Question

Five years ago, the State of Oklahoma issued $2,000,000 of 7% coupon, 20-year semiannual payment, tax-exempt bonds. The bonds had 5 years of call protection, but now the state can call the bonds if it chooses to do so. The call premium would be 5% of the face amount. Today 15-year, 5%, semiannual payment bonds can be sold at par, but flotation costs on this issue would be 2%. What is the net present value of the refunding? Because these are tax-exempt bonds, taxes are not relevant.

call premium = 5% * 2000000 = 100000

floatation cost = 2% * 2000000 = 40000

total investment outlay = 140000

interest on old bond = 7%/2 * 2000000 = 70000

interest on new bond = 5%/2 * 2000000 = 50000

savings = 20000

PV of savings = 20000 * PVIFA(2.5%, 30) = 418606........ how did they get the 418606 can you spell it out for me please im not getting that?

Answer 1

PVIFA means Present Value Annuity Factor. it helps in calculating present value of cash flows which occur constantly for certain period like $20000 which occurs for 30 years

The Formula of PVIFA = (1 - (1+Interest)^-n)) / Interest

PVIFA(2.50%,30) = (1 - (1+2.50%)^-30)) / 2.50%

PVIFA(2.50%,30) = (1 - 0.47674)) / 2.50%

PVIFA(2.50%,30) = 0.523257 / 2.50%

PVIFA(2.50%,30) = 20.9303

PV of Savings = 20000 * PVIFA(2.5%, 30)

PV of Savings = 20000 * 20.9303

PV of Savings = $418605.85 rounded off to $418606

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