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IAI Actuarial Core Principles · Business Finance · Key principles of finance

A perpetuity pays Rs 12,000 a year, with the first payment due at the end of year 4. The discount rate is 10% per annum. Given 1.1^3 = 1.331, what is the present value today (nearest rupee)?

The present value is about Rs 90,158. A perpetuity is valued one period before its first payment, so at the end of year 3 it is worth 12,000 divided by 0.10, or Rs 1,20,000. Discounting this back three years at 10% gives Rs 90,158.

  1. ARs 1,20,000
  2. BRs 90,158Correct
  3. CRs 1,06,000
  4. DRs 1,32,000
  5. Rs 82,000

Explanation

Value one year before the first payment (end of year 3) = 12,000/0.10 = 1,20,000. Discount 3 years: 1,20,000/1.331 = Rs 90,158. Rs 1,20,000 forgets the deferral. Rs 82,000 approximates discounting 4 years, which wrongly uses one period too many.

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