3. (25 pts) Mr. Smith is deciding whether to invest $50,000 in the Daltex Oil Co
ID: 3358842 • Letter: 3
Question
3. (25 pts) Mr. Smith is deciding whether to invest $50,000 in the Daltex Oil Company. If the company will sel shares of stock publicly within the year, he will double his money; otherwise he will earn only the unattractive return of 5% for the year. Mr. Smith may take his other choice-buying a 10% (interest rate) savings certificate. He believes there is about an even chance (50/50) the Daltex will go public (P(P) -0.5). Mr. Smith makes his decisions on the basis of expected monetary values (EMV). 1) Fill the decision table for missing outcomes and find Mr. Smith's choice (on EMV) 2) Now if Mr. Smith knows from an annual report that Daltex is going public. Here is a change of 0.9 that they will say so in the report and only a 0.1 chance that they will deny it. On the other hand, if they are not going public there is a chance of 0.5 that they will say that they are not and 0.5 chance that they will lie and say they are. Use 'inverse probability law' to estimate the probability of that company will go public if he reads the report is saying so, P(P Y), where P stands for their going public, Y stands for their saying they will. And find Mr. Smith's choice again under your estimation. Daltex to Does not to tc public Invest in ( Daltex Buy 0.5 0.5 $55,000 -10 0.5 0.5Explanation / Answer
1)
Daltex go public
Does not go public
Invest in Daltex
A ($100,000)0.5
B ($52,500)0.5
Buy savings
C ($55,000)0.5
D ($55,000)0.5
Cell A: Question suggest that if Daltex goes public the investment would double.
Cell B: Question suggest that if Daltex does not go public the investment would earn only the return of 5% for the year.
Cell C & D: If the savings certificate was bought, the investment would earn the return of 10% for the year and it does not concern with Daltex going public or not.
Invest in Daltex
Buy Savings
Returns
$50,000
$2,500
$5,000
$5,000
Probabilities
0.5
0.5
0.5
0.5
Compute the EMV for investing in Daltex as follows:
EMVDaltex = (50000*0.5) + (2500*0.5)
= 26250
Now, Compute the EMV for investing in savings certificate as follows:
EMVDaltex = (5000*0.5) + (5000*0.5)
= 5000
Conclusion: As the EMV of investing Daltex is maximum, under EVM criterion Mr. Smith should choose to invest in Daltex.
2)
Consider E1 be the event of Daltax going public.
Consider E2 be the event of Daltax not going public.
Consider A be the event of Daltax accepts in the report that they are going public.
Write the respective probabilities as follows:
P (E1) = 0.5 P (E2) = 0.5
P (A|E1) = 0.9 P (A|E2) = 0.5
Now, compute the probability of Daltex going public and accepting that will as follows:
P (E1|A) = {P (E1)* P (A|E1)}/[{ P (E1)* P (A|E1)}+{ P (E2)* P (A|E2)}]
= (0.5*0.9)/[(0.5*0.9) + (0.5*0.5)]
=0.643
Conclusion: The probability P (P|Y), where P stands for their going public and Y stands for their saying they will is 0.643.
Also, compute the probability of Daltex not going public and accepting that will as follows:
P (E2|A) = {P (E2)* P (A|E2)}/[{ P (E1)* P (A|E1)}+{ P (E2)* P (A|E2)}]
= (0.5*0.5)/[(0.5*0.9) + (0.5*0.5)]
=0.357
Compute the EMV for investing in Daltex when going public as follows:
EMVGoing Public = (50000*0.643)
= 32150
Compute the EMV for investing in Daltex when not going public as follows:
EMVGoing Public = (2500*0.357)
= 892.5
Conclusion: As the EMV of Daltex going public is maximum, under EVM criterion Mr. Smith should choose to invest in Daltex.
Daltex go public
Does not go public
Invest in Daltex
A ($100,000)0.5
B ($52,500)0.5
Buy savings
C ($55,000)0.5
D ($55,000)0.5
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