Chapter 14 -- Risk and Managerial Options in Capital Budgeting14-*
Total Project Risk
Managerial Options
ANNUAL CASH FLOWS: YEAR 1
PROPOSAL A
.40
.05
.25
Probability
Cash Flow ($)
Proposal A
CF1 P1 (CF1)(P1)
$ -3,000 .05 $ -150
1,000 .25 250
5,000 .40 2,000
9,000 .25 2,250
13,000 .05 650
The expected cash flow = $5,000
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ANNUAL CASH FLOWS: YEAR 1
PROPOSAL B
.40
.05
.25
Probability
Cash Flow ($)
Proposal B
CF1 P1 (CF1)(P1)
$ -1,000 .05 $ -50
2,000 .25 500
5,000 .40 2,000
8,000 .25 2,000
11,000 .05 550
The standard deviation of Proposal B < Proposal A. ( $2,846 < $3,795 )
The standard deviation = SQRT (8,100,000) = $2,846
The expected cash flow = $5,000
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Projects have risk that may change from period to period.
Projects are more likely to have continuous, rather than discrete distributions.
Cash Flow ($)
Probability Tree Approach
A graphic or tabular approach for organizing the possible cash-flow streams generated by an investment. The presentation resembles the branches of a tree. Each complete branch represents one possible cash-flow sequence.
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Probability Tree Approach
Basket Wonders is examining a project that will have an initial cost today of $900. Uncertainty surrounding the first year cash flows creates three possible cash-flow scenarios in Year 1.
-$900
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-$900
Probability Tree Approach
Each node in Year 2 represents a branch of our probability tree.
The probabilities are said to be conditional probabilities.
-$900
Project NPV Based on Probability Tree Usage
The probability tree accounts for the distribution of cash flows. Therefore, discount all cash flows at only the risk-free rate of return.
The NPV for branch i of the probability tree for two years of cash flows is
NPV = S (NPVi)(Pi)
$ 2,238.32
$ 1,331.29
$ 1,059.18
$ 344.90
$ 72.79
-$ 199.32
-$ 1,017.91
-$ 1,562.13
-$ 2,106.35
-$900
NPV on the Calculator
Remember, we can use the cash flow registry to solve these NPV problems quickly and accurately!
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Solving for Branch #3:
Step 2: Press 2nd CLR Work keys
Step 3: For CF0 Press -900 Enter keys
Step 4: For C01 Press 1200 Enter keys
Step 5: For F01 Press 1 Enter keys
Step 6: For C02 Press 900 Enter keys
Step 7: For F02 Press 1 Enter keys
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Solving for Branch #3:
Step 8: Press keys
Step 10: For I=, Enter 5 Enter keys
Step 11: Press CPT key
Result: Net Present Value = $1,059.18
You would complete this for EACH branch!
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Branch NPVi
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NPVi
$ 2,238.32
$ 1,331.29
$ 1,059.18
$ 344.90
$ 72.79
-$ 199.32
-$ 1,017.91
-$ 1,562.13
-$ 2,106.35
.02 $ 101,730.27
.12 $ 218,149.55
.06 $ 69,491.09
.21 $ 27,505.56
.24 $ 1,935.37
.15 $ 4,985.54
.02 $ 20,036.02
.10 $ 238,739.58
.08 $ 349,227.33
Variance = $1,031,800.31
The expected NPV = -$ 17.01
Simulation Approach
An approach that allows us to test the possible results of an investment proposal before it is accepted. Testing is based on a model coupled with probabilistic information.
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Market size, selling price, market growth rate, and market share
Investment cost analysis
Operating and fixed costs
Factors we might consider in a model:
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Simulation Approach
Each variable is assigned an appropriate probability distribution. The distribution for the selling price of baskets created by Basket Wonders might look like:
$20 $25 $30 $35 $40 $45 $50
.02 .08 .22 .36 .22 .08 .02
The resulting proposal value is dependent on the distribution and interaction of EVERY variable listed on slide 14-30.
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Simulation Approach
Each proposal will generate an internal rate of return. The process of generating many, many simulations results in a large set of internal rates of return. The distribution might look like the following:
INTERNAL RATE OF RETURN (%)
Contribution to Total Firm Risk: Firm-Portfolio Approach
Combining projects in this manner reduces the firm risk due to diversification.
CASH FLOW
NPVP = S ( NPVj )
NPVP is the expected portfolio NPV,
NPVj is the expected NPV of the jth NPV that the firm undertakes,
m is the total number of projects in the firm portfolio.
m
Determining Portfolio Standard Deviation
sP = S S sjk
sjk is the covariance between possible NPVs for projects j and k,
s jk = s j s k r jk .
sj is the standard deviation of project j,
sk is the standard deviation of project k,
rjk is the correlation coefficient between projects j and k.
m
8 Combinations
E E + 1 E + 1 + 2 E + 2 E + 1 + 3 E + 3 E + 2 + 3
E + 1 + 2 + 3
A, B, and C are dominating combinations from the eight possible.
A
B
C
E
Managerial (Real) Options
Management flexibility to make future decisions that affect a project’s expected cash flows, life, or future acceptance.
Project Worth = NPV + Option(s) Value
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Managerial (Real) Options
Expand (or contract)
Allows the firm to expand (contract) production if conditions become favorable (unfavorable).
Abandon
Postpone
Allows the firm to delay undertaking a project (reduces uncertainty via new information).
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Previous Example with Project Abandonment
Assume that this project can be abandoned at the end of the first year for $200.
What is the project worth?
-$900
Project Abandonment
The optimal decision at the end of Year 1 is to abandon the project for $200.
$200 >
-($266.67)
-$900
The standard deviation* = SQRT (740,326) = $857.56
The expected NPV* = $ 71.88
Thus, $71.88 = -$17.01 + Option