Question

Consider a bond with a coupon rate of 10% and annual coupons. The par value is $1,000, and the bond has 5 years to maturity. The yield to maturity is 9%. What is the value of the bond? (in dollars)

987

1008

1006

918

1087

1020

996

1039

971

956

Answer 1

Price of the bond is calculated by solving the below equation:

F Price = Sum of Discounted coupons +7 (1 + r)" 1- (1+r)-n 1000 Price = Coupon x = *(1 +0.09)5 1-(1+0.09) -5 1000 Price = (0.10 x 1000) x = 0.09 (1 + 0.095 Price = 1038.90 - +-

This can be verified from the below schedule:

Year	CF	Discount Factor	Discounted CF
0	$             -	1/(1+0.09)^0=	1	1*0=	$              -
1	$    100.00	1/(1+0.09)^1=	0.917431193	0.91743119266055*100=	$       91.74
2	$    100.00	1/(1+0.09)^2=	0.841679993	0.84167999326656*100=	$       84.17
3	$    100.00	1/(1+0.09)^3=	0.77218348	0.772183480061064*100=	$       77.22
4	$    100.00	1/(1+0.09)^4=	0.708425211	0.708425211065196*100=	$       70.84
5	$1,100.00	1/(1+0.09)^5=	0.649931386	0.649931386298345*1100=	$     714.92
				Price= Sum of all Discounted CF	$ 1,038.90