Question

A 10-year bond pays semi-annual coupons at j2= 9.3% and has a yield rate of j2 = 7.8%. If the book value immediately after the 7th coupon payment is $1047.77, and the book value immediately after the 11th coupon payment is $1027.81, what is the bond's face value?

Answer 1

We will find the value by discounting cash flow to the 7th and 11th years. As payment for the 7th coupon and 11th coupon is already made we will not consider coupon till 7th and 11th payment respectively.

				(in term of x)	Value after 7th coupon payment	Value after 11th coupon payment
			0
			1
			2
			3				Considering the face value of the bond is x
			4				Coupon Amount =	(0.093/2)*x
			5				Yield rate (semi-annual)	0.039
			6
We want to find the value of bond after 7th and 11th coupon payment. Hence, we will not consider any coupon payment till the 7th and 11th year for respective part as this payment has already been made.			7		0.0465
1		8	0.0465	0.044754572
2		9	0.0465	0.04307466
3		10	0.0465	0.041457806
4		11	0.0465	0.039901642	0.0465
	5	1	12	0.0465	0.03840389	0.044754572
	6	2	13	0.0465	0.036962358	0.04307466
	7	3	14	0.0465	0.035574935	0.041457806
	8	4	15	0.0465	0.034239591	0.039901642
	9	5	16	0.0465	0.032954371	0.03840389
	10	6	17	0.0465	0.031717393	0.036962358
	11	7	18	0.0465	0.030526846	0.035574935
	12	8	19	0.0465	0.029380987	0.034239591
	13	9	20	1.0465	0.636410175	0.741650518
					1.075359224	1.056019972
					1.075359224*(x) = 1047.77	1.05601997161602 * (x) = 1027.81
					From any of the above equations, we can solve for x. The value of x should be very close in both the cases as x here is the face value of the same bond.
				x =	974.3441788	973.2865169
				You may take the average of both values, in that case, face value would be 973.8153479