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Suppose the First National Bank of Duluth has $500.00 million in total assets with an average...

Suppose the First National Bank of Duluth has $500.00 million in total assets with an average asset duration of five years. Assume that the bank’s liabilities are comprised of $86.75 million of demand deposits and $163.75 million in bonds with a 4.00% coupon rate (which pays annually) and a five year time-to-maturity. Further assume that current market interest rates are at 9.00% per annum.


Calculate the duration of the bank’s bonds. (Using Duration formula, Not Excel)
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Answer #1
Year cash flow from bonds present value of cash flow = cash flow/(1+r)^n r = 9% present value of cash flow = cash flow/(1+r)^n r = 9% present value of cash flow* year
1 6.55 6.55/1.09^1 6.009174312 6.009174312
2 6.55 6.55/1.09^2 5.513003956 11.02600791
3 6.55 6.55/1.09^3 5.057801794 15.17340538
4 6.55 6.55/1.09^4 4.640185132 18.56074053
5 170.25 170.25/1.09^5 110.6508185 553.2540926
value of bond = sum of present value of cash flow 6.009+5.513+5.057+5.640+110.650 131.8709837
sum of ( present value of cash flow*year) 6.09+11.026+15.173+18.560+553.254 604.0234207
Maculay's duration = sum of (present value of cash flow) / value of bond 604.023/131.870 4.58
Modified duration Maculay's duration/(1+r)^n 4.58/(1.09) 4.20
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