Transcript COST-BENEFIT ANALYSIS

DEV 567: Project and
Program Analysis
Lecture 6
Cash Flow, Sensitivity, Breakeven Analysis and Simulation
Why Cash Flows?

Cash flows, and not accounting
estimates, are used in project
analysis because:

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They measure actual economic wealth.
They occur at identifiable time points.
They have identifiable directional flow.
They are free of accounting definitional
problems.
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The Meaning of RELEVANT Cash Flows.
A relevant cash flow is one which will
change as a direct result of the
decision about a project.
 A relevant cash flow is one which will
occur in the future. A cash flow
incurred in the past is irrelevant. It is
sunk.
 A relevant cash flow is the difference
in the firm’s cash flows with the
project, and without the project.

3
Cash Flows: A Rose by Any Other Name Is Just as
Sweet.
 Relevant
cash flows are also
known as: Marginal
cash flows.
 Incremental cash flows.
 Changing cash flows.
 Project cash flows.
4
Categories of Cash Flows

Project cash flows may be separated into
two categories:

Capital cash flows

The initial investment
 Outflows, purchasing assets and initial working capital

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Additional middle-way investments such as upgrades
and increases in working capital investments
Terminal cash flows
 Inflows, proceeds from sale, salvage value of the asset net
of tax, recovery of remaining working capital
 Outflows, cost of asset disposal, environmental
rehabilitation, redundancy payment to employees

Operating cash flows: cash inflows from sales,
cash outflows for marketing and advertising,
payments for wages, utilities, raw materials
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Essentials in Cash Flow Identification

Principle of the stand-alone project
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Indirect of synergistic effects
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Evaluation of the proposed project purely on its own
merits, in isolation from any other activities or the
projects of the firm
Negative effects, new model of car, lower sales of
existing model, must be deducted from future cash flows
Positive effects, pharmacy adjacent to doctor’s clinic,
favorable impact on clinics cash flows to be added to
pharmacy project’s cash flows
Opportunity cost principle: the most valuable
alternative that is given up if the proposed
investment project is undertaken

Use of existing resources, space, building, rental value,
market value
6
Essentials in Cash Flow Identification

Sunk cost, is an amount spent in the past in
relation to the project, but which cannot now be
recovered or offset by the current decision

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Overhead costs
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
Past consulting expenses
Utilities, executive salaries
With or without the project, incremental costs to be
included
Treatment of working capital



Current assets (inventories, accounts receivables)
minus current liabilities (accounts, wages payable)
Increases in working capital is treated as cash outflows
even though there is no actual cash outflow, opportunity
cost
Capital flows, not operational flows, it is a fund
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Essentials in Cash Flow Identification

After-tax cash flows
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Must be accounted for as a cash outflow, not
based on net cash flow but on taxable income
Treatment of depreciation


Is not a cash flow
In project appraisal, what is relevant is not the
accounting depreciation but tax allowable
depreciation to measure the tax effect
Investment allowance, enhances NPV
 Financing flows, excluded. double
counting, included in the discount rate

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Essentials in Cash Flow Identification

Within-year timing of cash flows

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
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Occurs at various points of time in a year
Standard practice is to assume that capital expenditure
occur at the beginning of the year and all other cash
flows occur at the end of the year
Points in cash flow timing is are set at the end of each
year. An initial outlay of Tk. 50,000 at the start of year
1will be timed as occurring at the end of year zero.
Inflation and consistent treatment of cash flows
and discount rates

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Nominal returns, incorporating the inflationary effect is
preferred over cash flow forecasts in real terms,
excluding the inflationary effects
Fisher effect
Consistency, cash flow in nominal terms- use nominal
discount rate; cash flow in real terms- use real discount
rate
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Project Cash Flows: Yes and No.
YES:- these are relevant cash flows:
 Incremental
 Incremental
 Incremental
 Incremental
 Incremental
future sales revenue.
initial outlay.
future salvage value.
working capital outlay.
future taxes.
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Project Cash Flows: Yes and No.

