Question

You own two bonds, each of which currently pays semiannual interest, has a coupon rate of 6 percent, a $1,000 face value, and 6 percent yields to maturity. Bond A has 12 years to maturity and Bond B has 4 years to maturity. If the market rate of interest rises unexpectedly to 7 percent, Bond _____ will be the most volatile with a price decrease of _____ percent.

A; 5.73

A; 3.44

A; 8.03

B; 7.97

B; 4.51

Answer 1

Bond A:

Face Value = $1,000

Annual Coupon Rate = 6.00%
Semiannual Coupon Rate = 3.00%
Semiannual Coupon = 3.00% * $1,000
Semiannual Coupon = $30

Time to Maturity = 12
Semiannual Period to Maturity = 24

If current interest rate is equal to the coupon rate, then the bond is selling at par.

If interest rate rises to 7%:

Annual Interest Rate = 7%
Semiannual Interest Rate = 3.50%

Price of Bond = $30 * PVIFA(3.50%, 24) + $1,000 * PVIF(3.50%, 24)
Price of Bond = $30 * (1 - (1/1.035)^24) / 0.035 + $1,000 / 1.035^24
Price of Bond = $919.71

Percentage Change in Price = ($919.71 - $1,000) / $1,000
Percentage Change in Price = -8.03%

Bond B:

Face Value = $1,000

Annual Coupon Rate = 6.00%
Semiannual Coupon Rate = 3.00%
Semiannual Coupon = 3.00% * $1,000
Semiannual Coupon = $30

Time to Maturity = 4
Semiannual Period to Maturity = 8

If current interest rate is equal to the coupon rate, then the bond is selling at par.

If interest rate rises to 7%:

Annual Interest Rate = 7%
Semiannual Interest Rate = 3.50%

Price of Bond = $30 * PVIFA(3.50%, 8) + $1,000 * PVIF(3.50%, 8)
Price of Bond = $30 * (1 - (1/1.035)^8) / 0.035 + $1,000 / 1.035^8
Price of Bond = $965.63

Percentage Change in Price = ($965.63 - $1,000) / $1,000
Percentage Change in Price = -3.44%

Bond A will be the most volatile with a price decrease of 8.03 percent.