Question

Problem 10-25

There is a 8.2 percent coupon bond with ten years to maturity and a current price of $1,039.10. What is the dollar value of an 01 for the bond? (Do not round intermediate calculations. Round your answer to 3 decimal places. Omit the "$" sign in your response.)

Dollar value

$

Answer 1

K = N

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

k=1

K =10

1039.1 =∑ [(8.2*1000/100)/(1 + YTM/100)^k]     +   1000/(1 + YTM/100)^10

k=1

YTM% = 7.63

Calculating modified duration

Period	Cash Flow	PV Cash Flow	Duration Calc
0	($1,039.10)
1	76.30	70.89	70.89
2	76.30	65.87	131.73
3	76.30	61.20	183.59
4	76.30	56.86	227.43
5	76.30	52.83	264.14
6	76.30	49.08	294.49
7	76.30	45.60	319.22
8	76.30	42.37	338.96
9	76.30	39.37	354.30
10	1,076.30	515.94	5,159.41
		Total	7,344.16

Macaulay Duration	7.07
Modified Duration	6.57

dollar value = modified duration*current price*1 percent change in YTM*0.01 = 6.57*1039.1*0.01*0.01=0.683