Question

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.

a. What will be the value of each of these bonds when the going rate of interest is (1) 5%, (2) 8%, and (3) 12%? Assume that there is only one more interest payment to be made on Bond S.

b. Why does the longer-term (15 year) bond fluctuate more when interest rates change than does the shorter-term bond (1 year)\

Please show work, Thanks!

Answer 1

a]	1] 5%:
	Value of bond L = 1000/1.05^15+100*(1.05^15-1)/(0.05*1.05^15) =	$      1,518.98
	Value of bond S = 1000/1.05+100/1.05 =	$      1,047.62
	2] 8%:
	Value of bond L = 1000/1.08^15+100*(1.08^15-1)/(0.08*1.08^15) =	$      1,171.19
	Value of bond S = 1000/1.08+100/1.08 =	$      1,018.52
	3] 12%:
	Value of bond L = 1000/1.12^15+100*(1.12^15-1)/(0.12*1.12^15) =	$         863.78
	Value of bond S = 1000/1.12+100/1.12 =	$         982.14
b]	The effect of discounting, when interest rate
	changes, is more in the later years. Hence, the
	PVs of the interest in the later years and the
	PV of the maturity value get discounted heavily
	in the case of the bond with longer maturity.