Before interest rates rise, both bonds are trading at par. Hence, their YTM equals their coupon rate.
If interest rates rise by 2%
The price of Laurel bond is calculated using PV function in Excel :
rate = 7.8%/2 (Converting annual YTM of bond into semiannual YTM)
nper = 3 * 2 (3 years remaining until maturity with 2 semiannual coupon payments each year)
pmt = 1000 * 5.8% / 2 (semiannual coupon payment = face value * coupon rate / 2)
fv = 1000 (face value receivable on maturity)
PV is calculated to be $947.41.
The price of Hardy bond is calculated using PV function in Excel :
rate = 7.8%/2 (Converting annual YTM of bond into semiannual YTM)
nper = 20 * 2 (20 years remaining until maturity with 2 semiannual coupon payments each year)
pmt = 1000 * 5.8% / 2 (semiannual coupon payment = face value * coupon rate / 2)
fv = 1000 (face value receivable on maturity)
PV is calculated to be $799.09.
If interest rates fall by 2%
The price of Laurel bond is calculated using PV function in Excel :
rate = 3.8%/2 (Converting annual YTM of bond into semiannual YTM)
nper = 3 * 2 (3 years remaining until maturity with 2 semiannual coupon payments each year)
pmt = 1000 * 5.8% / 2 (semiannual coupon payment = face value * coupon rate / 2)
fv = 1000 (face value receivable on maturity)
PV is calculated to be $1056.20.
The price of Hardy bond is calculated using PV function in Excel :
rate = 3.8%/2 (Converting annual YTM of bond into semiannual YTM)
nper = 20 * 2 (20 years remaining until maturity with 2 semiannual coupon payments each year)
pmt = 1000 * 5.8% / 2 (semiannual coupon payment = face value * coupon rate / 2)
fv = 1000 (face value receivable on maturity)
PV is calculated to be $1278.41.
This shows that long the maturity of the bond, higher the sensitivity of the bond price to changes in interest rates. In other words, bonds with longer maturities have higher interest rate risk.
Interest Rate Risk Laurel, Inc., and Hardy Corp. both have 5.8 percent coupon bonds outstanding, with...
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