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NISM Certifications · NISM-Series-X-A: Investment Adviser (Level 1) · Time Value of Money

Caselet: Anita, aged 40, is offered a perpetual annuity-style payout from a trust: Rs 60,000 at the end of every year forever, with the first payment one year from today. She uses a discount rate of 8% per annum. A rival product pays Rs 60,000 at the start of every year forever (first payment today) at the same discount rate. What is the difference in present value of the rival product over the first (ordinary) one?

The difference is Rs 60,000. The ordinary perpetuity is worth 60,000 divided by 0.08, or Rs 7,50,000, while the perpetuity due adds the immediate first payment of Rs 60,000, giving Rs 8,10,000, so the gap equals one payment.

  1. ARs 60,000Correct
  2. BRs 4,800
  3. CRs 7,50,000
  4. DRs 7,50,000 less Rs 60,000, i.e. Rs 6,90,000

Explanation

Ordinary perpetuity PV = 60,000/0.08 = 7,50,000. The perpetuity due has the same flows with an extra payment today, so its PV = 7,50,000 + 60,000 = 8,10,000. The difference is Rs 60,000. Rs 4,800 is 8% of 60,000, a wrong calculation.

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