Question

To make provision for the possible impact of recessions in the future, Albany Mutual Bank would like to set up a reserve fund. The fund will earn an interest rate of 6% per annum. If the fund pays a fixed amount of $12 million to the bank annually for an infinite period, starting two years from today and the annual payment grows at 2.5% per annum, how much does the bank need in the fund today?

Answer 1

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The given case is of a growing perpetual annuity. where D1 = $12 Million, r = 6% and g = 2.50%

PV of Growing perpetuity 1 year from now (because $12 Million is of Year 2) = $12 Million / (6% - 2.50%) = $342,857,142.86

PV of Growing perpetuity = $342,857,142.86 / 1.06 = $ 323.45 Million

Hence, bank needs to fund $323.45 Million today to receive $12 Million second years onwards with 2.50% growth rate.