Question

Compute the price of a $1,000 par value, 11 percent (semi-annual payment) coupon bond with 22 years remaining until maturity assuming that the bond's yield to maturity is 17 percent? (Round your answer to 2 decimal places and record your answer without dollar sign or commas).

Answer 1

Solution :

  Statement showing calculation of Price of the bond

Sl.No.	Particulars	Period	Cash Flow (1)	Annuity Factor @ 8.5 % (2)	Discounted Cash Flow (3) = (1) * (2)
1	Half yearly Interest ( $ 1,000 * 11 % * (6/12))	1 – 44	$ 55	11.439864	$ 629.192520
2	Maturity Amount	44	$ 1,000	0.027612	$ 27.612000
3	Price of the bond = ( $ 629.192520 + $ 27.612000 ) = $ 656.804520				$ 656.804520
4	Price of the bond ( when rounded off to two decimal places)				$ 656.80

Note :

1.Since Interest is payable half yearly and the no. of years to maturity is 22 years, the price per bond is calculated by converting 22 years into (22 *2) = 44 half yearly periods

2.Thus, the Interest earned per period = $ 1000 * 11 % * (6/12) = $ 55

3. Since the Interest is paid semi annually the discount rate used is = 17 % * (6/12) = 8.5 %

4. Interest earned during the 44 periods is discounted using PVIFA ( 8.5 % , 44 ) = 11.439864

5.The Present value of $ 1,000 recoverable at maturity is to be calculated using the half yearly discount rate of (17 * (6 /12) ) = 8.5 %

6. Thus PVF ( 8.5 % , 44 ) = 0.027612