Question

What is the value (to the nearest cent) of a 4 year 5.9% coupon bond with a face value of $1,000. The yield-to-maturity on the bond is 11.7% and the bond makes semi-annual coupon payments.

Select one: a. $818.84 b. $2447.84 c. $822.71 d. $642.37

Answer 1

Solution:

Statement showing calculation of value of the bond

Sl.No.	Particulars	Period	Cash Flow (1)	Annuity Factor @ 5.85 % (2)	Discounted Cash Flow (3) = (1) * (2)
1	Half yearly Interest ( $ 1,000 * 5.9 % * (6/12))	1 - 8	$ 29.50	6.246827	$ 184.281397
2	Maturity Amount	8	$ 1,000	0.634561	$ 634.561000
3	Value of the bond				$ 818.842397
4	Value of the bond ( when rounded off to the nearest cent )				$ 818.84

Notes:

Since Interest is payable half yearly and the no. of years to maturity is 4 years, the price per bond is calculated by converting 4 years into (4 * 2) = 8 half yearly periods

1. Thus, the Interest earned per period = $ 1000 * 5.9 % * (6/12) = $ 29.5

2. Since the Interest is paid semi annually the discount rate used is = 11.7 % * (6/12) = 5.85 %

3. Interest earned during the 8 periods is discounted using PVIFA ( 5.85 % ,8 ) = 6.246827

4. The Present value of $ 1,000 recoverable at maturity is to be calculated using the half yearly discount rate of ( 11.7 % * (6 /12) ) = 5.85 %

Thus PVF ( 5.85 % , 8) = 0.634561

Thus the solution to the question is Option a. $ 818.34