NO:- these are not relevant cash flows:
Changed future depreciation.
 Reallocated overhead costs.
 Adjusted future accounting profit.
 The cost of unused idle capacity.
 Outlays incurred in the past.

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Cash Flows and Depreciation: Always a Problem.
Depreciation is NOT a cash flow.
 Depreciation is simply the accounting
amortization of an initial capital cost.
 Depreciation amounts are only
accounting journal entries.
 Depreciation is measured in project
analysis only because it reduces taxes.

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Other Cash Flow Issues.
Tax payable: if the project changes
tax liabilities, those changed taxes are
a flow of the project.
 Investment allowance: if a taxing
authority offers this ‘extra depreciation’
concession, then its tax savings are
included.
 Financing flows: interest paid on debt,
and dividends paid on equity, are NOT
cash flows of the project.

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Other Cash Flow Issues.
In project analysis, cash inflows are
timed as at the end of a year, and
capital outlays are timed as at the start
of a year.
 Forecast inflated cash flows must be
discounted at the nominal discount
rate, not the real discount rate.

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Using Cash Flows
All relevant project cash flows are set out
in a table.

The cash flow table usually reads across in
End of Years, starting at EOY 0 (now) and
ending at the project’s last year.
 The cash flow table usually reads down in
cash flow elements, resulting in a Net
Annual Cash Flow. This flow will have a
positive or negative sign.

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Delta Project Cash Flows
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Project start date 2001
Capital outlay in year 1 is $ 1 million; year 3 is
$0.5 million
Economic life 8 years
Working capital Y0-2000; Y1-2500; Y2-3100; Y33600; Y4-4000; Y5-4300;Y6-4500; Y7-3000, Y80.
Salvage value in Y8-$16,000
Depreciation on initial investment is 12.5% p.a.
upgrade depreciates @$100,000 for years 4-8.
Sales forecasts
After tax salvage value
Accounting income
Workbook 2.1
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Asset expansion project cash flows

Initial investment
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Net operating cash flows
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Initial investment in plants and working capital
Add back depreciation
Exclude depreciation from costs
Add tax shield of depreciation (tax rate x
depreciation)
Terminal cash flows

Proceeds from sale of assets minus taxes on
sale of an assets plus recovery of working
capital
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Asset replacement project cash flows

Initial investment

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Incremental operating cash flows

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Initial investment in plants and working capital
minus proceeds from sale of old asset plus
taxes on sale of old assets
Operating cash flow of new assets minus
operating cash flow of old assets
Terminal cash flow

Proceeds from sale of new asset- proceeds
from sale of old asset - taxes on sale of old
assets- taxes on sale of an assets-taxes on
sale of old assets plus recovery of working
capital
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Project Cash Flows: Summary
Only
future, incremental,
cash flows are Relevant.
Relevant Cash Flows are
entered into a yearly cash
flow table.
Net Annual Cash Flows are
discounted to give the
project’s Net Present Value.
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Overarching principles:

We only need to estimate cash flows
that change as a result of accepting
the project (incremental cash flows).

The amount of, and the timing of the
cash flow must be estimated, not the
accounting profit/loss by ordinary
accounting methods.
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There are generally three kinds of
cash flows that can be affected by
a capital budgeting project:
1) Initial period cash flow
2) Operating cash flow
3) Terminal year cash flow
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Since taxes are cash flows,
we must include taxes in
our cash flow estimates.
All estimated cash flows
should be after-tax cash
flow estimates!
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Cash flow type #1: Initial period cash flows
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These are simply any cash flows that occur in
the initial period of the project’s life (period
0).
For example, assume that a new investment
project would require spending $20 million for
new capital machines, plus $3 million for
additions to working capital (increases in cash
balances, inventory, and accounts receivable).
The initial period cash flow = -$20 + -$3
= -$23 million.
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Cash flow type #2: Operating cash flow

Accounting income for a period could be
a measure of cash flow, except that
depreciation (an expense, but not a
cash flow) was subtracted in calculating
it.

