Question

What is the price of a 7­-year, 8.8% semi-annual coupon bond with $1,000 face value if the yield to maturity on similar bonds is 4.4%? Round to the nearest cent.

Answer 1

Solution:

Statement showing calculation of Price of the bond

Sl.No.	Particulars	Period	Cash Flow (1)	Annuity Factor @ 2.2 % (2)	Discounted Cash Flow (3) = (1) * (2)
1	Half yearly Interest ( $ 1,000 * 8.8 % * (6/12))	1 – 14	$ 44	11.937573	$ 525.253227
2	Maturity Amount	14	$ 1,000	0.737373	$ 737.373
3	Price of the bond				$ 1,262.626613
4	Price of the bond ( when rounded off to the nearest cent )				$ 1,262.63

Note:

1.Since Interest is payable half yearly and the no. of years to maturity is 7 years, the price per bond is calculated by converting 7 years into (7 *2) = 14 half yearly periods

2.Thus, the Interest earned per period = $ 1000 * 8.8 % * (6/12) = $ 44

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

4. Interest earned during the 14 periods is discounted using PVIFA ( 2.2 %, 14 ) = 11.937573

5.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 %

6. Thus PVF ( 2.2 % , 14 ) = 0.737373