Question

What is the price today of a Tin-Tan Inc.'s bond? The bond matures in 15 years, has a coupon rate of 10%, and has, today, a yield to maturity (YTM) of 8%. The bond has semiannual coupon payments and a par value of $1,000.

	1,135.90
	875.38
	828.41
	1,172.92
	1,197.93

Answer 1

Solution:         

Statement showing calculation of Price of the bond today

Sl.No.	Particulars	Period	Cash Flow (1)	Annuity Factor @ 4 % (2)	Discounted Cash Flow (3) = (1) * (2)
1	Half yearly Interest ( $ 1,000 * 10 % * (6/12) )	1 – 30	$ 50	17.292033	$ 864.601650
2	Maturity Amount	30	$ 1,000	0.308319	$ 308.319000
3	Price of the bond today = (1) + (2) = $ 864.601650 + $ 308.319000 = $ 1,172.920650	$ 1,172.920650
4	Price of the bond today ( when rounded off to two decimal places)	$ 1,172.92

Thus the solution is option 4 = $ 1,172.92

Note :

1.Since Interest is payable half yearly and the number of years to maturity is 15 years, the price of the bond is calculated by converting 15 years into (15 * 2) = 30 half yearly periods

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

3. Since the Interest is paid semi annually the discount rate used is = 8 % * (6/12) = 4 %

4. Interest earned during the 30 periods is discounted using PVIFA ( 4 %, 30 ) = 17.292033

5.The Present value of face value of $ 1,000, recoverable at maturity is to be calculated using the half yearly discount rate of ( 8 % * (6 /12) ) = 4 %. Thus PVF ( 4 %, 30 ) = 0.308319