CAT 2025 Lesson : Caselets - Case 2

Read the following and answer the questions that follow

An automobile company’s annual sales of its small cars depends on the state of the economy as well as on whether the company uses some high profile individual as its brand ambassador in advertisements of its product. The state of the economy is “good”, “okay” and “bad” with probabilities 0.3, 0.4 and 0.3 respectively. The company may choose a high profile individual as its brand ambassador in TV ads or may go for the TV ads without a high profile brand ambassador.

If the company fixes price at Rs. 3.5 lakh, the annual sales of its small cars for different states of the economy and for different kinds of TV ads are summarized in table 1. The figures in the first row are annual sales of the small cars when the company uses a high profile individual as its brand ambassador in its TV ads and the ones in the second row are that when the company does not use any brand ambassador in TV ads, for different states of the economy.



Without knowing what exactly will be the state of the company in the coming one year, the company will either have to sign a TV ad contract with some high profile individual, who will be the company’s brand ambassador for its small car for the next one year, or go for a TV ad without featuring any high profile individual. It incurs a cost of Rs. 3.45 lakh (excluding the payment to the brand ambassador) to put a car on the road.

When the company’s profit is uncertain, the company makes decisions on basis of its expected profit. If the company can earn a profit xi with probability pi (the probability depends on the state of economy), then the expected profit of the company is $\sum _{i} \ x_{i} \ p_{i}$
[XAT 2010]

4) The maximum that the company can afford to pay its brand ambassador is

(1) Rs. 10.0 crore
(2) Rs. 10.6 crore
(3) Rs. 10.8 crore
(4) Rs. 12.0 crore
(5) Rs. 16.4 crore

5) Mr. Khan, a popular film actor, agreed to sign the contract to become the company’s brand ambassador for Rs. 9 crore. The cost to the company of putting a car on the road also got escalated. The maximum escalation in cost of putting a car on the road, for which the company can afford to sign the contract with Mr. Khan is

(1) Rs. 900
(2) Rs. 967
(3) Rs. 1250
(4) Rs. 1267
(5) Rs. 1333

6) Mr. Khan, a popular film actor, agreed to sign the contract to become the company’s brand ambassador for Rs. 9 crore. The cost to the company of putting a car on the road also got escalated by Rs. 1000. If the company signs the contract with Mr. Khan, its profit will

(1) increase by Rs. 40 lakh
(2) increase by Rs. 60 lakh
(3) decrease by Rs. 20 lakh
(4) decrease by Rs. 40 lakh
(5) decrease by Rs. 50 lakh

Solution

Case Solution: For a clear understanding about the case you need to observe that the company will gain a profit on each cars, but when the brand ambassador is used the sales of the company will increase. As a result, the profit for the company will also increase. This profit is an additional profit for the company.

Thus the company can afford to pay brand ambassador an amount which is less than or equal to the additional profit.

Selling Price of each car is 3.5 lakh
Cost price of each car is 3.45 lakh

Profit of each car = 3.5 – 3.45 = 0.05 lakh = Rs. 5000

Total Profit = Profit per car $\%$ Number of cars
Expected profit = $\sum x_i w_i$ = Total Profit $\times$ probability = Profit per car $\times$ Number of cars $\times$ Probability
The probability of number of cars sold in the state of the economy “good”, “okay” and “bad” are 0.3, 0.4 and 0.3

The actual number of of cars sold under the probability in each state of economy is given below


With a brand ambassador the company will sell 24,000 more cars.

4) The maximum that the company can afford to pay the brand ambassador is the profit Rs. 5000 for each 24,000 cars
= 5000$\times$24000= 12 crore

Answer: (4) 12 crore.

5) Total of 24,000 cars more cars are sold when a brand ambassador is contracted.
If Mr. Khan is contracted for 9 crore then the profit for the company will be greater than or equal to the 9 crore Profit $\times$ number of cars > $\geq$ Contract amount
Profit $\times$ 24,000 $\geq$ 9$\times$ 10^7
Profit $\geq$ 3750
A minimum profit of Rs. 3750 is required to cover the amount
Actual profit = 5000
Maximum escalation of cost = 5000 – 3750 = Rs.1250

Answer: (3) Rs.1250

6) From the above question we know if Mr. Khan is contracted with 9 crore we can have a maximum of escalation cost of Rs. 1250
If Rs. 1000 is escalated, then the profit is Rs. 250 for each car
Total profit = 250 times 24000 = 60 lakh

Alternatively
Profit on each car = Rs. 5000
Increased cost on each car = Rs. 1000
New profit = Rs. 4000
Total profit = 4000$\times$24000= 9.6 crore
Contract amount to Mr. Khan = 9 crore
Actual Profit = 9.6 – 9 = 0.6 crore = 60 lakh

Answer: (2) Increased by Rs. 60 lakh

Answer:
4) (4) Rs. 12.0 crore
5) (3) Rs. 1250
6) (2) increase by Rs. 60 lakh