Question

Problem 3 - Bonds

Suppose we sell an 8 year bond, with coupon rate =7 %.

The face value of the Bond is $1000. The market rate is 8 %.

1. What is the price of the bond ?

2. What is the interest expense in the first two years ?

Answer 1

• All working forms part of the answer
• Working for Price of the Bond

	Bond Face Value		Market Interest rate (applicable for period/term)
PV of	$                     1,000.00	at	8.0%	Interest rate for	8	term payments
PV of $1	0.540268885
PV of	$                     1,000.00	=	$                     1,000.00	x	0.540268885	=	$                540.27	A
Interest payable per term	at	7.0%	on	$               1,000.00
Interest payable per term	$                           70.00
PVAF of 1$	for	8.0%	Interest rate for	8	term payments
PVAF of 1$	5.746638944
PV of Interest payments	=	$                       70.00	x	5.746638944	=		$                402.26	B
				Bond Value (A+B)			$                942.53

• Requirement 1

Since Market rate is more than the Bond’s interest rate, the Bonds will be issued at the discount.

Face Value (given) = $ 1,000
Price of Bonds = $ 942.53 [calculated above]

• Requirement 2

Working for all 8 years

Period	Cash payment	Interest expense	Discount on Bonds payable amortised	Carrying Value of Bond
	[A = $1000 x 7%]	[B = D x 8%]	[C = B – A]	[ D = D + C]
Issued				$                            942.53
Year 1	$                           70.00	$                     75.40	$                          5.40	$                            947.94
Year 2	$                           70.00	$                     75.83	$                          5.83	$                            953.77
Year 3	$                           70.00	$                     76.30	$                          6.30	$                            960.07
Year 4	$                           70.00	$                     76.81	$                          6.81	$                            966.88
Year 5	$                           70.00	$                     77.35	$                          7.35	$                            974.23
Year 6	$                           70.00	$                     77.94	$                          7.94	$                            982.17
Year 7	$                           70.00	$                     78.57	$                          8.57	$                            990.74
Year 8	$                           70.00	$                     79.26	$                          9.26	$                         1,000.00

Hence, The Interest expense for the first two years [based on above working] will be:
Year 1: $ 75.40
Year 2: $ 75.83