Question

In July 1993, Disney issued a bond with $300,000,000 in face value.

The coupon rate was 7.55%, paid semi-annually.

The maturity was July 15, 2093. (100 years)

The yield at issuance was 7.55%, so the bond was issued at par.

Assume a $100 par value throughout.

1. Approximate the modified duration (based on semi-annual yields) using the approximation formula.

Answer 1

		Bond Duration approximation Formula:
		(P(down)-P(up))/(2*P0*Dy)
		P0=Price of the Bond
		P(down)=Price if yield is decreases
		P(up)=Price if yield increases
		Dy=Change in yield
		In this Case,
		P0= Price of Bond	$100
		Semi annual Interest rate =(7.55/2)%	0.03775
		Dy=Change in Semi annual interest rate =0.5%=	0.005
		P(down)=Bond Price with interest rate =	0.03275	(0.03775-0.005)
	Rate	Interest rate	0.03275
	Nper	Number of semi annual periods=100*2	200
	Pmt	Semi annual Coupon payment =(100*7.55%)/2	$3.775
	PV	p(down)=Bond Price if yield decreases	$115.08
		(Using PV function of excel)
		Dy=Change in Semi annual interest rate =0.5%=	0.005
		P(up)=Bond Price with interest rate =	0.04275	(0.03775+0.005)
	Rate	Interest rate	0.04275
	Nper	Number of semi annual periods=100*2	200
	Pmt	Semi annual Coupon payment =(100*7.55%)/2	$3.775
	PV	p(up)=Bond Price if yield Increases	$88.28
		(Using PV function of excel)
		Bond Duration in Semi annual Periods:
		(115.08-88.28)/(2*100*0.005)=	26.80
		Bond Duration in Years =26.80/2=	13.40