G. CinquettiCorporation (GCC), uses a cost of capital of 10 percent to evaluate average-risk projects, and it adds or subtracts 3 percentage
points to evaluate projects of more or less risk. The company uses coefficient of variation (CV) to measure riskiness of the projects.
Currently, two mutually exclusive projects are under consideration by GCC. Both have a cost of $400,000 and will last 4 years. Project A has a
coefficient variable (CV) of 2.30 andwill produce annual end of year cash flows of $71,104. Project B, with CV 1.70 will produce cash flows of
$146,411 at the end of Years 3 and 4 only.
Which project Cinquetti Corporation should accept. Please show you calculations and write a paragraph of 4 lines toexplain your approach to
solve this problem.
GCC classifies a project of average-risk, if project’s CV is 2.00.
Show your workstep by step. Please be clean and neat.
Explain, in words, the approach that you have used to solve this problem in 5 lines.
Capital Budgeting and Uncertainty
• So far we have evaluated projects under assumption that they are equally risky. Now we relax this assumption and we incorporate risk
into capital budgeting analysis.
• Risk in capital budgeting is uncertainty about a project’s future cash flow and profitability. We should modify capital budgeting rules
to allow for different levels of risk for different project. Generally there are three questions to be answered when we incorporate risk into
capital budgeting:
1) What Type of risk is relevant to capital budgeting
2) What is appropriate measure of risk for a new projects (or a set of new projects): how we measure risk.
3) Finally, how we adjust for risk and incorporate it in project evaluation?
• Types of risk relevant to capital budgeting:
1) Stand-Alone Risk
2) Corporate Risk
3) Market Risk
• Stand-Alone Risk
Analysis of a project’s stand-alone risk starts by determining uncertainty of project’s cash flows:
Techniques used in assessing project’s stand-alone risk:
1) Sensitivity analysis (What if? Changing one variable keeping other variables constant)
2) Scenario analysis (Worse Case Scenario, Base case Scenario, Best Case Scenario: To deal with probability distribution and to change
more than one variable at a time: to see combined effects of changes in variables. It brings in the probabilities of changes in the key
variables. It compares Best and Worse
NPVs with the E(NPV) of the project under consideration.
3) Simulation
Uses a computer program to simulate future events to estimate NPV and riskiness of the project. Specifically, computer, at random, selects a
value for each underlying variables of NPV (variable cost per unit, sale volume, unit price etc) and calculate NPV. This process is repeated
1500 times (or more). So a large number of NPVs are calculated, then the mean , standard deviation and Coefficient of variation of these NPVs
are calculated where mean of NPVs is E(NPV) of the project and SD and CV of NPVs are used as a measure of risk of the project
Probability Distribution:
A firm is considering a $30,000 investment. This investment will generate cash saving from operating cost. The following estimates of cash
saving, useful life and their probability of occurrence have been given:
Annual cash inflow Probability Useful life of the investment Probability
$6000 0.20 4 years 0.20
$8000 0.50 5 years 0.60
$10,000 0.30 6 years 0.20
E(CF) = (6,000)x(0.20)+ (8,000)x(0.50) + +(10,000)x(0.30) = $8200
E(N) = (4)x(0.20)+ (5)x(0.60) + (6)x(0.20)=
= 5 years
Let WACC =K =10%
Compare σ =$1400 and CV = 0.17 with average project’s σ and CV to get a sense of the riskiness of this project and then adjust WACC for risk.
Marco Masini Corporation (MMC) is considering the following project for which you are assigned to calculate E(NPV).
Year 1
Cash Flow Probability
$500,000 40%
$300,000 60%
Year 2
If the cash flow in year 1 is $500,000 then
Cash Flow Probability
$700,000 70%
$600,000 30%
If the cash flow in year one is $300,000 then
Cash Flow Probability
$300,000 40%
$200,000 50%
$100,000 10%
You are also provided with the following information:
• Expected life of the project 2 years.
• Initial investment of the project is $500,000.
• WACC =13%
Solution
Cost Pro. CF,Year1 Pro. CF,Year2 NPV at 13% Joint Weighted
Pr. NPV
70% 700,000 490,670 28% 137387.6
40% 500,000
30% 600,000 412,360 12% 49483.2
500,000
40% 300,000 430 24% 103.2
60% 300,000 50% 200,000 -77,880 30% -23364
10% 100,000 -156,190 6% -9371.4
E(NVP) 154238.6
• Generally two approaches are used in capital budgeting in order to adjust for risk after we determine which project is riskier.
A) Risk adjusted discount rate: In this approach, the manager adjusts the firm’s cost of capital upward as projects become riskier. This
approach rests on the fact that, on average, investors demand higher return for riskier project. One way to adjust discount rate in this
framework is to use CAPM (Capital Asset Pricing Model). In this way beta coefficient of the project, return on market portfolio and return on
risk free asset must be estimated before adjusting for risk. See this example:
B) Certainty Equivalent: In this approach manager specifies at what point firm is indifferent to make a choice between a certain cash flow and
expected value of a risky cash flow. Specifically, this approach converts the uncertain cash flows into certainty equivalent cash flows and
they are the cash flows that the manager would accept with certainty in exchange for the risky cash flows. After uncertain cash flows are
converted into certain cash flows, the manager can use risk free rate of return as discount rate to calculate NPV. The uncertain cash flows are
calculated based on “certainty equivalent coefficients”(CEC) defined as:
CEC = (certain cash flow)/expected cash flow.
We note that in the “certainty equivalent” approach manager adjusts the cash flows to reflect risk while in “risk adjusted discount rate”
manager adjusts discount rate to reflect risk. So
• In Certainty equivalent: expected cash flows are adjusted downward to reflect risk.
• In Risk Adjusted Discount Rate: Required rate of return (cost of capital) is adjusted upward to reflect risk while cash flows are
constant.
Example
XYZ Corporation is considering a project with an expected life of 4 years, the initial certain cash outlay of $50,000, the expected cash
inflows and “certainty equivalent coefficients as follows:
Year Cash
inflow Certainty equivalent
coefficient Equivalent certain cash inflow
1 $10,000 0.95 0.95×10,000=9,500
2 15,000 0.80 0.80×15,000=12,000
3 20,000 0.70 0.70×20,000=14,000
4 25,000 0.60 0.60×25,000=15,000
Suppose risk free rate=Krf = 5%
The difficult part of this approach involves the estimation of certainty equivalent coefficients.
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