Question

there is a 4.8 percent coupon bond with six years to maturity and a current price of $1,048.30. What is the dollar value of an 01 for the bond? (Do not round intermediate calculations. Round your answer to 3 decimal places. Omit the "$" sign in your response.) Dollar value $

Answer 1

K = N

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

k=1

K =6

1048.3 =∑ [(4.8*1000/100)/(1 + YTM/100)^k]     +   1000/(1 + YTM/100)^6

k=1

YTM% = 3.88

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,048.30)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	48.00	1.04	46.21	46.21
2	48.00	1.08	44.48	88.96
3	48.00	1.12	42.82	128.46
4	48.00	1.16	41.22	164.88
5	48.00	1.21	39.68	198.40
6	1,048.00	1.26	834.01	5,004.04
			Total	5,630.96

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

=5630.96/(1048.3*1)

=5.371513

Modified duration = Macaulay duration/(1+YTM)

=5.37/(1+0.0388)

=5.170883

dollar value = -modified duration*current price*1 percent change in YTM

Dollar value = -5.17*1048.3*0.01

Dollar value = -54.2

DV01 = Dollar value*0.01

=-54.19711*0.01

-0.5419711