Question

There is a 5.4 percent coupon bond with nine years to maturity and a current price of $1,055.20. What is the dollar value of an 01 for the bond? (Do not round intermediate calculations. Round your answer to 3 decimal places. Omit the "$" sign in your response.)

Dollar value

$

Answer 1

K = N

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

k=1

K =9

1055.2 =∑ [(5.4*1000/100)/(1 + YTM/100)^k]     +   1000/(1 + YTM/100)^9

k=1

YTM% = 4.64

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,055.20)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	54.00	1.05	51.61	51.61
2	54.00	1.09	49.32	98.63
3	54.00	1.15	47.13	141.39
4	54.00	1.20	45.04	180.16
5	54.00	1.25	43.04	215.22
6	54.00	1.31	41.13	246.81
7	54.00	1.37	39.31	275.17
8	54.00	1.44	37.57	300.54
9	1,054.00	1.50	700.75	6,306.72
			Total	7,816.25

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

=7816.25/(1055.2*1)

=7.407364

Modified duration = Macaulay duration/(1+YTM)

=7.41/(1+0.0464)

=7.078903

dollar value = modified duration*current price*1 percent change in YTM*0.01 =7.0789*1055.2*0.01*0.01=0.747