Question

Problem 5-09 Bond Valuation and Interest Rate Risk The Garraty Company has two bond issues outstanding. Both bonds pay $100 annual interest plus $1,000 at maturity. Bond L has a maturity of 15 years, and Bond S has a maturity of 1 year. What will be the value of each of these bonds when the going rate of interest is 5%? Assume that there is only one more interest payment to be made on Bond S. Round your answers to the nearest cent. Bond L $ Bond S $ What will be the value of each of these bonds when the going rate of interest is 8%? Assume that there is only one more interest payment to be made on Bond S. Round your answers to the nearest cent. Bond L $ Bond S $ What will be the value of each of these bonds when the going rate of interest is 11%? Assume that there is only one more interest payment to be made on Bond S. Round your answers to the nearest cent. Bond L $ Bond S $ Why does the longer-term (15-year) bond fluctuate more when interest rates change than does the shorter-term bond (1 year)? I. Shorter-term bonds have more interest rate risk than longer-term bonds. II. Longer-term bonds have more interest rate risk than shorter-term bonds. III. Longer-term bonds have more reinvestment rate risk than shorter-term bonds. -Select-IIIIIIItem 7

Answer 1

Price of any bond is present value of all cashflows associated with the bond (namely coupons and maturity value).

It is mathematically represented as:

Where P is the price of bond, C is the coupon on bond, i is the prevailing market interest rate and n is number of years to maturity.

At 5% market interest rate

For Bond S: n = 1, C = $100, M = $1000, i = 5%

P = $1,047.62

Bond L: n = 15, C = $100, M = $1000, i = 5%

P = $1,518.98

At 8% market interest rate

For Bond S: n = 1, C = $100, M = $1000, i = 8%

P = $1,018.52

Bond L: n = 15, C = $100, M = $1000, i = 8%

P = $1,171.19

At 11% market interest rate

For Bond S: n = 1, C = $100, M = $1000, i = 11%

P = $990.99

Bond L: n = 14, C = $100, M = $1000, i = 11%

P = $928.09

The longer-term (15-year) bond fluctuate more when interest rates change than does the shorter-term bond (1 year) because Longer-term bonds have more interest rate risk than shorter-term bonds. Interest rate risk is measured by 'Duration' which is higher for bond with longer maturities or lower coupon bonds. In our question, all else same, Bond L has longer term to maturity, hence higher duration and hence higher sensitivity to interest rates.