Question

Laurel, Inc., and Hardy Corp. both have 9 percent coupon bonds outstanding, with semiannual interest payments, and both are priced at par value. The Laurel, Inc., bond has four years to maturity, whereas the Hardy Corp. bond has 15 years to maturity.

If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds?(Negative answers should be indicated by a minus sign. Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))

Percentage change in price of Laurel %
Percentage change in price of Hardy %
If interest rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of these bonds be then? (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))

Percentage change in price of Laurel %
Percentage change in price of Hardy %

Answer 1

If interest rate rises by 2%

Laurel Inc:

Percentage change in price = -0.0633 or -6.33%

Hardy Corp:

Percentage change in price = -0.1453 or -14.53%

If interest rate falls by 2%

Laurel Inc:

Percentage change in price = 0.06874 or 6.874%

Hardy Corp:

Percentage change in price = 0.1839 or 18.39%

Step-by-step explanation:

Lets assume that both the bonds have a face value of $1000 and an initial coupon rate and interest rate of 9%. As the bonds are priced at par initially, this means that the interest rate or YTM is also 9%

If interest rates rises by 2%

We will first calculate the price of both the bonds then calculate the percentage change in prices.

To calculate the price of the bond today, we will use the formula for the price of the bond. As the bond is a semi annual bond, the coupon payment, number of periods and semi annual YTM will be,

When interest rates rise by 2%.

Laurel Inc

Coupon Payment (C) = 1000 * 0.09 * 6/12 = 45

Total periods (n) = 4 * 2 = 8

New interest rate = 9% + 2% = 11%

New interest rate or YTM (semi annual) = 0.11 * 6/12 = 0.055 or 5.5%

The formula to calculate the price of the bonds today is attached.

Bond Price = 45 * [( 1 - (1+0.055)^-8) / 0.055] + 1000 / (1+0.055)^8

Bond Price = $936.6543 rounded off to $936.65

Percentage change in price = (936.65 - 1000) / 1000 = -0.0633 or -6.33%

Hardy Corp

Coupon Payment (C) = 1000 * 0.09 * 6/12 = 45

Total periods (n) = 15 * 2 = 30

New interest rate = 9% + 2% = 11%

New interest rate or YTM (semi annual) = 0.11 * 6/12 = 0.055 or 5.5%

The formula to calculate the price of the bonds today is attached.

Bond Price = 45 * [( 1 - (1+0.055)^-30) / 0.055] + 1000 / (1+0.055)^30

Bond Price = $854.6625 rounded off to $854.66

Percentage change in price = (854.66 - 1000) / 1000 = -0.1453 or -14.53%

When interest rate falls by 2%

Laurel Inc

Coupon Payment (C) = 1000 * 0.09 * 6/12 = 45

Total periods (n) = 4 * 2 = 8

New interest rate = 9% - 2% = 7%

New interest rate or YTM (semi annual) = 0.07 * 6/12 = 0.035 or 3.5%

The formula to calculate the price of the bonds today is attached.

Bond Price = 45 * [( 1 - (1+0.035)^-8) / 0.035] + 1000 / (1+0.035)^8

Bond Price = $1068.7395 rounded off to $1068.74

Percentage change in price = (1068.74 - 1000) / 1000 = 0.06874or 6.874%

Hardy Corp

Coupon Payment (C) = 1000 * 0.09 * 6/12 = 45

Total periods (n) = 15 * 2 = 30

New interest rate = 9% - 2% = 7%

New interest rate or YTM (semi annual) = 0.07 * 6/12 = 0.035 or 3.5%

The formula to calculate the price of the bonds today is attached.

Bond Price = 45 * [( 1 - (1+0.035)^-30) / 0.035] + 1000 / (1+0.035)^30

Bond Price = $1183.9204 rounded off to $1183.92

Percentage change in price = (1183.92 - 1000) / 1000 = 0.1839 or 18.39%