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CS Executive · Corporate Accounting and Financial Management · Time Value of Money

A scheme pays Rs 10,000 at the end of each year, forever, to a trust. The discount rate is 8% per annum. What is the present value of this perpetuity, and what happens to it if the rate rises to 10%?

The perpetuity is worth Rs 1,25,000 at 8%, being the annual payment divided by the rate. At 10% it is worth Rs 1,00,000. Present value moves inversely with the discount rate, so the rise in rate reduces it.

  1. ARs 1,25,000; it falls to Rs 1,00,000Correct
  2. BRs 1,25,000; it rises to Rs 1,00,000
  3. CRs 80,000; it falls to Rs 1,00,000
  4. DRs 1,00,000; it falls to Rs 1,25,000

Explanation

PV of perpetuity = C / r = 10,000 / 0.08 = Rs 1,25,000. At 10%, PV = 10,000 / 0.10 = Rs 1,00,000. A higher rate lowers the value, so the PV falls.

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