ASSIGNMENT # $3$

Decision Analysis and Project Management

Assignment must be typed $($i$.$e$.$ can NOT be

handwritten$),$ neat, readable, and well$-$organized. However, it is ok to plot GRAPHS by hand and to

SCAN$/$INCLUDE them within the PDF document file if they are large, legible, and properly labeled

and that their calculations are typed within the rest of the assignment. Plotting

using Excel, a paint tool or hand plotting is OK$.$

Submitted assignment solutions $($if applicable$)$ must include $$managerial statements$$ that

communicate the results of the analyses in plain language.

Problem $1(35$ points$)$

Petro Enterprises is a small oil exploration business. They have a nontransferable short$-$term option to

drill on a certain plot of land. Two recent dry holes have depleted Petro's net liquid assets to $$130,000.$

The president must decide whether Petro should exercise its short$-$term option or allow it to expire. $($It

will expire in two weeks if drilling is not commenced by then.$)$ The president has the opportunity of

paying for a seismic test run in the next few days, which could help determine if it is worth drilling.

To conserve capital and maintain flexibility, Petro subcontracts all drilling and seismic tests. It can

have the seismic test performed on short notice at overtime rates for a fixed fee of $$30,000$ and the well

can be drilled for a fixed fee of $$100,000.$ If oil is found, Petro must decide whether to develop the oil

field itself or sell the rights. A large oil company has agreed that if Petro drills and discovers oil, it will

purchase all Petro's rights for $$400,000.$

The company's geologist has examined the geology of the region and states that there is a $0\mathrm{.}55$

probability that if a well is sunk, oil will be discovered. Data on the reliability of the seismic test

indicate that if the test is favourable, the probability of finding oil will increase to $0\mathrm{.}85$ but that if the

test is unfavourable, it will fall to $0\mathrm{.}1.$ The geologist has computed that there is a $0\mathrm{.}6$ probability that

the result will be favourable if the test is made.

Unfortunately, if oil is discovered, it is not possible to know the extent of the find before the decision

as to whether to sell the rights to the land expires. Experience suggests that if oil is found, there is a

$0\mathrm{.}2$ probability that it is a small reservoir, $0\mathrm{.}7$ probability that it is a medium reservoir and $0\mathrm{.}1$

probability that it is a large reservoir. Petro estimates its profits $($not including costs associated with

exploration$)$ from developing the oil field itself to be $$200,000$ if the reservoir discovered is a small

one, $$350,000$ if it is a medium reservoir and $$800,000$ if it is a large one.

Using a Decision Tree, determine Petro's best policy in terms of whether to take advantage of the

seismic test and whether to develop or sell the rights if oil is found. Present your answer in a format of

a Report to Management $($i$.$e$.,$ Verbally communicate the decision strategy$).$

heres the answer i got, but can you make a decision tree please on paper so i can see. thanks!

Step $1$

Introduction

Petro Enterprises faces a critical decision regarding a short$-$term drilling option on a plot of land. With limited liquid assets of $$130,000$ and the option expiring in two weeks, the president must decide whether to drill, conduct a seismic test, or let the option expire. This decision involves understanding the costs and potential profits associated with drilling, the probabilities of discovering oil, and the subsequent choices of selling rights or developing the field. The report aims to evaluate these options using a decision tree analysis to determine the best course of action for Petro Enterprises.

Explanation:

Petro Enterprises must decide whether to drill, conduct a seismic test, or let their option expire, considering costs, probabilities, and potential profits. This report uses decision tree analysis to find the best course of action.

Step $2$

Decision Tree Ansalysis

Building the Decision Tree

$1.$ Initial Decision Node:

$-$ Conduct Seismic Test

$-$ Do not conduct Seismic Test

$2.$ Seismic Test Outcome Node:

$-$ Favorable Test Result

probability$)$

$-$ Unfavorable Test Result

probability$)$

$3.$ Drilling Decision Node $($if Seismic Test is conducted$)$:

$-$ Drill $($additional

cost$)$

$-$ Do not drill

$4.$ Oil Discovery Node $($after drilling$)$:

$-$ Oil Found $($if drilled and test is favorable:

probability, if test is unfavorable:

probability, if no test:

probability$)$

$-$ No Oil Found

$5.$ Profit Calculation Node:

$-$ Sell rights for

$-$ Develop field:

$-$ Small Reservoir

$-$ Medium Reservoir

$-$ Large Reservoir

Explanation:

Construct a decision tree to evaluate options, including the seismic test outcome, drilling decision, oil discovery probabilities, and potential profits from selling or developing the oil field.

Expected Monetary Value $($EMV$)$ Calculations

Without Seismic Test:

$1.$ Drill:

$-$ Oil found:

probability