Operating cash flow equals
Net Income + Depreciation
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Operating cash flow will be affected
whenever a revenue or expense is
changed on the income statement.
For example, operating cash flow is
increased/decreased if a project results
in increased/decreased sales revenues.
 Operating cash flow is
decreased/increased if a project results
in increased/decreased expense of
some kind.

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Continuing with the example project:
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Assume the business currently has sales of
$95 million and cash operating expenses of
$65 million, plus $15 million of depreciation
expense.
Assume the tax rate = 30%.
Net income = ($95 - $65 - $15) x (1 - .3)
= $10.5 million.
Operating cash flow = Net income +
depreciation = $10.5 + $15 = $25.5 million
per year.
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Class Exercise
Assume that accepting the new
investment project would increase the
business sales by $10 million, and
increase the operating costs by $4
million, plus increase depreciation
expense by $2 million. What is the
incremental operating cash flow for
the project?
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Operating cash flow with the new
project = ($105 - $69 - $17) x (1.3) + $17 = $30.3 million.

The incremental operating cash flow
for the project equals the change in
cash flows from before accepting the
project to after accepting it = $30.3 $25.5 = $4.8 million per year.
(Assume these benefits continue the
same each year for 10 years.)
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It is usually easiest to compute this
incremental cash flow by just using the
incremental numbers themselves. Thus,

The relevant incremental operating cash flow
for the example project =
+ Inc. in sales revenue ……… $10 million
- Inc. in op. costs (expenses) ….. 4 million
- Inc. in depreciation expense … 2 million
= Inc. in EBT …………………. 4 million
- Inc. in taxes (@ 30%) …..…... 1.2 million
= Inc. in EAT …………….…..
2.8 million
+ Inc. in depreciation expense … 2 million
= Inc. in operating cash flow ….. $ 4.8 million
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Notice that this method of calculating the
incremental operating cash flow requires
you to simply identify every item in the
company’s income statement that changes,
and then to calculate the change in net
income that results. Finally, the operating
cash flow equals the change in net
income plus the change in
depreciation.
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Cash flow type #3: Terminal year cash flows
These cash flows consist of any residual
values (salvage values) recovered from
the project at the end of its useful life.
 For our example, assume that at the
end of the
project’s life, the machines
could be sold to net $100,000 after
taxes, and that the working capital ($3
million) is recovered in full.
 Thus, the terminal year cash flow (year
10) for the project = $3.1 million.

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The complete cash flows for the
example project are:
Periods:
0
1-10
10
- $23
+ $ 4.8
+ $ 3.1
Assume that the cost of capital for
the project equals 10%, the NPV is
calculated to be $7.69 million.
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Since the NPV > 0 we know the project is a good
one.

We could alternatively have made the decision
using the IRR method. IRR of the project can
be calculated to be 17%. Since this is > the
10% cost of capital, the project should be
accepted..

We could also have (alternatively) made the
decision using the PI method. PI = 1.33,
which is > 1.00.
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Class Exercise 2
Consider another example:
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Assume the Widget Company is considering an
investment to replace a production machine with
a more efficient one.
Assume the new machine costs $100,000, and
the old machine has a book value of $15,000 and
a current salvage value of $25,000.
Assume the tax rate is 30%.
What are the relevant cash flows for the project
analysis, and should the replacement be
accepted?
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First, determine the initial period
cash flows:
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The $100,000 purchase price of the new machine
is an immediate cash outflow.
The $25,000 salvage value of the old asset would
be an immediate cash inflow.
Taxes on the gain from sale of the old asset is
also an immediate cash outflow.
Taxes = 30% x (SV-BV) = .3 x (25,000-15,000)
= $3,000.
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The total initial period (period 0)
incremental cash flows for the
replacement project are:

