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Rajat is sales manager of Dubin Computers Ltd. and looks after Delhi market. The company sells laptops in India. He is currently trying to select a distributor for coming five years. The distributor ensures that the products are accessible to the customers in the market. Market share of a company depends on the coverage by the distributor. The total profit potential of the entire laptop market in Delhi is Rs. 5 crores in the current year and present value of next four years’ cumulative profit potential is Rs. 15 crores. The first choice for Rajat is to enter into long-term contract with a distributor M/s Jagan with whom Dubin has done business in the past, and whose distribution system reaches 55 percent of all potential customers. At the last moment, however, a colleague suggests Rajat to consider signing a one-year contract with other distributors. Distributors M/s Bola and M/s James are willing to be partner with Dubin. Although a year ago M/s Bola’s and M/s James’s coverage reached only 40 and 25 percent of customers respectively, they claim to have invested heavily in distribution resources and now expect to be able to reach 60 percent and 75 percent of customers respectively. The probability of M/s Bola’s claim and M/s James’s claim to be true is 0.60 and 0.20 respectively. The knowledge about distributors’ coverage will evolve over time. The assumption is that the true level of coverage offered by the new distributors could be discovered, with certainty, through a one-year trail, and this trail will reveal exactly one of the two levels of coverage: for example in case of M/s Bola – 40 percent (as it was last year) or 60 percent (as claimed). In addition, it is also assumed that whatever the coverage is for both distributors, it will not change over time. Rajat narrows down on three choices, which are as follows:
Choice 1. Give a five year contract to the familiar distributor M/s Jagan.
Choice 2. Give a one year contract to the new distributor M/s Bola, and base next year’s decision to renew contract with M/s Bola on observed coverage for next four years or enter into a four years' contract with M/s Jagan.
Choice 3. Give a one-year contract to the new distributor M/s James, and base next year’s decision to renew contract with M/s James on observed coverage for next four years or enter into a four years contract with M/s Jagan..
If the distributor M/s James claims a coverage of 55% instead of 75% and probability of this claim to be true is 0.70 instead of 0.20 then which of the following statement is true?
We are left with 3 choices.
Choice 1:
The first choice is to give the contract to M/S Jagan. In this case, we know that Jagan's market reach is 55%. It has been given that the total profit potential is 5 crores in the present year and 15 crores in the next 4 years.
Therefore, the expected value of profit earned for choice 1 is 0.55*(5+15) = Rs.11 crore.
Choice 2:
Give the contract to M/s Bola for one year and based on the performance, renew the contract with him for the next 4 years or give M/S Jagan the contract for the next 4 years.
Let us assume that M/S Bola retains the contract for all 5 years. Rajat will renew the contract only if M/S Bola's claim that their market reach is 60% is true. The probability of the claim being true is 0.6.
Therefore, the EV of return if M/S Bola bags the contract for all 5 years = 0.6*0.6*(5+15) = Rs. 7.2 crores.
Let us assume that M/S Bola's claim is false. The probability of the claim being false is 1-0.6 = 0.4.
Now, if the claim is false, Rajat will terminate the contract by the end of the year and will partner with M/S Jagan for the next 4 years. Also, we have historic data that M/S Bola reaches 40% of the customers. Even if the claim is false, the laptops will reach 40% of the customers in the first year and 55% of the customers from the second year (Since M/S Jagan will bag the contract).
Therefore, the EV of profit in this case is 0.4*0.4*5+0.4*0.55*15 = 0.8 + 3.3 = Rs.4.1 crores.
Therefore, the total EV if M/S Bola bags the contract the first year is 7.2+4.1 = Rs.11.3 crores.
It has been given in this question that M/S James claims a coverage of 55% and the probability of this being true is 0.7.
Choice 3:
Give the contract to M/s James for one year and based on the performance, renew the contract with him for the next 4 years or give M/S Jagan the contract for the next 4 years.
Let us assume that M/S James retains the contract for all 5 years. Rajat will renew the contract only if M/S Jame's claim that their market reach is 55% is true. The probability of the claim being true is 0.7.
Therefore, the EV of return if M/S James bags the contract for all 5 years = 0.7*0.55*(5+15) = Rs. 7.7 crores.
Let us assume that M/S James's claim is false. The probability of the claim being false is 1-0.7 = 0.3.
Now, if the claim is false, Rajat will terminate the contract by the end of the year and will partner with M/S Jagan for the next 4 years. Also, we have historic data that M/S James reaches 25% of the customers. Even if the claim is false, the laptops will reach 25% of the customers in the first year and 55% of the customers from the second year (Since M/S Jagan will bag the contract).
Therefore, the EV of profit in this case is 0.3*0.25*5+0.3*0.55*15 = 0.375 + 2.475 = Rs.2.85 crores.
Therefore, the total EV if M/S Bola bags the contract the first year is 7.7+2.85 = Rs.10.55 crores.
EV of choice 1 = Rs. 11 crores
EV of choice 2 = Rs. 11.3 crores
EV of choice 3 = Rs. 10.55 crores
Arranging the choices by EV, we get, Choice 2 > Choice 1 > Choice 3.
Choice 2 is more profitable than choice 3. Therefore, option B is true and hence, option B is the right answer.
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