Risk and uncertainty

1
Risk and uncertainty in investment decisions
2
Relationship between risk and return
The risk of an asset is completely determined if
all possible outcomes (returns) are given along
with the probability for each outcome.
Histogram of the annual rates of return from the
US stock market from 1926 2000
Numberof years
Return ()
(Source Ibbotson Associates, 2001 Yearbook)
3
Relationship between risk and return
The riskier the asset, i.e. the higher the
variability of its annual rates of return, the
higher the average value of its annual rates of
return.
(Source Ibbotson Associates, 2001 Yearbook)
4
Portfolio diversification reduces risk
Firm-specific risk
Portfolio Risk
Totalrisk
Market risk
Level of Portfolio Diversification
Market risk is the risk associated with the
entire market.
Firm-specific (unique, unsystematic) risk is the
risk associated with factors peculiar to a
particular firm.
5
Capital asset pricing model (CAPM)
Expected return for a specific firm



? slope

required return for firm i
Return on firm

risk-free rate of return



return on market
measure for the market risk of firm i
Return on market
Note does not contain firm-specific risk.
Why?
Betas for selected US common stocks August 1996
July 2001
6
Practical guide to investment appraisals

• Estimate all cash flows of the project
• Include only incremental cost
• Include indirect cost
• Disregard sunk cost
• Include opportunity cost
• Adjust for taxes
• Ignore financing cost (cost of capital is
  included via the discount rate)
• Calculate project NPV
• Assess the impact of uncertainties on project NPV

• It is often convenient to distinguish between the
  cash flows of 3 project stages
• Initial cash flow (Initial purchase,
  installation, proceeds from old assets, etc.)
• Annual cash flows (revenues, fixed costs,
  variable costs, taxes, etc.)
• Terminal cash flow (sale of assets, project
  termination costs, etc.)

7
Accounting for uncertainty in investment
appraisals

• The discount rate in NPV-based investment
  appraisals is chosen to reflectthe level of risk
  involved in a project.
• Often, the probabilities of possible outcomes are
  not known this creates uncertainty.
• Once the discount rate is chosen, it should be
  studied how uncertainty in theestimated values
  of the various project parameters impacts the
  appraisal outcome.
• There are three standard assessment methods to do
  this
• Sensitivity analysis
• Scenario analysis
• Break-even analysis

8
Consider the following project Market
introduction of electrically powered scooters in
CA
9
What are the expected cash flows of the project?
10
NPV-based investment appraisal
Revenues R MS TM P 37.5
million Annual variable cost VC MS TM UC
30 million Pretax profit PP R-VC-FC-D
Annual operating cash flow CF (R VC FC
D)(1 TR) D (37.5 30 3
1.5)0.5 1.5 3
3
3
3
3
3
3
3
3
3
3
-15
1
2
3
4
5
6
7
8
9
10
years
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Sensitivity analysis
Q What is the sensitivity of the project NPV
with regard to unit variable cost UC?
12
Sensitivity analysis Assess the dependence of
the project NPV on the project parameters by
varying project parameters individually, one at a
time.
13
However, often the project parameters are
interrelated. Varying the parameters individually
is then not the most realistic way to assess
uncertainty Scenario analysis Here, different,
but consistent combinations of the project
parameters are investigated
Consider the following scenario A sharp rise in
oil prices accompanied by a recession and a jump
of the inflation rate
14
Scenario analysis For each scenario of project
parameters, the project NPV is calculated
15
Break-even analysis Calculate the PVs of cash
in- and outflows as a function of a project
parameter
Sales in million
16
Break-even analysis is a good way to assess
operating leverage, i.e. project exposure to
fixed costs.
PV (in millions)
PV (inflows)
PV (outflows)
Break-even point (NPV0)
Scooter Sales (in thousand)
85
17
Break-even analysis based on accounting costs and
revenues Calculate annual accounting costs and
revenues as a function of a project parameter
Annual R MSTMP Sales 375
Annual C VC FC D Tax
SalesUC FC D TRSales(P UC)
FC D SalesUC TR(P
UC) (1 TR)(FC D)
Sales337.5 2.25
Sales in million
18
Break-even analysis based on accounting costs and
revenues Yields a lower break-even point than
the same analysis based on PVs.
PV (in millions)
Total revenues
Total costs
Break-even point (Net profits0)
Scooter Sales (in thousand)
60
19
Question Why does a break-even analysis based
on the accounting costs and revenues of
theproject yield lower break-even scooter sales
than break-even analysis based on the present
values of the project cash flows?