Question

In: Finance

Both Bond A and Bond B have 7.4 percent coupons and are priced at par value....

Both Bond A and Bond B have 7.4 percent coupons and are priced at par value. Bond A has 7 years to maturity, while Bond B has 18 years to maturity. If interest rates suddenly rise by 1 percentage points, what is the difference in percentage changes in prices of Bond A and Bond B? (i.e., Bond A - Bond B). The bonds pay coupons twice a year.

(A negative value should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

Expert Solution

Bond A:

Face Value = $1,000

Annual Coupon Rate = 7.40%
Semiannual Coupon Rate = 3.70%
Semiannual Coupon = 3.70% * $1,000
Semiannual Coupon = $37

Time to Maturity = 7
Semiannual Period to Maturity = 14

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

So, current interest rate is 7.40%

If interest rate increases by 1%:

Annual Interest Rate = 8.40%
Semiannual Interest Rate = 4.20%

Price of Bond = $37 * PVIFA(4.20%, 14) + $1,000 * PVIF(4.20%, 14)
Price of Bond = $37 * (1 - (1/1.042)^14) / 0.042 + $1,000 / 1.042^14
Price of Bond = $947.87

Percentage Change in Price = ($947.87 - $1,000) / $1,000
Percentage Change in Price = -5.21%

Bond B:

Face Value = $1,000

Annual Coupon Rate = 7.40%
Semiannual Coupon Rate = 3.70%
Semiannual Coupon = 3.70% * $1,000
Semiannual Coupon = $37

Time to Maturity = 18
Semiannual Period to Maturity = 36

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

So, current interest rate is 7.40%

If interest rate increases by 1%:

Annual Interest Rate = 8.40%
Semiannual Interest Rate = 4.20%

Price of Bond = $37 * PVIFA(4.20%, 36) + $1,000 * PVIF(4.20%, 36)
Price of Bond = $37 * (1 - (1/1.042)^36) / 0.042 + $1,000 / 1.042^36
Price of Bond = $908.02

Percentage Change in Price = ($908.02 - $1,000) / $1,000
Percentage Change in Price = -9.20%

Difference in Percentage Changes = Percentage Changes in Price of Bond A - Percentage Changes in Price of Bond B
Difference in Percentage Changes = (-5.21%) - (-9.20%)
Difference in Percentage Changes = 3.99%

jeff jeffy answered 1 year ago

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