-$100,000 + $25,000 - $3,000 = $78,000.
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Next, we calculate the operating
cash flows:

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Assume the new machine would reduce
operating costs by $35,000 per year for the
next 8 years, compared to using the old
machine. Depreciation expense would also
increase by $12,500 per year for 8 years.
Net income will increase by ($35,000 12,500) x (1-.3) = $15,750.
Op. CF = Net Income + Depreciation =
$15,750 + $12,500 = $28,250 per year, for
8 years.
Note that this is an annuity of benefits.
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Assume that both the old machine and
the new one would be fully depreciated
after 8 years.


With the new machine, sale in year 8 for
$5,000 => taxable gain on the sale equal to
the salvage value minus the book value =
($5,000 – 0) = $5,000. Tax on this gain =
$5,000 x .3 = $1,500.
With the old machine, sale in year 8 for $500
=> taxable gain on the sale equal to the
salvage value minus the book value = ($500
– 0) = $500.Tax on this gain = $500 x .3 =
$150.
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Altogether, then, the total terminal
year cash flow equals
= incremental salvage value of $4,500 incremental taxes of $1,350
 = $4,500 - $1,350 = $3,150.
 This cash flow in year 8 is in addition
to the regular $28,250 operating cash
flow
of that year (already
computed).

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Important:
While in general, any cash flow affected
by a project is relevant, we do not
include any cash flows that are
financing costs.
 For example, we do not include interest
expense or lease payments.
 The reason for this is that all financial
cash flows are implicitly included in the
cost of capital used to find NPV (or used
to compare to IRR). To include the
financial cash flows and then discount
them to PV would be to double count
their impact.

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Project Analysis Under Risk
Incorporating risk into project
analysis through adjustments to the
discount rate, and by the certainty
equivalent factor.
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Introduction: What is Risk?
Risk is the variation of future
expectations around an expected
value.
 Risk is measured as the range of
variation around an expected value.
 Risk and uncertainty are
Interchangeable words.

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Where Does Risk Occur?

In project analysis, risk is the
variation in predicted future cash
flows.
Forecast Estimates of
Varying Cash Flows
End of
Year 0
End of
Year 1
-$1,257
-$760
-$235
$127
$489
$945
End of
Year 2
?
?
?
?
?
-$876
-$231
$186
$875
$984
End of
Year 3
?
?
?
?
?
-$546
-$231
$190
$327
$454
?
?
?
?
?
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Handling Risk
There are several approaches to handling risk:
 Risk may be accounted for by (1) applying a
discount rate commensurate with the riskiness of
the cash flows, and (2), by using a certainty
equivalent factor
 Risk may be accounted for by evaluating the project
using sensitivity and breakeven analysis.
 Risk may be accounted for by evaluating the
project under simulated cash flow and discount
rate scenarios.
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Using a Risk Adjusted Discount Rate

The structure of the cash flow
discounting mechanism for risk is:-
 The $ amount used for a ‘risky cash flow’ is the
expected dollar value for that time period.
 A ‘risk adjusted rate’ is a discount rate calculated to
include a risk premium. This rate is known as the
RADR, the Risk Adjusted Discount Rate.
45
Defining a Risk Adjusted Discount
Rate
Conceptually, a risk adjusted discount
rate, k, has three components:1. A risk-free rate (r), to account for the
time value of money
2. An average risk premium (u), to
account for the firm’s business risk
3. An additional risk factor (a) , with a
positive, zero, or negative value, to
account for the risk differential
between the project’s risk and the
firms’ business risk.

