Question

Two bonds are available for purchase in the financial markets. The first bond is a 5 year, $1000 bond that pays an annual coupon of 10%. The second bond is a 5 year, $1000 zero coupon bond.

What is the duration of the coupon bond if the current yield to maturity is 8%? 10%? 12%

Calculate the duration for the zero-coupon bond with a YTM of 8%, 10%, 12%.

What is the duration of these bonds two years in the future, if the YTM remains at 8%?

Answer 1

Coupon Bond
Par value =	$1,000	Coupon =	0.1
YTM =	0.08	Maturity =	5

Time	Cash Flow	PVIF (8%)	PV of CF	PV*CF*T
1	$100.00	0.9259	92.59	92.59
2	$100.00	0.8573	85.73	171.47
3	$100.00	0.7938	79.38	238.15
4	$100.00	0.7350	73.50	294.01
5	$1,100.00	0.6806	748.64	3743.21
		Price =	1079.85
			Numerator =	4539.43
			Duration = Numerator/Price
			Duration =	4.20

YTM =

0.1

Maturity =

5

Time	Cash Flow	PVIF (10%)	PV of CF	PV*CF*T
1	$100.00	0.9091	90.91	90.91
2	$100.00	0.8264	82.64	165.29
3	$100.00	0.7513	75.13	225.39
4	$100.00	0.6830	68.30	273.21
5	$1,100.00	0.6209	683.01	3415.07
		Price =	1000.00
			Numerator =	4169.87
			Duration = Numerator/Price
			Duration =	4.17

YTM =

0.12

Maturity =

5

Time	Cash Flow	PVIF (12%)	PV of CF	PV*CF*T
1	$100.00	0.8929	89.29	89.29
2	$100.00	0.7972	79.72	159.44
3	$100.00	0.7118	71.18	213.53
4	$100.00	0.6355	63.55	254.21
5	$1,100.00	0.5674	624.17	3120.85
		Price =	927.90
			Numerator =	3837.31
			Duration = Numerator/Price
			Duration =	4.14

B) YTM=8%

Time	Cash Flow	PVIF (8%)	PV of CF	PV*CF*T
1	0	0.9259	0.00	0.00
2	0	0.8573	0.00	0.00
3	0	0.7938	0.00	0.00
4	0	0.7350	0.00	0.00
5	$1,000.00	0.6806	680.58	3402.92
		Price =	680.58
			Numerator =	3402.92
			Duration = Numerator/Price
			Duration =	5.00

YTM=10%

Time	Cash Flow	PVIF (10%)	PV of CF	PV*CF*T
1	0	0.9091	0.00	0.00
2	0	0.8264	0.00	0.00
3	0	0.7513	0.00	0.00
4	0	0.6830	0.00	0.00
5	$1,000.00	0.6209	620.92	3104.61
		Price =	620.92
			Numerator =	3104.61
			Duration = Numerator/Price
			Duration =	5.00

YTM= 12 %

Time	Cash Flow	PVIF (12%)	PV of CF	PV*CF*T
1	0	0.8929	0.00	0.00
2	0	0.7972	0.00	0.00
3	0	0.7118	0.00	0.00
4	0	0.6355	0.00	0.00
5	$1,000.00	0.5674	567.43	2837.13
		Price =	567.43
			Numerator =	2837.13
			Duration = Numerator/Price
			Duration =	5.00