Both Bond Bill and Bond Ted have 10.2 percent coupons, make semiannual payments,

Question

Both Bond Bill and Bond Ted have 10.2 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 Bond Bill % Bond Ted % 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 Bond Bill % Bond Ted %

Explanation / Answer

Both Bond Bill and Bond Ted have 11.2 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 3 percent, what is the percentage change in the pri

2: If rates were to suddenly fall by 3 percent instead, what would be the percentage change

The bonds are priced at par, means the market rate of interest and the coupon rate of interest for the bonds are same.

Requirement 1: If interest rates suddenly rise by 3 percent, what is the percentage change in the price of these bonds?

If the interest rate rise by 3%, the market rate of interest = 11.2 + 3 = 14.4%

The market value of the bonds will be as follows:

Coupon rate = 11.2%

Semi-annual interest = 11.2% * $1000 * 0.50 = $56

Semi-annual market rate of interest after a rise by 3% = 14.2 / 2 = 7.1%

Bill's Bond:

Years to maturity = 4 years

Semi-annual period = 8

Market Value = $56 x PVAF(7.1%, 8) + $1,000 x PVIF(7.1%, 8)

......................= ($56 x 5.948) + ($1,000 x 0.578)

......................= $333.09 + $578

......................= $911.09

Percentage change in price = ($911.09 - $1,000) / $1,000

.............................................= -8.89%

Ted's Bond

Years to maturity = 21 years

Semi - annual period = 42

Market Value = [$56 x PVIFA (7.1%, 42)] + [$1000 x PVIF (7.1%, 42)]

.......................= ($56 x 13.295) + ($1,000 x 0.056)

.......................= $744.52 + $56

.......................= $800.52

Percentage change in price = ($800.52 - $1,000) / $1,000

.............................................= -19.95%

Requirement 2: If rates were to suddenly fall by 3 percent instead, what would be the percentage change in the price of these bonds?

If the interest rate fall by 3%, the market rate of interest = 11.2 - 3 = 8.2%

The market value of the bonds will be as follows:

Coupon rate = 11.2%

Semi-annual interest = 11.2% * $1000 * 0.50 = $56

Semi-annual market rate of interest after a fall by 3% = 8.2 / 2 = 4.1%

Bill's Bond:

Years to maturity = 4 years

Semi-annual period = 8

Market Value = $56 x PVAF(4.1%, 8) + $1,000 x PVIF(4.1%, 8)

......................= ($56 x 6.605) + ($1,000 x 0.725)

......................= $369.88 + $725

......................= $1,094.88

Percentage change in price = ($1,094.88 - $1,000) / $1,000

.............................................= 9.49%

Ted's Bond

Years to maturity = 21 years

Semi - annual period = 42

Market Value = [$56 x PVIFA (4.1%, 42)] + [$1000 x PVIF (4.1%, 42)]

.......................= ($56 x 19.879) + ($1,000 x 0.185)

.......................= $1,113.22 + $185

.......................= $1,298.22

Percentage change in price = ($1,298.22 - $1,000) / $1,000

.............................................= 29.82%

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