Question

As the Manager of a growing beauty product company, you are considering widening the product range by launching a new product: a hair dressing tonic. The incremental profit is $700 per unit and the necessary investment in equipment is $39 million. The marketing department has given you the estimated demand as follows:

Units demanded 30,000 40,000 50,000 60,000 70,000

Probability 0.05 0.10 0.20 0.30 0.35

QUESTION:

1) Compute the expected profits for all the possible events (states of nature)

2) Prepare a pay-off table for this decision situation

3) Advise the board of directors whether the new product should be introduced.

Hint: Use the expected value criterion

4) The board has now resolved to obtain expert information and is in the process of contracting a marketing consultancy firm for this purpose.

Suggest the maximum amount that your company should be willing to pay for the consultancy.

Support your answer with the relevant workings.

Answer 1

Answer to Question 1&2:-

Units Demanded Probability(p) Profit per unit  Expected profit Investment Pay-off

300000 0.05 $700 $10,50,000 $390,00,000 $(3,79,50,000)

40000 0.10 $700 $28,00,000 $390,00,000 $(3,62,00,000)

50000 0.20 $700 $70,00,000 $3,90,00,000 $(3,20,00,000)

60000 0.30 $700 $1,26,00,000 $3,90,00,000 $(2,64,00,000)

70000 0.35 $700 $1,71,50,000 $3,90,00,000 $(2,18,50,000)

Answer to Question 3:

Expected Value Criterion= Average of Expected Profits taking probability as Weight

  

Expected profit Probability(p) Expected Value Criterion(x)

$10,50,000 0.05 $52,500

$28,00,000 0.10 $2,80,000

$70,00,000 0.20 $14,00,000

$1,26,00,000 0.30 $37,80,000

$1,71,50,000 0.35 $60,02,500

Total = $1,15,15,000

Expected Value Criterion = xp/p =1,15,15000/1 =1,15,15,000

The new product should not be introduced as Expected Value Criterion is less than Initial Cost of Investment.

Answer to Question 4

The maximum amount Company can pay to Consultancy or is willing to pay to Consultancy is not determinable as the Coimpany is not profit making and the Company is still unable to recover initial cost of Investment. Once the Company recovers cost of Investment, Cost of Consultancy can be determined