In May 2000, the U.S. Treasury issued 30-year bonds with a coupon rate of 6.25%, paid...

In May 2000, the U.S. Treasury issued 30-year bonds with a coupon rate of 6.25%, paid semiannually. A bond with a face value of $1,000 pays $31.25 (1,000 × 0.0625 / 2) every six months for the next 30 years; in May 2030, the bond also repays the principal amount, $1,000.

(a) What is the value of the bond if, immediately after issue in May 2000, the 30-year interest rate increases to 7.5%?

(b) What is the value of the bond if, immediately after issue in May 2000, the 30-year interest rate decreases to 5.0%?

(c) On a graph in Excel, show how the value of the bond changes as the interest rate changes (plot the value as a function of the interest rate). At what interest rate is the value of the bond equal to its face value of $1,000?

Solutions

Expert Solution

Value of the bond is calculated using the PV function in Excel with these inputs :

rate = 7.50% / 2 (converting annual rate into semiannual rate)

nper = 30 * 2 (30 years to maturity with 2 semiannual periods in each year)

pmt = 31.25 (semiannual coupon payment)

fv = 1,000 (face value of the bond receivable on maturity)

PV is calculated to be $852. This is the value of the bond today

Value of the bond is calculated using the PV function in Excel with these inputs :

rate = 5% / 2 (converting annual rate into semiannual rate)

nper = 30 * 2 (30 years to maturity with 2 semiannual periods in each year)

pmt = 31.25 (semiannual coupon payment)

fv = 1,000 (face value of the bond receivable on maturity)

PV is calculated to be $1,193. This is the value of the bond today

The value of the bond is equal to $1000 (par value) when the interest rate is 6.25% (which is the coupon rate)

jeff jeffy answered 8 months ago

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