Question

What is the price of a 15-year, 10% semi-annual coupon, $1,000 par value bond if the nominal (the YTM) is 5%?

Answer 1

Solution:         

Statement showing calculation of price of the bond

Sl.No.	Particulars	Period	Cash Flow	Annuity Factor @ 2.5 %	Discounted Cash Flow
1	Half yearly Interest ( $ 1,000 * 10 % * (6/12))	1 - 30	$ 50	20.9303	$ 1,046.5146
2	Maturity Amount	30	$ 1,000	0.4767	$ 476.70
3	Price of the bond = (1) + (2)				$ 1,523.2146
4	Price of the bond ( when rounded off to two decimal places)				$ 1,523.21

1. Since Interest is payable half yearly and the no. of years to maturity is 15 years, the price per bond is calculated by converting 15 years into (15 *2) = 30 half yearly periods

2. Thus, the Interest earned per period = $ 1000 * 10 % * (6/12) = $ 50

3. Since the Interest is paid semi annually the discount rate used is = 5 % * (6/12) = 2.5 %

4. Interest earned during the 30 periods is discounted using PVIFA ( 2.5 % , 30 ) = 20.9303

5. The Present value of $ 1,000 recoverable at maturity is to be calculated using thehalf yearly discount rate of (5 * (6 /12) ) = 2.5 %

Thus PVF ( 2.5 % , 30 ) = 0.4767