Question

2) a. What is the duration of a 5-year 8% annual coupon bond with a par value of $100 if the prevailing continuously compounded interest rate is 10%? b. What is the duration of a 5-year 12% annual coupon bond with a par value of $100 if the prevailing continuously compounded interest rate is 10%? What does this tell you about the relationship between coupon rates and duration? Comment. c. What is the duration of a 5-year 8% annual coupon bond with a par value of $100 if the prevailing continuously compounded interest rate is 12%? What does this tell you about the relationship between interest rates and duration?

Please do not use excell tables or excell formulas because it has to be handwritten, please write formulas and explanation. Thank you

Answer 1

Solution:

a)Calculation of duration of bond

Year	Cash flow(Coupon+Maturity value)(a)	Present value factor @10%(a*b)	Present value(a*b)	Weight	Weighted present value
1	$8	0.9091	7.2728	1	7.2728
2	$8	0.8264	6.6112	2	13.2224
3	$8	0.7513	6.0104	3	18.0312
4	$8	0.6830	5.4640	4	21.856
5	($8+100)	0.6209	67.0572	5	335.286
Total	92.4156		395.6684

Duration=Sum of Weighted present value/Present value of bond

=$395.6684/$92.4156

=4.28

b)Calculation of duration of bond

Year	Cash flow(Coupon+Maturity value)(a)	Present value factor @10%(a*b)	Present value(a*b)	Weight	Weighted present value
1	$12	0.9091	10.9092	1	10.9092
2	$12	0.8264	9.9168	2	19.8336
3	$12	0.7513	9.0156	3	27.0468
4	$12	0.6830	8.196	4	32.784
5	($12+$100)	0.6209	69.5408	5	347.704
			107.5784		438.2776

Duration=438.2776/107.5784

=4.07

From the above,we can conclude that-higher the coupon rate lower will be the duration pf bond.

c)

Calculation of duration of bond

Year	Cash flow(Coupon+Maturity value)(a)	Present value factor @12%(a*b)	Present value(a*b)	Weight	Weighted present value
1	$8	0.8929	7.1432	1	7.1432
2	$8	0.7972	6.3776	2	12.7552
3	$8	0.7118	5.6944	3	17.0832
4	$8	0.6355	5.084	4	20.336
5	($8+100)	0.5674	61.2792	5	306.396
Total	85.5784		363.7136

Duration=363.7136/85.5784

=4.25

Since the duration of bond with 10% interest(4.28) is higher than the duration of 12% interest rate bond(4.25),thus it can say that-higher the inetrest rate,lower will be the duration.