Question

1. A potential investor must decide between purchasing two bonds: Bond M pays $45000 in 7 years; Bond N pays $45000 in 19 years. (assume that $45000 is the only payment the bondholder receives.)

1. If the interest rate is 2.73 percent, what is the value of each bond?
2. If the interest rate increases to 3.75 percent, what is the value of each bond today? Which bond has a larger percentage change in value?

Based on the example above, complete the two blanks in this sentence: “The value of a bond [rises/falls] when the interest rate increases, and bonds with a longer time to maturity are [more/less] sensitive to changes in the interest rate”

Answer 1

A

Present value of bond M = 45000/1.0273^7 = $37267.61

Present value of bond N = 45000/1.0273^19 = $26975.16

B.

Present value of bond M = 45000/1.0375^7 = $34777.29

Present value of bond N = 45000/1.0375^19 = $22358.29

% change in the value of bond M = (34777.29-37267.61)/37267.61 = -6.68%

% change in the value of bond N = (22358.29-26975.16)/26975.16 = -17.12%

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Correct Answer:

Falls

More

Bond's value is inversely proportional to the interest rate. Further, long term bonds are more sensitive to the interest rates.