Question

The Acton-Boxborough School District will issue a 30-year bond with a face value of $ 5,000,000 to construct a new building for the district’s junior high school. The bond has a stated annual interest (coupon rate) of 5 percent, and the district will make interest (coupon) payments based on the stated interest rate twice a year.

a) What is the semiannual interest (coupon) payment? (semiannual = every six months)

b) How much will the school district receive from the bond offering under the following conditions:

a. Market interest rates increase to 8% at the time of the offering. (Assuming interests are compounded semiannually).

b. Market interest rates decrease to 5% at the time of offering. (Assuming interests are compounded semiannually)

Answer 1

Face Value of bond = $ 5,000,000

Bond maturity = 30 years

coupon rate = 5%

a)

Semi-annual coupon = Face Value of bond * coupon rate / 2 = $ 5,000,000 * 5%/2 = $125,000

b)

a.

Market interest rate = 8%

Semi-annual Market interest rate = 8%/2 = 4%

price of the bond can be calculated using the PV function in spreadsheet

PV(rate, number of periods, payment amount, future value, when-due)

Where, rate = semi-annual market interest rate = 4%

number of periods = 30 years = 60 semi-annual periods

payment amount = semi-annual coupon = $125,000

future value = face value of bond = $ 5,000,000

when-due = when is the coupon payment made each semi-annual period = end = 0

Bond price = PV(4%, 60, 125000, 5000000, 0) = $3,303,238.25

b.

Market interest rate = 5%

Semi-annual Market interest rate = 5%/2 = 2.5%

price of the bond can be calculated using the PV function in spreadsheet

PV(rate, number of periods, payment amount, future value, when-due)

Where, rate = semi-annual market interest rate = 2.5%

number of periods = 30 years = 60 semi-annual periods

payment amount = semi-annual coupon = $125,000

future value = face value of bond = $ 5,000,000

when-due = when is the coupon payment made each semi-annual period = end = 0

Bond price = PV(2.5%, 60, 125000, 5000000, 0) = $5,000,000.00