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

A perpetuity pays Rs 9,000 at the end of year 1 and grows at 5% a year. Its present value is Rs 90,000 at a given discount rate. What is the discount rate? Also, if payments were level at Rs 9,000 at that same rate, what would be the PV?

The discount rate is 15% and the level perpetuity would be worth Rs 60,000. Rearranging the growing perpetuity formula gives r equal to 9,000 over 90,000 plus 5%, which is 15%; then 9,000 divided by 0.15 is 60,000.

  1. A15%; Rs 60,000Correct
  2. B10%; Rs 90,000
  3. C15%; Rs 1,80,000
  4. D14%; Rs 64,286

Explanation

90,000 = 9,000/(r-0.05), so r-0.05 = 0.10 and r = 15%. Level perpetuity PV = 9,000/0.15 = Rs 60,000. Option with 10% forgets to add back the growth rate.

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