1/1.110)/0.1] = 750.98
Equivalent Annual Cost
_______________________________________________________________________________
44
– The EAC for the Cadillac air cleaner is $750.98
Cheaper air cleaner:
– EAC = 2,895.39 /[(1-1/1.15)/0.1] = 763.80
– The EAC for the cheaper air cleaner is $763.80
– When we incorporate the fact that the Cadillac cleaner
lasts twice as long as the cheaper air cleaner, the Cadillac
cleaner is actually cheaper
Equivalent Annual Cost
_______________________________________________________________________________
45
costs
t=1 (1.10)
5
PV = $1,000∑ $500 t = 2,895.39
• There can be issues with using NPV based on
estimates
• Using projectedcash flows – what if the projections
are inaccurate?
– This is forecasting risk
– Projecting over longer periods increases the possibility of
error
– Highly competitive markets decrease the chance of
positive NPV investments. Potential competition cannot be
ignored
46
Evaluating NPV estimates
_______________________________________________________________________________
• Here the firm considers the NPV of an
investment under several different outcomes
– These are the best case, the worst case and the
base case (the most likely outcome)
– Other cases can be considered if required
• This is a way of determining the impact of
forecast errors
• The firm still has to decide whether to take
the project or not
Scenario Analysis
_______________________________________________________________________________
47
Consider an investment that costs $200,000 and has a 5 year life.
There is no salvage and depreciation is straight line.
The required returns is 12% and the tax rate is 34%
In the base case, the NPV is $15,567 but there are three
scenarios to consider
Year Base Case Worse
Case
Best Case
Unit Sales 6,000 5,500 6,500
Price per unit 80 75 85
VC per unit 60 62 58
FC 50,000 55,000 45,000
Scenario Analysis Example
_______________________________________________________________________________
48
The pro-forma statements for these scenarios are:
Base case: NI = 19,800; CF = 59,800; NPV = 15,567; IRR = 15.10%
Worse case: NI = -15.510; CF = 24,490; NPV = -111,719; IRR = -14.40%
Best case: NI = 59,730; CF = 99.730; NPV = 159,504; IRR = 40.90%
Year Base Case Worse Case Best Case
Sales 480,000 412,500 552,500
VC 360,000 341,000 377,000
FC 50,000 55,000 45,000
Depreciation 40,000 40,000 40,000
EBIT 30,000 -23,500 90,500
Taxes 10,200 -7,990 30,770
Net income 19,800 -15,510 59,730
Scenario Analysis Example
_______________________________________________________________________________
49
• This technique measures the impact on NPV
of a change to any one aspect of the project
whilst holding all other aspects the same
• This is a way of highlighting the impact of
forecasting errors on NPV calculations
• As before, the firm still has to determine
whether to accept the project or not
Sensitivity Analysis
_______________________________________________________________________________
50
• This is the analysis of the level of operations
necessary to cover all operating costs
– It is sometimes called cost-volume-profit analysis
– There will be a certain number of units that the company
must produce in order to cover its costs.
• Breakeven analysis is also used to:
– Evaluate the profitability associated with different levels of
sales
Break-Even Analysis
_______________________________________________________________________________
51
• Variable costs (VC) are the product of the number
of units produced and the cost per unit
VC = Q×v
• Fixed costs (FC) are set during the investment
• Total costs (TC) are the sum of VC and FC
TC =VC + FC = Q×v + FC
• Sales are the product of price and the number of
units produced
S = P ×Q
Break-Even Analysis
_______________________________________________________________________________
52
Co
s
t
s
/
R
e
v
e
n
u
e
(
$
)
Fixed operating costs are a constant value
Sales (units)
Break-Even Analysis
_______________________________________________________________________________
53
Co
s
t
s
/
R
e
v
e
n
u
e
(
$
)
Fixed costs
Sales (units)
Adding variable
costs gives the
total operating
cost
Break-Even Analysis
_______________________________________________________________________________
54
Co
s
t
s
/
R
e
v
e
n
u
e
(
$
)
Fixed costs
Sales (units)
Adding Sales Revenue
Total Operating Costs
Break-Even Analysis
_______________________________________________________________________________
55
Co
s
t
s
/
R
e
v
e
n
u
e
(
$
)
Fixed costs
Sales (units)
Adding Sales Revenue
Total Operating Costs
Operating Break-even Point
Break-Even Analysis
_______________________________________________________________________________
56
Co
s
t
s
/
R
e
v
e
n
u
e
(
$
)
Below the break-even point, the project
makes a loss
Fixed costs
Sales (units)
Adding Sales Revenue
Total Operating Costs
Break-Even Analysis
_______________________________________________________________________________
57
Co
s
t
s
/
R
e
v
e
n
u
e
(
$
)
Above the break-even point, the project
makes money
Fixed costs
Sales (units)
Adding Sales Revenue
Total Operating Costs
Break-Even Analysis
_______________________________________________________________________________
58
• Common tool for analyzing the relationship
between sales volume and profitability
• There are three common break-even measures
‒ Accounting break-even: sales volume at which
NI = 0
‒ Cash break-even: sales volume at which OCF = 0
‒ Financial break-even: sales volume at which
NPV = 0
11-58
Break-Even Analysis
_______________________________________________________________________________
59
• Recall net income:
Net income = (Sales −Variable Costs - Fixed Costs - Depreciation)
×(1- T)
NI = (S -VC - FC - D)×(1−T )= (PQ - vQ - FC - D)×(1−T )
• Accounting break-even is the quantity of sales
that gives net income of zero
Break-Even Analysis
_______________________________________________________________________________
60
• Rearranging for the quantity of units sold gives
NI = (PQ - vQ - FC - D)×(1−T )= 0
