QT Assignment Waterman Case_Group 10_Section F

Quantitative Techniques III

Assignment 1

Waterman Engineering Corporation

Submitted to

Prof. Vinaysingh Chawan

Group 10 Section F Name Aditya Balaraman Ashwani Kansal Ganesh Prasad NivruttiArote Guthi Phani Himaja Kumar Vibhore S Nitish Sivaramakrishnan

1

Roll Number 2012PGP014 2012PGP071 2012PGP113 2012PGP453 2012PGP179 2012PGP322

1. Decision diagram for Waterman’s decision problems and evaluate the after tax net liquid assets of the company at each possible end position. (‘000s) 0

Before Tax

No go Norwood go

(‘000s) After Tax (x+57) 20.8 77.8

without restriction 0.5

40

with restriction 0.2

10

5.2

62.2

-30

-15.6

41.4

-30

-15.6

41.4

40

20.8

77.8

5.2

62.2

-10.4

46.6

- 31.2

25.8

41.6

98.6

26

83

refused 0.3

No go

0

Prescott go

necessary 0.4 unnecessary 0.6

Prescott-Norwood

Nec HT

0.5 without restriction

Go

0.2 with restriction 0.4 0.6

0.3 refused Unnec HT

0.5

without restriction

0.2 with restriction 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) Norwood contract

without restrictions

Variable X

x+ 57

u(x+57)

20.8

77.8

0.878185

(150-110) =40 0.5 2

with restrictions

0.2

Refused

0.3

(120-110) =10 (150-180) =-30

5.2

62.2

0.769357

-15.6 6.76

41.4 63.76

0.524019 0.750169

P(Y)

Prescott Antenna

Necessary

0.4

unnecessary

0.6

Variable y (140-90-10-70) =-30 (140-90-10) =40

P(Z) Necessary unnecessary Necessary Restriction unnecessary Necessary Reject unnecessary NorwoodPrescott no restriction

-15.6 20.8 6.24

Z

0.2 0.3 0.08 0.12 0.12 0.18

y+ 57 41.4

0.524019

77.8 0.878185 63.24 0.736518

z+57 5.2 41.6 -10.4 26 -31.2 5.2 13

u(y+57)

62.2 98.6 46.6 83 25.8 62.2 70

u(z+57) 0.769357 0.96812 0.601751 0.905511 0.051246 0.769357 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 go for Norwood deal 2. If waterman utility function was linear, what would be the value to him of the Norwood deal 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 deal

6.76

Prescott deal

6.24

Both

13

3

3. According to the utility curve in exhibit 2 and the addendum, what are the values to him (certainty equivalents) of the deals individually and together? By considering the utility curve and the addendum we get the following certainity equivalent values Deals

Certainty Equivalent

Norwood deal

3.0187

Prescott deal

1.5425

Both

2.5334

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 formula Risk Premium= Expected Monetary Value- Certainty Equivalents Deals

Risk Premium

Norwood deal

3.7413

Prescott deal

4.6975

Both

10.4666

5. Why is or is not the value of the deals together equal to the sum of individual values in 2 and 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 Premiums The 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 Risk Premium formula has Certainty Equivalent component in it , (Risk Premium (deal) = EMV (deal) – Certainty equivalent (deal) ) 4

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 than Prescott 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 doesn’t 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 use to 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 by accepting 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 Ua(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 concluding by 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

5

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 after Norwood deal

nec not nec

0.4 0.6

Ua (57+y) 57+y -15.6 41.4 0.5240 20.8 77.8 0.8782 0.7365

As per the data mentioned in the case, license for Norwood deal will be issued after 15 th of December and therefore deal cannot be completed before that. So, the deal may take more than 4 months 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 utility function in 10? The certainity equivalent is 0.098071645 for Prescott deal post Norwood deal.

6

7

Annexure 59.53339 60.0187 58.54252

-0.01152 0.745743 0.000413 -0.01138 0.750169 2.46E-08 -0.01183 0.736518 4.46E-07

8

57 77.8 62.2 41.4

41.4 77.8

62.2 98.6 46.6 83 25.8 62.2

-0.01233 -0.00709 -0.01073 -0.01894

0.721645 0.878185 0.769357 0.524019

-0.01894 0.524019 -0.00709 0.878185

-0.01073 -0.00409 -0.01634 -0.00618 -0.03475 -0.01073

0.769357 0.96812 0.601751 0.905511 0.051246 0.769357

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

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