Both Bond Bill and Bond Ted have 9.6 percent coupons, make semiannual payments,

Question

Both Bond Bill and Bond Ted have 9.6 percent coupons, make semiannual payments, and are priced at par value. Bond Bill has 6 years to maturity, whereas Bond Ted has 23 years to maturity. Requirement 1: If interest rates suddenly rise by 3 percent, what is the percentage change in the price of these bonds

If rates were to suddenly fall by 3 percent instead, what would be the percentage change in the price of these bonds? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).)

Explanation / Answer

When a bond is sold at par, its yield to maturity (YTM) is equal to the coupon rate. So the initial Yield to maturity for both the bonds will be 9.6 percent. Taking $1000 as a face value, the coupon interest will be $48 i.e. [$1,000 *(9.6%/2)]

1. If YTM rises by 3 percent i.e. 12.6%:

Bond price will be:

Bond Bill

= $48(PVIFA 6.3%, 12) + $1000(PVIF 6.3%,12) = $48(8.384) + $1000(0.497) = $402.43 + $497 = $899.43

Percentage change in price = (New Bond Price - Original Bond Price)/Original Price

Substitute:

= ($899.43 - $1000)/$1000 = -0.1005 or -10.05%

Bond Ted

= $48(PVIFA 6.3%, 46) + $1000(PVIF 6.3%,46) = $48(15.456) + $1000(0.073) = $741.88 + $73 = $814.88

Percentage change in price = (New Bond Price - Original Bond Price)/Original Price

Substitute:

= ($814.88 - $1000)/$1000 = -0.1851 or -18.51%

2. If YTM falls by 3 percent i.e. 6.6%:

Bond price will be:

Bond Bill

= $48(PVIFA 3.3%, 12) + $1000(PVIF 3.3%,12) = $48(9.954) + $1000(0.701) = $1178.79

Percentage change in price = (New Bond Price - Original Bond Price)/Original Price

Substitute:

= ($1178.79 - $1000)/$1000 = 0.1787 or 17.87%

Bond Ted

= $48(PVIFA 3.3%, 46) + $1000(PVIF 3.3%,46) = $48(24.519) + $1000(0.264) = $1440.91

Percentage change in price = (New Bond Price - Original Bond Price)/Original Price

Substitute:

= ($1440.91 - $1000)/$1000 = -0.4409 or 44.09%

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