Question

You have the following bond : 5-year 6% coupon with annual interest payments YTM IS 6%

A. Calculate price and duration of this bond

B. Calculate new price if YTM instantly inceases to 8%

C. Calculate new duration based on part B.

D. What can you conclude about relationship between market interest rates and Duration

Answer 1

A	Maturity of Bond		5 yrs
	Coupon Rate		6%
	YTM		6%
	Assuming the bond face value is $1000
	Year	Cash flow	Discount factor @ 6%	Present Value
	1	60	0.9434	56.60
	2	60	0.8900	53.40
	3	60	0.8396	50.38
	4	60	0.7921	47.53
	5	1060	0.7473	792.09
	Price of Bond			1000.00
	Since, Coupon rate and YTM is same 6%, the present value of Bond is also $ 1000
	Duration = Sum((t*c)/(1+i)^t) + (n*m)/(1+i)^n)/P
	Sum(5*60)/(1.06^5) + 5*1000/(1.06^5))/1000
	Duration = 4.52 yrs
B	New Price if YTM increases to 8%
	Price of Bond
	Year	Cash flow	Discount factor @ 8%	Present Value
	1	60	0.9259	55.56
	2	60	0.8573	51.44
	3	60	0.7938	47.63
	4	60	0.7350	44.10
	5	1060	0.6806	721.42
	Price of Bond			920.15
C	Duration	Sum(5*60)/(1.08^5) + 5*1000/(1.08^5))/920.15
	Duration = 5.85 yrs
D	With increase in YTM, the duration of the bond increases