技术经济学习题及答案(6)

14. 一公司正在考虑购买一块新探区，租赁土地费用为10万美元。根据现有资料分析，在此探区钻井成功的概率是20%，且钻井成功后可得现值为120万美元。一旦购买，另一个方案是进行三维地震勘探以增加钻井成功的机会。根据对附近地区的考察，地震勘探后获得良好结果的概率是0.70，如果得到良好的结果，钻井成功的概率可增加到80%。如果地震勘探没有取得良好的结果，钻井成功的概率减至0.05。地震勘探的经营费用估计是30万美元，钻井费用估计是10 万美元。试对上述情况进行决策。 Solution

This problem requires decision making at several occasions. The three major decisions are: whether to by a lease, whether to conduct a seismic survey, and whether to drill a well. It is easier to represent these decisions using a schematic representation. Figure shows each representation.

This representation is conventionally called a decision tree. In this decision tree, the decision nodes(the point at which a decision needs to be made) are shown by open squares. Open circles represent the probability node. In this decision tree, there are five decision nodes, indicating the point at which a decision node to be an isolated one where depending upon the EMV for each alternative, we can select the alternative which has the highest EMV. Buy lease 5 Don’t Buy Lease Favorable PS=0.7 a Seismic 4 Unfavorable PS=0.3 Drill PS=0.8 1 No Drill Drill PS=0.05 2 No Seismic Drill PS=0.2 3 No Drill No Drill 21

Consider node 1 where after a favorable seismic survey, we need to make a decision as to whether to drill or not to drill. Using Equation EMV= Ps(NPV)s+Pf(NPV)f= Ps(NPV)s+(1- Ps )(NPV)f =Ps[(NPV)s－(NPV)f]+(NPV)f

If we drill the well,

(NPV)s=120－10－10－30=70

In the above calculation, 120 represents the present worth if the well is successful, 10 represents the cost of drilling, another 10 represents the cost of leasing and 30 represents the cost of seismic survey, (NPV)f=－10－10－30=－50 Therefor,

EMV=0.8[70－(－50)]+(－50)=46 If we do not drill the well, EMV= － 40

Where –40 represents the cost of leasing and cost of conducting seismic survey.

Comparing the two expected values, we should decide to drill the well if the seismic survey is favorable.

The (EMV) corresponding to the selected decision is carried forward for further analysis.

At decision node 2, we can carry out a similar analysis. This node represent a decision of drilling a well if the seismic survey is unsuccessful. If we drill the well,

EMV=0.05[70－(－50)] －50=－44 If we do not drill the well, EMV=－40

Where －40 represents the cost of leasing and the cost of conducting a seismic survey.

Since EMV drilling option will result in a bigger loss, we should select the option of not drilling the well.

At decision node 3, where we have to consider drilling a well without conducting a seismic survey,

(NPV)s=120－10－10=100

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120 represent the present worth if the well is successful, the two 10 values represent the cost of leasing and the cost of drilling represent respectively.

There is no cost of seismic for this option. If we decide to drill a well, EMV=0.2[100－(－20)]－20=4

If the option of not drilling the well is chosen, EMV=－10

Where －10 represent the cost of leasing the land.

Comparing the two options, we need to select the option of drilling the well.

After we have made the decision at the three nodes, we can redraw our decision tree as follows, Buy lease 5 Don’t Buy Lease EMV=0 Seismic 4 Favorable PS=0.7 a Unfavorable PS=0.3 No Seismic EMV=46 EMV= - 40 EMV=4 We have a probability node after deciding to conduct a seismic survey. We can calculate the EMV at probability,

n

EMV??P?EMV?ii?1i

WHERE PI represent the probability of the event I, and (EMV)I represent the

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expected monetary value of the event i.

The EMV at probability node ―a‖ is, EMV=0.7×46+0.3×（－40）＝20.2

Consider the decision node 4. The EMV if we conduct a seismic survey is 20.2; if we don’t conduct a seismic survey, it is 4. Therefor, we should select the option of conducting the seismic survey. Therefor, the decision tree now can be drawn as,

Looking at the decision tree for Figure, the option to select is to buy the lease.

15. 有三个可行的方案在不同市场情况下的收益如（表6－16）所示， 试根据期望值及标准差选择方案。

表6－16 市场景气程度 单位：万元 方 案 方案Ⅰ收益 方案Ⅱ收益 方案Ⅲ收益 好（P好＝0.25） 300 400 100 可以（P可以＝0.5） 200 200 240 差（P差＝0.25） －80 －200 0 EMV=20.2 Buy lease 5 Don’t Buy Lease EMV=0

解：计算结果如表所示：

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方案 Ⅰ Ⅱ Ⅲ E(x) 155 150 145 E(x2) 44100 70000 31300 E(x)2 24025 22500 21025 D(x) 20075 47500 10275 σ（x） 141.69 217.94 101.37 cov 0.914 1.453 0.699 根据期望值应选Ⅰ方案；而根据标准差则选择Ⅲ方案。

16. 若经过普查和详查需在某构造上钻探，现有两个方案，方案Ⅰ是先钻一口井，方案Ⅱ是同时钻两口井。取得利润情况如（表6－17）所示。试用期望值和离差系数选择方案。

表6 利润情况表 单位：万元 状 况 发现大油田 发现小油田 干 井 方 案 Ⅰ 净 利 360 110 －30 概 率 0.2 0.6 0.2 方 案 Ⅱ 净 利 350 70 －60 概 率 0.4 0.5 0.1 解：计算结果如表所示：

方案 Ⅰ Ⅱ E(x) 132 169 E(x2) 33360 51810 E(x)2 17424 28561 D(x) 15936 23249 σ（x） cov 126.24 0.956 152.48 0.902

第八章 习题参考答案

4. 拟建某工程项目固定资产投资为1200万元，流动资金240 万元（其中自有流动资金80万元），其余所需资金全部为贷款。其中固定资产投资借款利率为12%， 流动资金借款利率为8%。固定资产折旧用平均使用年限法，寿命期末固定资产残值为50 万元。 基准折现率12%，所得税率为33%，投资使用计划如表1所示，其他数据如表2、表3所示。 表1 投资使用计划表 单位：万元 年 份 固定资产投资借款 流动资金投资借款 流动资金中自有资金 1 500 2 600 3 100 100 80 4 60 25

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