Both Bond Bill and Bond Ted have 7 percent coupons, make semiannual payments, an

Question

Both Bond Bill and Bond Ted have 7 percent coupons, make semiannual payments, and are priced at par value. Bond Bill has 3 years to maturity, whereas Bond Ted has 20 years to maturity.

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).)

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).)

Both Bond Bill and Bond Ted have 7 percent coupons, make semiannual payments, and are priced at par value. Bond Bill has 3 years to maturity, whereas Bond Ted has 20 years to maturity.

Explanation / Answer

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

Requirement 1: Increase of 2% in interest rates

For Bond Bill

New yield = 9%

Semiannual yield = 9%/2 = 4.5%

No of periods = 3yrs*2 payments/yr = 6

Coupon = 1000*7%/2 = 35

With 2% increase in rates, Price of Bond Bill can be calculated in Excel as =PV(4.5%,6,-35,-1000). This is equal to 948.42

So % change in price = (948.42-1000)/1000 = -5.16%

For Bond Ted

New yield = 9%

Semiannual yield = 9%/2 = 4.5%

No of periods = 20yrs*2 payments/yr = 40

Coupon = 1000*7%/2 = 35

With 2% increase in rates, Price of Bond Bill can be calculated in Excel as =PV(4.5%,40,-35,-1000). This is equal to 815.98

So % change in price = (815.98-1000)/1000 = -18.40%

Requirement 2: Decrease of 2% in interest rates

For Bond Bill

New yield = 5%

Semiannual yield = 5%/2 = 2.5%

No of periods = 3yrs*2 payments/yr = 6

Coupon = 1000*7%/2 = 35

With 2% decrease in rates, Price of Bond Bill can be calculated in Excel as =PV(2.5%,6,-35,-1000). This is equal to 1055.08

So % change in price = (1055.08-1000)/1000 = 5.51%

For Bond Ted

New yield = 5%

Semiannual yield = 5%/2 = 2.5%

No of periods = 20yrs*2 payments/yr = 40

Coupon = 1000*7%/2 = 35

With 2% decrease in rates, Price of Bond Bill can be calculated in Excel as =PV(2.5%,40,-35,-1000). This is equal to 1251.03

So % change in price = (1251.03-1000)/1000 = 25.10%

Hope this detailed explanation helped ! Let me know in case of any queries.

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