Question

A 100,000 par value bond with a term of 4 years and a coupon rate of 8% payable semi-annually is purchased to yield 4% convertible semi-annually.

Find the following:

1. the purchase price,
2. the premium/discount amortized in the 8^th coupon payment,
3. the total amount of interest due over the term of the bond (from a bond amortization perspective).

Answer 1

Requirement 1- Purchase price = $114,651

Requirement 2- The premium/discount amortized in the 8^th coupon payment= $1960.78 or $1961

Requirement 3= $17,349……..(32000-14651)

Bonds issue price is calculated by ADDING the:

Discounted face value of bonds payable at market rate of interest, and

Discounted Interest payments amount (during the lifetime) at market rate of interest.

	Annual Rate	Applicable rate		Face Value	$     1,00,000.00
Market Rate	4.00%	2.00%		Term (in years)	4
Coupon Rate	8.00%	4.00%		Total no. of interest payments	8

Calculation of Issue price of Bond
	Bond Face Value		Market Interest rate (applicable for period/term)
PV of	$ 1,00,000	at	2.00%	Interest rate for	8	term payments
PV of $1	0.85349
PV of	$ 1,00,000	=	$   1,00,000	x	0.85349	=	$       85,349	A
Interest payable per term	at	4%	on	$          1,00,000
Interest payable per term	$ 4,000
PVAF of 1$	for	2.0%	Interest rate for	8	term payments
PVAF of 1$	7.32548
PV of Interest payments	=	$            4,000.00	x	7.32548	=		$       29,302	B
				Bond Value (A+B)			$   1,14,651

Amortization table
Period	Cash payment	Interest expense	Premium on Bonds payable	Carrying Value of Bond
Issued at the end of 2011			$       (14,650.96)	$     1,14,650.96
Year 1 First half	$   4,000.00	$          2,293.02	$         (1,706.98)	$     1,12,943.98
Year 1 Second half	$   4,000.00	$          2,258.88	$         (1,741.12)	$     1,11,202.86
Year 2 First half	$   4,000.00	$          2,224.06	$         (1,775.94)	$    1,09,426.92
Year 2 Second half	$   4,000.00	$          2,188.54	$         (1,811.46)	$     1,07,615.46
Year 3 First half	$   4,000.00	$          2,152.31	$         (1,847.69)	$     1,05,767.77
Year 3 Second half	$   4,000.00	$          2,115.36	$         (1,884.64)	$     1,03,883.12
Year 4 First half	$   4,000.00	$          2,077.66	$         (1,922.34)	$     1,01,960.78
Year 4 Second half	$   4,000.00	$          2,039.22	$         (1,960.78)	$     1,00,000.00