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MCQ: Legacy Inc. recently issued bonds that mature in 10 years. They have a par value...

MCQ: Legacy Inc. recently issued bonds that mature in 10 years. They have a par value of $1,000 and annual coupon of 6%. The current market interest rate is 8.5%. If the bonds pay interest semiannually, what will be the price of the bonds? Select one:

a. 582.73

b. 833.82

c. 782.42

d. 1200.85

e. 1125.75

Expert Solution

Solution:

The price of the bond is = $ 833.82

The solution is Option b.

Statement showing calculation of Price of the bond

Sl.No.	Particulars	Period	Cash Flow (1)	Annuity Factor @ 4.25 % (2)	Discounted Cash Flow *(3) = (1) (2)**
1	Half yearly Interest ( $ 1,000 * 6 % * (6/12))	1 – 20	$ 30	13.294366	$ 398.830980
2	Maturity Amount	20	$ 1,000	0.434989	$ 434.989000
3	Price of the bond = $ 398.830980 + $ 434.989000	$ 833.819980
4	Price of the bond ( when rounded off to two decimal places )	$ 833.82

Note :

1.Since Interest is payable half yearly and the no. of years to maturity is 10 years, the price per bond is calculated by converting 10 years into (10 *2) = 20 half yearly periods

2.Thus, the Interest earned per period = $ 1,000 * 6 % * (6/12) = $ 30

3. Since the Interest is paid semi annually the discount rate used is = 8.5 % * (6/12) = 4.25 %

4. Interest earned during the 20 periods is discounted using PVIFA ( 4.25 %, 20 ) = 13.294366

5.The Present value of $ 1,000 recoverable at maturity is to be calculated using the half yearly discount rate of ( 8.5 % * (6 /12) ) = 4.25 %

Thus PVF ( 4.25 %, 20 ) = 0.434989

jeff jeffy answered 2 years ago

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