XAT 2015 — LRDI Question 9
Answer the questions on the basis of information given in the following case.
A few years back Mr. Arbit and Mr. Boring started an oil refinery business. Their annual earing is currently just 50,000 million rupees. They are now exploring various options to improve the business. Mr. Xanadu, a salesperson from Innovative Technology Solutions (ITS), is trying to sell a new oil refinery technology to Mr. Arbit and Mr. Boring. This technology could potentially enhance their annual earning to 150,000 million rupees within a year. But they have to make one-time investment of 100,000 million rupees to implement the technology. If the technology is not successful, the investment would be lost. Mr. Arbit and Mr. Boring are discussing about possible risks of the investment.
Mr. Arbit and Mr. Boring did not invest in the new technology, but the new technology is a big success. Repentant, they are now estimating the additional amount they would have earned (i.e. forgone earnings) had they invested in the new technology. However, the two owners differed on expected lifespan of the new technology. Mr. Arbit expected lifespan to be 5 years, whereas, Mr. Boring expected it to be 2 years. After the technology gets out-dated, the earnings from the business would drop back to 50,000 million rupees.
What would be the difference between two expected foregone earnings after 5 years of the technology investment, if yearly earnings are deposited in a bank @10%, compounded annually?
Note: Forgone Earnings = (Earnings from business with new technology) – (Earnings from business without new technology)
Answer & solution
- A
231,200 million rupees
331,000 million rupees
- C
400,510 million rupees
- D
431,000 million rupees
- E
464,100 million rupees
Forgone Earnings (F) = Earnings with new technology – Earnings without new technology
Let X = (Earnings without new technology for 5 years),
Let Y and Z be A’s and B’s respective earnings with new technology.
FA = Y – X
FB = Z – X
FA – FB = Y – Z
Both A and B use the new technology in the first 2 years. For the last 3 years, only A uses the technology.
Y = (Earnings with new technology for first 2 years) + (Earnings with new technology for last 3 years)
Z = (Earnings with new technology for first 2 years) + (Earnings without new technology for last 3 years)
∴ Y – Z = (Earnings with new technology for last 3 years) – (Earnings without new technology for last 3 years)
Earnings of the third year, with (or without) new technology, are placed at compound interest for 2 years. Similarly, earnings of the fourth year are placed at C.I. for 1 year and earnings of the last year do not earn any interest.
∴ Y – Z = [(150 × 1.12 + 150 × 1.1 + 150) – (50 × 1.12 + 50 × 1.1 + 50)] ×1000 million
= [(100) × 1.12 + (100) × 1.1 + 100)] ×1000 million
= 331000 million
Hence, option (b).