46
Calculating a
Risk Adjusted Discount Rate
A risky discount rate is conceptually defined
as:
k=r+u+a
Unfortunately, k, is not easy to estimate.
Two approaches to this problem are:
1. Use the firm’s overall Weighted Average Cost of
Capital, after tax, as k . The WACC is the overall rate
of return required to satisfy all suppliers of capital.
2. A rate estimating (r + u) is obtained from the
Capital Asset Pricing Model, and then a is added.
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Calculating the WACC
Assume a firm has a capital structure of:
50% common stock, 10% preferred stock,
40% long term debt.
Rates of return required by the holders of each are :
common, 10%; preferred, 8%; pre-tax debt, 7%.
The firm’s income tax rate is 30%.
WACC = (0.5 x 0.10) + (0.10 x 0.08) +
(0.40 x (0.07x (1-0.30)))
= 7.76% pa, after tax.
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The Capital Asset Pricing Model
This model establishes the covariance
between market returns and returns
on a single security.
 The covariance measure can be used
to establish the risky rate of return, r,
for a particular security, given
expected market returns and the
expected risk free rate.

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Calculating r from the CAPM

The equation to calculate r, for a
security with a calculated Beta is:
 Where : E ~
r  is the required rate of
return being calculated, R f is the risk free
rate:  is the Beta of the security, and Rm
is the expected return on the market.
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Beta is the Slope of an Ordinary
Least Squares Regression Line
Share Returns Regressed On Market
Returns
Returns of Share, %
pa
0.12
-0.10
0.10
0.08
0.06
0.04
0.02
-0.05
0.00
-0.020.00
0.05
0.10
0.15
0.20
-0.04
Returns on Market, % pa
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The Regression Process
The value of Beta can be estimated as the regression coefficient
of a simple regression model. The regression coefficient ‘a’
represents the intercept on the y-axis, and ‘b’ represents Beta,
the slope of the regression line.
rit  a  bi rmt  uit
Where,
rit = rate of return on individual firm i’s shares at time t
rmt = rate of return on market portfolio at time t
uit = random error term (as defined in regression
analysis)
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The Certainty Equivalent Method:
Adjusting the cash flows to their ‘certain’
equivalents
The Certainty Equivalent method adjusts the
cash flows for risk, and then discounts these
‘certain’ cash flows at the risk free rate.
CF1  b CF2  b
NPV 

etc  CO
1
2
1  r 
1  r 
Where: b is the ‘certainty coefficient’ (established by
management, and is between 0 and 1); and r is the
risk free rate.
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Analysis Under Risk :Summary




Risk is the variation in future cash flows
around a central expected value.
Risk can be accounted for by adjusting the
NPV calculation discount rate: there are two
methods – either the WACC, or the CAPM
Risk can also be accommodated via the
Certainty Equivalent Method.
All methods require management judgment
and experience.
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Risk and Project Appraisal

People are generally risk-averse
Simply looking at the expected value of the net present
value may not be enough
Consider a choice between two prizes, you can
have Tk. 100,000 for certain or a lottery ticket
which will pay Tk. 200,000 with a probability of 0.5
and Tk. 0 with a probability of 0.5, which one will
you choose?
Please note that the two choices have the same
expected value
 Certainty equivalent

An amount that would be accepted in lieu of a
chance to receive a possibly higher, but uncertain,
amount.
55
Risk and Project Appraisal (Contd.)

A graphical illustration




Risk aversion: decreasing marginal utility of wealth concave
function relating wealth and utility
Risk neutral: constant marginal utility of wealth
Risk lover: increasing marginal utility of wealth
Utility function
U (W )  W
1
2
Consider two projects, A and B which have the following
Payoffs
State
Probability
1
0.6
2
0.4
Expected value
Expected utility
Project A
Project B
$100,000
$0
$60,000
189.7
$50,000
$50,000
$50,000
223.6
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Risk and Project Appraisal (Contd.)
57
Risk and CBA (Contd.)
According to expected value criteria project A is preferred
E[UA] = 0.6*(100,0001/2)=189.7
E[UB] = 0.6*(50,0001/2)+0.4*(50,0001/2) =223.6
We can calculate the certainty equivalent of the two
projects
For project A,
For Project B,
U(CE) = 189.7
U(CE) = 223.6
CE1/2= 189.7
CE1/2= 223.6
CE = 36,000
CE = 50,000
Because project B has the greater certainty equivalent, it is
the preferable project
If people are risk neutral, then expected net present value will
give the right answer

