Question

Calculate duration on a ten-year, $1,000 face-value, 10% coupon bond when its yield to maturity is 20%. Show all of your work in a table showing cash payments, present value of cash payments and weighted maturity of those cash payments.

Answer 1

K = N

Bond Price =∑ [( Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =10

Bond Price =∑ [(10*1000/100)/(1 + 20/100)^k]     +   1000/(1 + 20/100)^10

k=1

Bond Price = 580.75

CF Σ '(1+iy Мас V3 В П

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($580.75)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	100.00	1.20	83.33	83.33
2	100.00	1.44	69.44	138.89
3	100.00	1.73	57.87	173.61
4	100.00	2.07	48.23	192.90
5	100.00	2.49	40.19	200.94
6	100.00	2.99	33.49	200.94
7	100.00	3.58	27.91	195.36
8	100.00	4.30	23.26	186.05
9	100.00	5.16	19.38	174.43
10	1,100.00	6.19	177.66	1,776.56
			Total	3,323.01

Macaulay duration =(∑ Duration calc)/(bond price*number of coupon per year)

=3323.01/(580.75*1)

=5.721931

Modified duration = Macaulay duration/(1+YTM)

=5.72/(1+0.2)

=4.768275