Question

# To make provision for the possible impact of recessions in the future, Albany Mutual Bank would...

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?

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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.

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