he state of Ohio needs to raise $25,000,000 for highway repairs. Officials are c
ID: 2388989 • Letter: H
Question
he state of Ohio needs to raise $25,000,000 for highway repairs. Officials are considering issuing zero coupon bonds, which do not require periodic interest payments. The current market interest rate for the bonds is 8 percent.What face value of bonds must be issued to raise the needed funds, assuming the bonds will be due in 30 years and compounded annually? Round your answer to nearest million.
a. face value of 30-year, 8% zero coupon bonds, compounded annually:
b. How would your answer change if the bonds were due in 50 years? Round your answer to two decimal places.
Face value of 50-year, 8% zero coupon bonds, compounded annually:
How would both answers change if the market interest rate were 6 percent instead of 8 percent?
c. Face value of 50-year, 6% zero coupon bonds, compounded annually:
Round your answer to the nearest million.
Explanation / Answer
Face value of 30-year, 8% zero coupon bonds Present Value =$25M Interest Rate = 8% Time = 30 years Future Value (face value) = 25*(1+.08)^(30) = $251.56M = $252M How would your answer change if the bonds were due in 50 years Future Value (face value) = 25*(1.08^50) = $1172.54M = $1173M How would both answers change if the market interest rate were 6 percent instead of 8 percent? Face value of 30-year, 6% zero coupon bonds Future Value (face value) = 25*(1+.06)^(30) = $143.59M = $144M Face value of 50-year, 6% zero coupon bonds Future Value (face value) = 25*(1+.06)^(50) = $460.50M = $461M
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