Question

You are considering a bond with a face value of $1 000 and a coupon rate of 2.0%. The bond has 16 year until maturity and coupon payments are paid semiannually. The yield to maturity on similar securities in the market is 8.3% What is the current price of this bond?

Answer 1

Solution:         

Statement showing calculation of Current price of the bond

Sl.No.	Particulars	Period	Cash Flow (1)	Annuity Factor @ 4.15 % (2)	Discounted Cash Flow (3) = (1) * (2)
1	Half yearly Interest ( $ 1,000 * 2 % * (6/12))	1 – 32	$ 10	17.537121	$ 175.37121
2	Maturity Amount	32	$ 1,000	0.272209	$ 272.209
3	Current price of the bond				$ 447.58021
4	Current price of the bond ( when rounded off to two decimal places)				$ 447.58

Note :

1.Since Interest is payable half yearly and the no. of years to maturity is 16 years, the price per bond is calculated by converting 16 years into (16 *2) = 32 half yearly periods

2.Thus, the Interest earned per period = $ 1000 * 2 % * (6/12) = $ 10

3. Since the Interest is paid semi annually the discount rate used is = 8.3 % * (6/12) = 4.15 %

4. Interest earned during the 32 periods is discounted using PVIFA ( 4.15 % , 32 ) = 17.537121

5.The Present value of $ 1,000 recoverable at maturity is to be calculated using the half yearly discount rate of (8.3 * (6 /12) ) = 4.15 %

6. Thus PVF ( 4.15 % , 32 ) = 0.272209