課程名稱︰成本效益分析
課程性質︰必修
課程教師︰江瑞祥
開課學院：社科院
開課系所︰政治系公行組
考試日期（年月日）︰96.01.19
考試時限（分鐘）：
是否需發放獎勵金：是 謝謝
（如未明確表示，則不予發放）
試題 :
Ⅰ.(30 Points)
Your company produces lawnmowers. You find that the Environmantal Protection
Agency (EPA) requires new standards for the lawnmowers yours company sells in
this country. You must modify this product to maintain your market position.
Your engineers tell you that you have 2 choices. One involves additional
insulation using known technology, and should meet the EPA requirements. The
other pioneers fuel cell technology that might fail to meet the EPA
requirements but could, if successful, position you to jump ahead of your
competition significantly. See Table below.
┌─────┬───────────────────────────────┐
│Approach │Possible Results of Design Approach--probability and financial│
│ to │return │
│System ├──────────┬──────────┬─────────┤
│Design │ Failure │ Good Product │ Great Success │
├─────┼──────────┼──────────┼─────────┤
│Standard │ 0.25 │ 0.75 │ 0 │
├─────┼──────────┼──────────┼─────────┤
│Fuel Cell │ 2/3 │ 0 │ 1/3 │
├─────┼──────────┼──────────┼─────────┤
│ │Loss of ﹩24 million│﹩16 million profit │﹩60million profit│
└─────┴──────────┴──────────┴─────────┘
(a).Draw decision tree for company’s choices, showing all outcomes and
probabilities.
(b).Which approach is the better? Assume company will base decision on
expected profit.
(c).Define the concept of "expected value of perfect information"(EVPI)
(d).Calculate the EVPI for perfect information from tests focused exclusively
on the outcomes of the "Fuel Cell"approach.
Ⅱ.(40 Points)
You could pay ﹩1 million to a lab research that would run tests on the Fuel
Cell technology. You believe, based on your experience with this lab
anticipates future outcomes correctly 80﹪of the time (that is, for example,
the lab will report "failure" 4/5 of the times when failure occurs). With
their information, you would revise your prior estimate of the probability of
success for the Fuel Cell technology, displayed in the Table from questionⅠ.
(a).Explain what Bayes’formula does.
(b).Write Bayes’formula.
(c).What is the estimated probability of failure for the Fuel Cell approach, if
the lab predicts failure? Show calculations that justify this conclusion.
(d).What is the estimated probability of "great success" for the Fuel Cell
approach, if the lab predicts great success? Show calculations that justify
this conclusion.
(e).Define "expected value of sample information"(EVSI)
(f).Calculate the EVSI for the lab investigation of the Fuel Cell process.
Ⅲ.(30 Points)
China Petroleum co.(CPC) is designing an undersea pipeline to an off-sea
field. It anticipates the possobolity that is line could be used in a
neighboring field. The basic design thus calls for a Y shaped layout, where
the single line from the shore has a branch to the second field.
CPC could insatll the branch now at an eatra cost of ﹩18 million. If the
price and quantity of crude justify the full exploitation of the second field,
the branch pipeline would be worth ﹩40 million. However, there is a good
chance, maybe 2 in 3, that CPC would only develop part of the second field, in
which case the branch pipeline would be worth only ﹩10 million. These results
would occur two years from now.
Alternatively, CPC could lay a line to a single field, and enable the
possibility of the branch link to the second field by creating in advance a
Y-junction in the pipeline. If CPC decide to develop the second field, it
would then, in two years, have tp pay ﹩20 million to lay the branch line.
(a).What kind of option is does this situation suggest? Explain your answer.
(b).Draw a diagram showing the payoffs from the option in the venture.
Now you need to assess the value of the Y-junction so that the Chief
Designer for the Pipeline can decide whaether this addition to the basic
system is worthwhile.
You may assume for this case that:
˙It will take 2 years to know if the second field will be developed and thus
the value of pipeline.
˙Similarly the value of the pipeline (﹩40 or 10 million) and the cost of ﹩20
million for later construction will arise in 2 years;
˙The pipeline could be sold to other companies at the stated values;
˙The discount rate for the company is 15﹪annually; and
˙The risk-free rate is 5﹪annually.
(c).Calculate the value of the option using decision analysis.
(d).Calculate the arbitrage enforced price for the option on this projects.
(e).Discuss and explain the similiarity or difference you get between the
value of the option given by the decision analysis and by the arbitrage
enforced pricing analysis.
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