Both Bond Bill and Bond Ted have 9.8 percent coupons, make semiannual payments,

Question

Both Bond Bill and Bond Ted have 9.8 percent coupons, make semiannual payments, and are priced at par value. Bond Bill has 7 years to maturity, whereas Bond Ted has 24 years to maturity. Requirement 1: If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds? (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places (e.g., 32.16).) Requirement 2: If rates were to suddenly fall by 2 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

Answer: Requirement 1:

Both Bond Bill and Bond Ted are priced at $1000 now.

For Bond Bill

New yield = 11.8%

Semiannual yield = 11.8%/2 = 5.9%

No of periods = 7 yrs*2 payments/yr = 14

Coupon = 1000*9.8%/2 = 49

With 2% increase in rates, Price of Bond Bill can be calculated in Excel as =PV(5.9%,14,- 49,-1000).

This is equal to 906.47

So % change in price = (906.47-1000)/1000 = -9.35%

For Bond Ted

New yield = 11.8%

Semiannual yield = 11.8%/2 = 5.9%

No of periods = 24 yrs*2 payments/yr = 48

Coupon = 1000*9.8%/2 = 49

With 2% increase in rates, Price of Bond ted can be calculated in Excel as =PV(5.9%,48,- 49,-1000).

This is equal to 841.33

So % change in price = (841.33-1000)/1000 = -15.87%

Answer: Requirement 2:

Both Bond Bill and Bond Ted are priced at $1000 now.

For Bond Bill

New yield = 7.8%

Semiannual yield = 7.8%/2 = 3.9%

No of periods = 7 yrs*2 payments/yr = 14

Coupon = 1000*9.8%/2 = 49

With 2% decrease in rates, Price of Bond Bill can be calculated in Excel as =PV(3.9%,14,- 49,-1000).

This is equal to 1106.33

So % change in price = (1106.33-1000)/1000 = 10.63%

For Bond Ted

New yield = 7.8%

Semiannual yield = 7.8%/2 = 3.9%

No of periods = 24 yrs*2 payments/yr = 48

Coupon = 1000*9.8%/2 = 49

With 2% decrease in rates, Price of Bond ted can be calculated in Excel as =PV(3.9%,48,- 49,-1000).

This is equal to 1215.54

So % change in price = (1215.54-1000)/1000 = 21.55%

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