(PQ - vQ - FC - D)= Q(P - v)− FC − D = 0
Q(P - v)= FC + D
(FC + D)
Q = (P −v)
Break-Even Analysis
_______________________________________________________________________________
61
•Accounting break-even and cash flow
Operating Cash Flow = EBIT + Depreciation - Taxes
OCF = (S −VC − FC − D)+ D - T
• We ignore taxes for simplicity
OCF = (S −VC − FC − D)+ D
OCF = QP − Qv − FC = Q(P − v)− FC
(OCF + FC)
Q = (P − v)
Break-Even Analysis
_______________________________________________________________________________
62
• Cash break-even is the point at which OCF=0
• Financial break-even is the point at which
NPV=0
– This is found be estimating the level of OCF that
gives NPV=0
– Then work backwards to find the amount of sales
that equate to this level of OCF
Break-Even Analysis
_______________________________________________________________________________
63
• A new product needs $5 million in initial investment and
depreciates to a salvage value of zero in 5 years
• The price of the new product is $25,000, variable cost
per unit is $15,000. Fixed costs are $1 million. The
required return is 18%
• Find:
– The accounting break-even point
– The operating cash flow at the accounting break-even point
(ignoring taxes)
– The cash break-even quantity and
– The financial break-even point
Break-Even Analysis Example
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• Start with the depreciation:
Depreciation = (Initial cost − Salvage)/ number of years
Depreciation = (5,000,000 − 0)/5 = 1,000,000
• Hence, the accounting break-even point is:
(FC + D) (1,000,000+ 1,000,000)
(25,000 −15,000) = 200 unitsQ = (P −v) =
Break-Even Analysis Example
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• Now the operating cash flow at the accounting
break-even point (ignoring tax):
Operating Cash Flow = EBIT + Depreciation
OCF = (S −VC − FC − D)+ D
OCF = ([200× 25,000]− [200×15,000]− 1,000,000)
OCF = 1,000,000
Break-Even Analysis Example
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• Next, the cash break-even quantity
• Recall that this is the point at which OCF=0
OCF = (S −VC − FC − D)+ D = S −VC − FC
OCF = PQ − Qv − FC = Q(P − v)− FC
(OCF + FC) (0 + 1,000,000)
Q = (P − v) = (25,000 −15,000) = 100 units
Break-Even Analysis Example
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• Finally, the financial break-even
• We know:
– Accounting break-even is 200 units
– Cash break-even is 100 units
• Financial break-even occurs when NPV=0
– We also know: n = 5, PV = 5,000,000, r = 18%.
– We need to know what OCF makes NPV = 0?
Break-Even Analysis Example
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• This question can be treated as an annuity
where C is the OCF:
1
r r(1+ r)
1
t
PVAt = C −
0.18(1.18) 5,000,000 = C −
5
1 1
0.18
C = 1,598,889
Break-Even Analysis Example
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• Now, using the formula:
• Since this is the level of OCF that gives NPV =0, the
question becomes can we sell more than 260 units
per year?
– If we can, then the project will make money.
(OCF + FC)
(P − v) =
(1,598,889 + 1,000,000)
(25,000 −15,000) = 260 unitsQ =
Break-Even Analysis Example
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• This example gives the following:
– The accounting break-even point is 200 units
– Cash break-even is 100 units
– Financial break-even point 260 units
• This illustrates an important point:
Cash BE < Accounting BE < Financial BE
Break-Even Analysis Example
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• Operating leverage measures the degree to
which a project relies on fixed costs
• It is also the relationship between the firm’s
sales revenue and EBIT
• A firm with a high proportion of fixed costs has
a high degree of operating leverage (DOL).
– This means that, if all other factors are held
constant, a small change in sales will bring about a
large change in ROE for a firm with a high DOL.
Operating Leverage
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• Can a firm control the DOL?
– Operating leverage is strongly influenced by
technology. Some firms need a lot of fixed assets
and this increases operating leverage.
– By carefully selecting investments, a firm can exert
some control over its operating leverage by trying
to limit fixed costs as much as possible.
• The DOL will have an impact on business risk.
– If all other things are held constant, a firm with
high DOL will have high business risk
Operating Leverage
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Operating leverage is measured using the
degree of operating leverage (DOL). This is the
percentage change in OCF relative to the
percentage change in quantity sold.
DOL = %∆OCF
%∆Q
• An alternative equation is:
DOL = 1 + FC
OCF
Operating Leverage
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• Extending on the previous example.
• Suppose sales are 300 units which exceeds all
three break-even measures
• What is the DOL at this sales level?
• Recall, in the absence of taxes
OCF = Q(P − v)− FC
OCF = 300(25,000 − 15,000)− 1,000,000 = 2,000,000
Operating Leverage Example
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• The DOL is:
DOL = 1 + FC = 1 + 1,000,000 = 1.5
OCF 2,000,000
• What happens to the OCF if unit sales increase
by 20%?
• Recall,
DOL = %∆OCF
%∆Q
Operating Leverage Example
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• Rearranging the equation gives:
%∆OCF = DOL(%∆Q)
• Therefore,
%∆OCF = DOL(%∆Q)= 1.5(0.20) = 0.30 = 30%
• And the OCF would increase to:
2,000,000(1.3) = 2,600,000
Operating Leverage Example
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77
• Pro-forma statements
• Depreciation
‒ Straight-line deprecation
‒ Modified accelerated cost recovery system
• Cost cutting and Replacement problem
• When a firm must choose between two machines
of unequal lives:
– the equivalent annual cost approach
• Break-even analysis
– Cash BE, accounting BE, financial BE
• Operating leverage
Summary
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