58
Sensitivity Analysis
Analyzing project risks by making
mechanical trial and error changes
to forecast values of selected
variables.
 Analyzing the risks of investment
projects, by changing the values of
forecasted variables.
 Finding the values of particular
variables which give the project a
Breakeven NPV of zero.

59
Process of Analysis




Identification of those variables which
will have significant impacts on the NPV,
if their future values vary around the
forecast values.
The variables having significant impacts
on the NPV are known as ‘sensitive
variables’.
The variables are ranked in the order of
their monetary impact on the NPV.
The most sensitive variables are further
investigated by management.
60
Management Use of Sensitivity and
Breakeven Analysis
Using Sensitivity:
Sensitive variables are investigated
and managed in two ways:
 (1) Ex ante; in the planning phase;
more effort is used to create better
forecasts of future values. If
management decides the project is
too risky, it is abandoned at this
stage.
61
Management Use of Sensitivity and
Breakeven Analysis
Using Sensitivity:
Sensitive variables are investigated and
managed in two ways:
•(2) Ex post; in the project execution phase;
management monitors the forecasted values. If
the project is performing poorly, it is
abandoned or sold off prior to its planned
termination.
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Management Use of Sensitivity and Breakeven
Analysis
Using Breakeven:
• Forecasted calculated Breakeven values of
variables are continuously compared against
actual outcomes during the execution phase.
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Terminology Within the Analysis
Sensitivity and Breakeven analyses are
also known as: ‘scenario analysis’, and
‘what-if analysis’.
 Point values of forecasts are known as:
‘optimistic’, ‘most likely’, and
‘pessimistic’.
 Respective calculated NPVs are known
as: ‘best case’, ‘base case’ and ‘worst
case’.
 Variables giving a ‘breakeven’ value,
return an NPV of zero for the project.

64
Steps in Sensitivity Analysis
Calculate the project’s NPV using the most likely value
estimated for each variable
 Select from the set of uncertain variables those which
the management feels may have an important bearing
on predicted project performance.
 Forecast pessimistic, most likely, and optimistic values
for each of these variables over the life of the project.
 Recalculate the project’s NPV for each of these three
levels of each variable. While each particular variable is
stepped through each of its three values, all other
variables are held at their most likely values.
 Calculate the change in NPV for the pessimistic to
optimistic range of each variable.
 Identify sensitive variables.
Important: Selection of appropriate variables, and
establishing valid upper and lower forecast values.

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Selection Criteria For Variables in the Analysis
Degree of management control.
 Management's confidence in the
forecasts.
 Amount of management experience
in assessing projects.
 Extrinsic variables more
problematic than intrinsic
variables.
 Time and cost of analysis.

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Real Life Examples Forecast Errors
Large blowouts in initial construction
costs for Sydney Opera House,
Montreal Olympic Stadium.
 Big budget films are shunned by
critics and public alike; e.g
‘Waterworld’: whilst cheap films
become classics; eg.‘Easy Rider’.
 High failure rate of rockets used to
launch commercial satellites.

