DYNAMIC STRATEGIC PLANNING

 

MID-SEMESTER QUIZ October, 1999

NOTE CAREFULLY!

The questions on the quiz test different capabilities. Furthermore, each question generally proceeds from easier to more difficult concepts. Examinees should therefore allocate their time optimally, by responding first to the questions that are easiest, and setting aside until the end the questions that are more difficult for them.

For your guidance, the points associated with each question are marked in parentheses alongside the question. They are calibrated with the time it should take to answer the question -- one point possible per minute.

The total number of points possible = 90

 

Name: _________________________________________

 

Question

Section

Maximum points

Actual points

1

a

4

 
 

b

2

 
 

c

4

 
 

d

3

 
 

e

3

 
 

f

3

 
 

g

3

 

2

a

3

 
 

b

8

 

3

a

6

 
 

b

5

 
 

c

4

 
 

d

6

 
 

e

6

 
 

f

5

 
 

g

15

 
 

h

6

 
 

i

4

 

Total

 

90

 

 

QUESTION 1

 

Given the production function: Z = 5 X0.6 Y0.2

And given the input cost function: C = 3 X2 + 2 Y

 

  1. (4pts) Calculate the marginal products and the marginal costs.
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  3. (2pts) State the conditions for optimal design as they apply to this case.
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  5. (4pts) Define in words the expansion path. Write the equation for the expansion path.
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  7. (3pts) Find the cost function associated with this technology.
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  9. (3pts) State and justify your conclusions about whether this production process exhibits economies of scale.
  10.  

     

     

     

     

     

     

  11. (3pts) Calculate the marginal rate of substitution at (X = 6; Y = 2).
  12.  

     

     

     

     

     

     

  13. (3pts) Is the feasible region convex? Please explain.

 

 

 

 

 

 

 

QUESTION 2

 

October 28, 1999. As often at that time, you are out of money and welcome the end of the month and your $3,500 pay. Except for the rent ($1,000) and for the $800 that will have to be available on the checking account for your monthly expenses, you are wondering how to make the best use of your money:

While having a drink with your best friend, you find out that you have won $1,000 in a lottery. Your friend jumps on the occasion, and asks you to lend him the $1,000.

 

  1. (3pts) Define the discount rate.
  2.  

     

     

     

     

  3. (8pts) Assuming that you do not want to take advantage of your friend and make a profit, but do not want to loose anything in the transaction either, how much would you ask your friend to pay you back in a year?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

QUESTION 3

 

January 2000. As the manager of International Chocolate Inc., you are reflecting over the exceptional sales level of your latest product, Millennium Crunch, during the Christmas - New Year season. You believe that you could certainly build on that success and develop a new line of production.

The initial investment cost for that new line is $2 million, but you are uncertain whether the demand you have observed will be sustained in the future:

Assuming that annual profits are received at the end of the year and that the discount rate is 15%, answer the following questions.

 

  1. (6pts) Evaluate the NPV of your investment in all three possible situations, and summarize it in the table below. Give the details of the computation. You can use the following information:
  2.  


    Number of periods

    Approximate series
    present value at

    5 %

    10 %

    15 %

    3

    2.72

    2.49

    2.28

    5

    4.33

    3.79

    3.33

    8

    6.46

    5.33

    4.50

    10

    7.72

    6.14

    5.02

    15

    10.4

    7.61

    5.85

    20

    12.5

    8.51

    6.26

     

     

     

     

     

     

     

    Summary

    Hit

    Fad

    Strong Product

    NPV

         

     

  3. (5pts) You have consulted your marketing department, and they have told you that Millenium Crunch has an equal probability of 30% of being a hit or a just a fad.
  4. Draw the decision tree, indicating all data.

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

  5. (4pts) If your goal is to maximize expected monetary value, would you invest the $2 million in the new line? Show calculations.
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  7. (6pts) You know that you could probably wait until next Thanksgiving and get a perfect vision of the market. Assuming that all possible outcomes are unchanged if you wait, draw the revised decision tree corresponding to the test of waiting until Thanksgiving for the certain information.
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  9. (6pts) If you choose to wait until next Thanksgiving, you will not be ready to market for the Christmas season either, and might very well lose one year of sales. You evaluate hence the overall true cost of conducting the test described in d) to be approximately $200,000.
  10. Do you think it might be worthwhile to wait? Show calculations and explain your choice.

     

     

     

     

     

     

     

     

     

  11. (5pts) Unsatisfied with this analysis and the risks of losing an opportunity, you wonder if a thorough marketing study could help you make a better decision.
  12. Draw the decision tree corresponding to a marketing test, omitting probabilities for the moment.

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

  13. (15pts) By experience, you know that the results of such marketing studies are only 60% reliable: when the product is a hit, the study actually concludes it is a hit only 60% of the time; in 20% of the cases, it would conclude it is a fad, and in another 20%, it would conclude it is a strong product.

Assuming that this reliability is independent of the actual event (the same would happen if it were a fad or a strong product), please compute all the revised probabilities that would result from a marketing study.

 

Hints:

  1. Notice the symmetry between the "hit" and "fad" events.
  2. You might find it easier to keep all calculations in the fraction form.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. (6pts) Add the probabilities calculated in g) to the decision tree drawn in f).
  2.  

     

  3. (4pts) How much would you be ready to pay for the marketing study? Show calculations.