Question

What is the value (to the nearest cent) of a 8 year 6.8% coupon bond with a face value of $1,000. The yield-to-maturity on the bond is 4.4% and the bond makes semi-annual coupon payments.

Select one:

a. $1160.38

b. $1662.16

c. $1158.95

d. $708.59

Answer 1

Solution :

Statement showing calculation of value of the bond

Sl.No.	Particulars	Period	Cash Flow	Annuity Factor @ 2.2 %	Discounted Cash Flow
1	Half yearly Interest ( $ 1,000 * 6.8 % * (6/12))	1 - 16	$ 34	13.365043	$ 454.411462
2	Maturity Amount	16	$ 1,000	0.705969	$ 705.969000
3	Value of the bond				$ 1,160.380462
4	Value of the bond ( when rounded off to the nearest cent )				$ 1,160.38

Notes:

Since Interest is payable half yearly and the no. of years to maturity is 8 years, the price per bond is calculated by converting 8 years into (8 *2) = 16 half yearly periods

1. Thus, the Interest earned per period = $ 1000 * 6.8 % * (6/12) = $ 34

2. Since the Interest is paid semi annually the discount rate used is = 4.4 % * (6/12) = 2.2 %

3. Interest earned during the 16 periods is discounted using PVIFA ( 2.2 % , 16 ) = 13.365043

4. The Present value of $ 1,000 recoverable at maturity is to be calculated using the half yearly discount rate of (4.4 % * (6 /12) ) = 2.2 %

Thus PVF ( 2.2 % , 16 ) = 0.705969

Thus the solution to the question is Option a. $ 1,160.38