67
Developing Optimistic and Pessimistic
Forecasts

(a) Use forecasting –error
information from the forecasting
methods: e.g. - upper and lower
bounds; prediction interval; expert
opinion; physical constraints, are
applied to the variables.
This method is formalized, but
arguable, slow and expensive.
68
Developing Optimistic and
Pessimistic Forecasts
•(b) Use ad hoc percentage changes: a fixed
percentage, such as 20%,or 30%, is added to
and subtracted from the most likely forecast
value.
This method is vague and informal, but
fast, popular, and cheap.
+20%
?
-20%
69
Sensitivity analysis example: Delta Project
Forecast Variable
Value
Variables for
sensitivity
analysis
Pessimistic
Optimistic
Initial outlay
$1,000,000
√
$1,200,000
$800,000
Upgrade cost(yr3)
$500,000
X
Project life
8 years
X
0
$32,000
Working capital
After year 0
X
Salvage value
$16,000
√
Tax depreciation
rate
12.5% p.a.
X
Sales volume
696,106+ 500,000
Units p.a. after
upgrade
√
Minus 1 SE of the
regression,-16701
-20% (400,000)
Plus 1 SE of the
regression, +16701
+20%(600,000)
Selling price
$0.50, 0.75 after
five years
√
$0.30
$0.90
Production costs
$0.10 per unit
√
$0.13
$0.08
Other costs
$50,000 p.a.
$55,000 after 5 yr
√
$70,000
$35,000
Company tax rate
30% p.a.
X
Required rate of
return
5.37% p.a.
√
12%
4%
70
Delta Project: Sensitivity Analysis Results
Variable
Sheet Number
Pessimistic NPV
Optimistic NPV
Range
Initial outlay
2(1),(2)
$856,208
$1,160,706
$304,498
Total asset salvage value
2(3),(4)
$1,001,089
$1,015,825
$14,736
Regressed sales forecasts
2(5),(6)
$972,600
$1,044,314
$71,714
Extra sales
2(7),(8)
$869,480
$1,147,434
$277,954
Unit selling prices
2(9),(10)
($431,798)
$2,379,109
$2,810,907
Unit production cost
2(11),(12)
$870,393
$1,100,500
$230,107
Other costs
2(13),(14)
$926,608
$1,082,594
$155,986
Required rate of return
2(15),(16)
$427,220
$1,166,326
$739,106
71
Delta Project: Sensitivity Analysis Results
• Workbook 8.1
72
Sensitivity Analysis

Sensitivity analysis
Partial sensitivity analysis
 Worst and best-case analysis
According to bridge supporters, the salvage value after 30
years will be $50 million. According to ferry supporters, the
bridge will have zero salvage value after 30 years


Profile
Cost
Bridge
supporters
100
Annual Salvage
NPV
Benefit value
5%
10%
12
50
96.0
16
Ferry
supporters
130
10
0
23.7
-35.7
73
Sensitivity Analysis
Profile
Cost
Annual Salvage
NPV
Benefit value
5%
10%
Bridge
supporters
100
12
50
96.0
16
130
12
50
66
-14
100
100
130
12
10
10
0
50
0
84.5
65.3
23.7
13.1
-2.9
-35.7
100
130
130
10
12
10
0
0
50
53.7
54.5
35.3
-5.7
-16.9
-32.9
Ferry
supporters
74
Sensitivity Analysis

Carry out sensitivity analysis changing




salvage value,e.g. plugging the bridge supporters salvage
value in ferry supporters profile
the discount rate
the construction costs
annual benefit
Discount rate
Construction
Annual
cost from 130 benefits from
to 100
10 to 12
Salvage value
from 0 to 50
5%
+30
+30.7
+11.5
10%
+30
+18.9
+2.8
75
Break-even Analysis: Product Unit Price
Project NPV
Thousands
Project NPV Versus Unit Selling Price
3500
3000
2500
2000
1500
1000
500
0
-5000.00
0.50
1.00
-1000
-1500
Unit Selling Price
1.50
Unit Price
Project NPV
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
-1,089,246
-760,522
-431,798
-152,699
78,041
308,148
538,254
768,361
1,228,575
1,458,682
1,688,789
1,918,895
2,149,002
2,379,109
2,609,216
2,839,323
76
Break-even Analysis: Required Rate of Return
Reqd Rate % Project NPV
Thousands
$1,166,326
$1,049,852
$941,407
$840,352
$746,103
$658,130
$575,947
$499,112
$427,220
$359,900
$296,814
$237,652
$182,127
$129,978
$80,964
$34,865
-$8,523
-$49,388
-$87,902
NPV in Dollars
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Project NPV Versus Required Rate of
Return
1,500
1,000
500
0
10
20
30
40
-500
Required Rate of Return
77
Break-even Analysis: Unit Production Cost
1,100,281
1,054,273
1,008,264
962,256
916,248
870,240
824,231
778,223
732,215
686,207
640,198
594,190
548,182
Project NPV
0.08
0.09
0.10
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.20
Thousands
Project NPV Versus Unit Production Cost
Unit Cost Project NPV
1,200
1,000
800
600
400
200
0
0.00
0.05
0.10
0.15
0.20
0.25
Unit Production Cost: Dollars
78
Outputs and Uses





