qt assignment waterman case_group 10_section f

8/12/2019 QT Assignment Waterman Case_Group 10_Section F

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Quantitative Techniques III

Assignment 1

Waterman Engineering Corporation

Submitted to

Prof. Vinaysingh Chawan

Group 10

Section F

Name Roll Number

Aditya Balaraman 2012PGP014Ashwani Kansal 2012PGP071

Ganesh Prasad NivruttiArote 2012PGP113

Guthi Phani Himaja 2012PGP453

Kumar Vibhore 2012PGP179

S Nitish Sivaramakrishnan 2012PGP322


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1. Decision diagram for Watermans decision problems and evaluate the after tax netliquid assets of the company at each possible end position.

(000s) (000s)

0 Before Tax After TaxNo go (x+57)

Norwood without restriction 0.5 40 20.8 77.8

go with restriction 0.2 10 5.2 62.2

refused 0.3

-30 -15.6 41.4

No go 0

Prescott -30 -15.6 41.4

go necessary 0.4

unnecessary 0.6

40 20.8 77.8

Prescott-Norwood Nec HT 0.5 without restriction 5.2 62.2

Go 0.2 with restriction

-10.4 46.6

0.4 0.3 refused

- 31.2 25.8

0.6 Unnec HT 0.5 without restriction 41.6 98.6

0.2 with restriction

26 83

refused

0.3

No go 5.2 62.2

0

The calculations at each node are shown in the payoff tables given below:

All the values in the tables are in 000s.Variables X,Y,Z are after tax values of Norwood, Prescott,Norwood-Prescott deal respectively. The values in the After tax column are calculated by

multiplying before tax value of the respective deal with (1-t)=0.52.

P(x) Variable X x+ 57 u(x+57)

Norwood

contract without

restrictions 0.5

(150-110)

=40

20.8 77.8 0.878185


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Prescott

Antenna

P(Y) Variable y y+ 57 u(y+57)

Necessary 0.4

(140-90-10-70)

=-30 -15.6 41.4 0.524019

unnecessary 0.6

(140-90-10)

=40 20.8 77.8 0.878185

6.24 63.24 0.736518

Norwood-

Prescott

P(Z) Z z+57 u(z+57)

no

restriction

Necessary 0.2 5.2 62.2 0.769357

unnecessary 0.3 41.6 98.6 0.96812

Restriction

Necessary 0.08 -10.4 46.6 0.601751

unnecessary 0.12 26 83 0.905511

Reject

Necessary 0.12 -31.2 25.8 0.051246

unnecessary 0.18 5.2 62.2 0.769357

13 70 0.745743

From the above tables it is evident that it is better to go for Norwood deal than Prescott. The

utility function of Norwood alone is higher than Norwood-Prescott deal . So, it is better to gofor Norwood deal

2. If waterman utility function was linear, what would be the value to him of the Norwooddeal alone? Prescott deal alone? Both together?

From the above tables we clearly know that when utility function is linear, the value can be

calculated using the Expected Monetary Value formula.

Deals Value

Norwood deal6.76

Prescott deal6.24

Both13

with

restrictions 0.2

(120-110)

=10 5.2 62.2 0.769357

Refused 0.3

(150-180)

=-30 -15.6 41.4 0.524019

6.76 63.76 0.750169


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3. According to the utility curve in exhibit 2 and the addendum, what are the values tohim (certainty equivalents) of the deals individually and together?

By considering the utility curve and the addendum we get the following certainity equivalentvalues

Deals Certainty Equivalent

Norwood deal3.0187

Prescott deal1.5425

Both2.5334

4. What are the Risk Premium in 2 and 3?In risk averse case we pay risk premium to avoid uncertainty. We can calculate Risk

Premium using the formulaRisk Premium= Expected Monetary Value- Certainty Equivalents

Deals Risk Premium

Norwood deal3.7413

Prescott deal4.6975

Both10.4666

5. Why is or is not the value of the deals together equal to the sum of individual values in 2and 3?

If we consider linear utility function, then we can see that the EMV of both the deals is equal

to the sum of the individual deals i.e., 6.76 + 6.24 =13. As it is risk neutral function it is

equal to the sum of both the deals.

