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CMA Intermediate · Financial Management and Business Data Analytics · Financial Institutions

Aarav Ltd. needs Rs 50 lakh for 90 days. A bank offers a loan at 12% p.a. simple interest with interest paid at maturity. Alternatively, Aarav can issue commercial paper at a discount of 11.5% p.a. for 90 days (360-day year, discount on face value). Face value of CP is set so that net proceeds are Rs 50 lakh. What is the approximate effective annual-rate comparison, using simple annualisation (interest/net proceeds x 360/90)?

CP costs about 11.84% p.a., which is cheaper than the 12% bank loan. The 90-day discount is 2.875% of face value, so proceeds are 97.125%. Dividing 2.875 by 97.125 gives 2.96% for the quarter, and annualising by four gives roughly 11.84%.

  1. ACP costs about 11.84% p.a., cheaper than the bank loanCorrect
  2. BCP costs 11.50% p.a., cheaper than the bank loan
  3. CCP costs about 11.84% p.a., costlier than the bank loan
  4. DCP costs 12.50% p.a., costlier than the bank loan

Explanation

Discount for 90 days = 11.5% x 90/360 = 2.875% of face value. Net proceeds = 97.125% of face. Cost on proceeds = 2.875/97.125 = 2.96% for 90 days; x4 = 11.84% p.a. This is below 12%, so CP is cheaper. Quoting 11.5% ignores that the discount is on face value, not proceeds.

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