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NISM Certifications · NISM-Series-X-B: Investment Adviser (Level 2) · Retirement Planning Basics

Mr. Rao needs a corpus at retirement that can fund Rs 12,00,000 a year of expenses forever, with the corpus earning a constant 6% a year and withdrawals fixed in nominal terms at the start of the year (an annuity due perpetuity). The corpus must equal the first withdrawal plus the present value of the later withdrawals. What corpus is required?

The required corpus is Rs 2,12,00,000. A perpetuity of Rs 12 lakh at 6% is worth Rs 2 crore when paid at year end. Because payments are made at the start of each year, the first Rs 12 lakh is needed immediately, so it is added.

  1. ARs 2,00,00,000
  2. BRs 2,12,00,000Correct
  3. CRs 1,88,00,000
  4. DRs 2,06,00,000

Explanation

Ordinary perpetuity value = 12,00,000 / 0.06 = Rs 2,00,00,000. With withdrawals at the start of the year, the first payment is made immediately, so add Rs 12,00,000, giving Rs 2,12,00,000. Rs 2,00,00,000 ignores the timing and Rs 1,88,00,000 subtracts instead of adds.

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