Question

On January 1, 2015, Brightstar Inc. issued $1,000,000 of 8%, semiannual 3-year coupon bonds.

1) The market interest rate on January 1, 2015 was 10%. Was the bond issued at par, a premium, or a discount?

Answer 1

Price of the bond is equal to present value of cash flows from it.

Lets assume par value of each bond is $ 1000

Particulars	Amount
Coupon Amount	$        40.00
Maturity Value per Bond	$   1,000.00
Disc Rate	5.00%

Coupon Amount =  $ 1000 * 8% * 6 / 12

= $ 40

Discount rate per annum is 10% , as the bonds are pai semi annualy . the Discount rate wil be 10% * 6/12 = 5%

Period	Cash Flow	PVF @5 %	Disc CF
1	$      40.00	0.9524	$      38.10
2	$      40.00	0.9070	$      36.28
3	$      40.00	0.8638	$      34.55
4	$      40.00	0.8227	$      32.91
5	$      40.00	0.7835	$      31.34
6	$      40.00	0.7462	$      29.85
6	$ 1,000.00	0.7462	$    746.22
Price of Bond	$    949.24

As the Price of the bond is $ 949.24 which is less than par value i.e., $ 1000, it means that the bonds are issued at discount

Plz Comment, if any further assistance is required.