But if we consider risk averse function, we can see that the utility curve is involved and the

value of both the deals is not equal to the sum of the individual deals (0.750169+ 0.745743 is

not equal to 0.745743).

6. Same question for Risk PremiumsThe risk premiums of both the deals will not be equal to the sum of individual deals.

We know from the above tables that EMV of both the deals is equal to the sum but Certainty

equivalents of both the deals is not equal to the sum of the individual deals . As RiskPremium formula has Certainty Equivalent component in it , (Risk

Premium (deal) = EMV (deal)Certainty equivalent (deal) )


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it is obvious that the risk premium of both the deals will not be equal to the sum of individual

deals.

7. If only Norwood or Prescott could be chosen, not both which should waterman prefer?Comparing Norwood deal with Prescott deal, the payoff for Norwood deal is more thanPrescott deal . So, Waterman should prefer Norwood deal not the Prescott.

8. Would the answer in 7 be same for all risk averse utility functions?The answer doesnt change even if we consider all risk averse utility functions. By all means

Norwood deal is better than Prescott deal.

9. Is waterman decreasingly risk averse?No. It is increasingly risk averse function as the utility graph is concave in shape.

10.If Waterman has already accepted the Norwood deal, what utility function could he useto evaluate further opportunities concluding by April 1, 1970, under what assumptions?

(Describe how to find values and find a few)

Assumptions:

Initially before accepting Norwood deal there was minimal risk involved. But byaccepting the Norwood deal , Waterman is exposed to more risk.

Norwood deal will be completed before the Prescott deal.Let us consider the position of Norwood before accepting the deal to be x and the utility

function be U(x). Then after accepting it will become equal to U a(x).

So, Ua(x) = U(x) + Risk involved by accepting Norwood deal

After Norwood deal

Prob values utility fn

0.5 20.8 u(x+20.8)

0.2 5.2 u(x+5.2)

0.3 -15.6 u(x-15.6)

Waterman can use the following utility function to evaluate further opportunities concludingby April 1, 1970.

Ua(x) = 0.5*U(x+20.8) + 0.2*U(x+5.2) + 0.3* U(x-15.6)

Eg. Consider x=60,

X+20.8 = 80.8 U(x+20.8) = 0.894408


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X+ 5.2 = 65.2 U(X+5.2)= 0.793958

X-15.6= 44.4 U(X-15.6) = 0.570776

Ua(X)= 0.5*0.894408 + 0.2*0.793958 +0.3 *0.570776

=0.777229

11.Does Prescott deal satisfy these assumptions?

Prescott 57+y

Ua

(57+y)

after

Norwood

deal

nec 0.4 -15.6 41.4 0.5240

not nec 0.6 20.8 77.8 0.8782

0.7365

As per the data mentioned in the case, license for Norwood deal will be issued after 15th

of

December and therefore deal cannot be completed before that. So, the deal may take more than 4months time whereas Prescott deal will take maximum 3 months time to complete. So, the

assumption that the Norwood deal is completed before Prescott is not valid here.

12.What would be the certainty equivalent for the Prescott deal according to the utilityfunction in 10?The certainity equivalent is 0.098071645 for Prescott deal post Norwood deal.


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Annexure

59.53339 -0.01152 0.745743 0.000413

60.0187 -0.01138 0.750169 2.46E-08

58.54252 -0.01183 0.736518 4.46E-07


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57 -0.01233 0.721645

77.8 -0.00709 0.878185

62.2 -0.01073 0.769357

41.4 -0.01894 0.524019

41.4 -0.01894 0.524019

77.8 -0.00709 0.878185

62.2 -0.01073 0.769357

98.6 -0.00409 0.96812

46.6 -0.01634 0.601751

83 -0.00618 0.905511

25.8 -0.03475 0.051246

62.2 -0.01073 0.769357

These values were used in the calculations in the above questions.

qt assignment waterman case_group 10_section f

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