Engineering Economic Analysis

(Chris Devlin) #1
EconomicDecision Trees 321

$0

$300 «$500 deductible)

$500

$0

$300

$13,000
FIGURE 10-6 Decision tree for buying auto collision insurance.

the owner must replace the vehicle with money from savings or a loan, or do without a vehicle
until the owner can afford to replace it.
Three accident severities are used to represent the range of possibilities: a 90% chance of no
accident, a 7% chance of a small accident (at$300, which is less than the deductible), and a 3%
chance of totaling the $13,000 vehicle. Since our driving habits are likely to be the same with and
without insurance, the accident probabilities are the Same for both chance nodes.
Even though this is a text on engineering economy, we have simplified the problem and
ignored the difference in timing of the cash flows. Insurance payments are made at the beginning
of the covered period, and accident costs occur during the covered period. Since car insurance is
usually paid semiannually, the results of the economic analysis are not changed significantly by the
simplification. We focus on the new concepts of expected value, economic decision trees, and risk.
What are the expected values for each alternative, and what decision is recommended?

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The expected values are computed by using Equation 10-5. Ifinsured, the maximum cost equals
~the deductible"'of $500.If selr-insure'O,the cost is the cosfof tile accident.


EVaccidentw/ins.=(0.9X 0)+ (0.07X 300) + (0.03X 500)=$36

'="= ~ =: 1:1I=;; = =
EVaccident w/oins.=(0.9X0) + (0.07X 300)+ (0.03X13,000)= $411

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