Each forecast value is entered into the
model,and one solution is given.
Solutions can be summarized
automatically, or individually by hand.
Variables are ranked in order of the
monetary range of calculated NPVs.
Management investigates the sensitive
variables.
More forecasting is done, or the project is
accepted or rejected as is.
79
Strengths and Weaknesses of Analysis

Strengths:





Easy to understand.
Forces planning discipline.
Helps to highlight risky variables.
Relatively cheap.
Weaknesses




Relatively unsophisticated.
May not capture all information.
Limited to one variable at a time.
Ignores interdependencies.
80
Introduction
Project risk analysis by simultaneous
adjustment of forecast values.
 Simulation allows the repeated
solution of an evaluation model.
 Each solution randomly selects
values from predetermined
probability distributions.
 All solutions are summarized into an
overall distribution of NPV values.
 This distribution shows management
how risky the project is.

81
Simulation Terminology




The treatment of risk by using simulation is
known as ‘stochastic’ modeling.
Other names for our term ‘Simulation’, are ‘Risk Analysis’, ‘Venture Analysis’,’Risk
Simulation’, ‘Monte Carlo Simulation’.
The name ‘Monte Carlo Simulation’ helps
visualization of repeated spins of the
roulette wheel, creating the selected values.
Each execution of the model is known as a
‘replication’ or ‘iteration’.
82
The Role of Simulation
Follows the initial creation and basic
testing of the representative model.
 Is sometimes used as a test of the
model.
 Emphasizes the need for formal
forecasting, and requires close
specification of the forecast variables.
 Draws managements attention to the
inherent risk in any project.
 Focuses attention on accurate model
building.

83
Probability Distributions of Forecast
Variables
Uniform: upper and lower
bounds required.
 Triangular: pessimistic,
most likely, and optimistic
values required
 Normal: mean and variance
required.
 Exponential: initial value
and growth factor required.

84
Process of Computation
per Replication




A value of a variable is selected
from its distribution using a
random number generator.
For example: Sales 90 units;
selling price per unit $2,350;
component cost per unit $1,100;
labour cost per unit $280.
These values are incorporated
into the model, and an NPV is
calculated for this replication.
The NPV for this replication is
stored, and later reported as one
of many in an overall NPV
distribution.
85
Making the Replications





Each replication is unique.
Selection of values from the distribution is
made according to the particular
distributions
The automated process is driven by a
random number generator.
Excel add-ons such as ‘@Risk’ and ‘Insight’
can be used to streamline the process.
About 500 replications should give a good
picture of the project’s risk.
86
Using the Output
 Management
can view the risk
of the project.
 Probability
of generating an
NPV between two given values
can be calculated.
 Probability
of loss is the area to
the left of a zero NPV.
87
Benefits and Costs of Simulation

Benefits





Focuses on a detailed definition and analysis of risk.
Sophisticated analysis clearly portrays the risk of a
project
Gives the probability of a loss making project
Allows simultaneous analysis of variables
Costs



Requires a significant forecasting effort.
Can be difficult to set up for computation.
Output can be difficult to interpret.
88