Both Bond Bill and Bond Ted have 12.2 percent coupons, make semiannual payments,
ID: 2457139 • Letter: B
Question
Both Bond Bill and Bond Ted have 12.2 percent coupons, make semiannual payments, and are priced at par value. Bond Bill has 4 years to maturity, whereas Bond Ted has 21 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).)
Percentage change in price
Bill's Bond ________% Ted's Bond _________%
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).)
Percentage change in price
Bill's Bond ________% Ted's Bond _________%
Explanation / Answer
The bonds are priced at par, means the market rate of interest and the coupon rate of interest for the bonds are same.
If the interest rate rise by 2%, the market rate of interest = 12.2 + 2 = 14.4%
The market value of the bonds will be as follows:
Coupon rate = 12.2%
Semi-annual interest = 12.2% * $1000 * 0.50 = $61
Semi-annual market rate of interest after a rise by 2% = 14.2 / 2 = 7.1%
Bill’s bond :
Years to maturity = 4 years
Semi-annual period = 8
Market value
= $61 * PVIFA (7.1%, 8) + $1000 * PVIF (7.1%, 8)
= $61 * 5.948 + $1000 * 0.578
= $940.83
Percentage change in price = (940.83 – 1000) / 1000 = -5.917% = - 5.92%
Ted’s Bond
Years to maturity = 21
Semi-annual period = 42
Market value
= $61 * PVIFA (7.1%, 42) + $1000 * PVIF (7.1%, 42)
= $61 * 13.295 + $1000 * 0.056
= $866.995 = $867
Percentage change in price = (867 – 1000) / 1000 = -13.30%
CASE 2:
If the rates suddenly fall by 2%, the market rate = 12.2 – 2 = 10.2%
And the semi-annual rate = 5.1%
Bill’s bond :
Years to maturity = 4 years
Semi-annual period = 8
Market value
= $61 * PVIFA (5.1%, 8) + $1000 * PVIF (5.1%, 8)
= $61 * 6.437 + $1000 * 0.672
= $1064.66
Percentage change in price = (1064.66 – 1000) / 1000 = 6.47%
Ted’s Bond
Years to maturity = 21
Semi-annual period = 42
Market value
= $61 * PVIFA (5.1%, 42) + $1000 * PVIF (5.1%, 42)
= $61 * 17.181 + $1000 * 0.124
= $1172.04
Percentage change in price = (1172.04 – 1000) / 1000 = 17.20 %
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