Question

The face value of a bond is $ 69000​, its stated rate is 7​%, and the term of the bond is five years. The bond pays interest semiannually. At the time of​ issue, the market rate is 8​%. Determine the present value of the bonds at issuance.

Present value of​ $1:

	​4%	​5%	​6%	​7%	​8%
5	0.822	0.784	0.747	0.713	0.681
6	0.790	0.746	0.705	0.666	0.630
7	0.760	0.711	0.665	0.623	0.583
8	0.731	0.677	0.627	0.582	0.540
9	0.703	0.645	0.592	0.544	0.500
10	0.676	0.614	0.558	0.508	0.463

Present value of ordinary annuity of​ $1:

	​4%	​5%	​6%	​7%	​8%
5	4.452	4.329	4.212	4.100	3.993
6	5.242	5.076	4.917	4.767	4.623
7	6.002	5.786	5.582	5.389	5.206
8	6.733	6.463	6.210	5.971	5.747
9	7.435	7.108	6.802	6.515	6.247
10	8.111	7.722	7.360	7.024	6.710

Answer 1

• All working forms part of the answer

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.

• Working

	Bond Face Value		Market Interest rate (applicable for period/term)
PV of	$                   69,000.00	at	4.0% [8% x 6/12]	Interest rate for	10	term payments
PV of $1 [4% , 10th period]	0.676
PV of	$                   69,000.00	=	$                  69,000.00	x	0.676	=	$          46,644	A
Interest payable per term	at	3.5% [7% x 6/12]	on	$            69,000.00
Interest payable per term	$                     2,415.00	[69000 x 3.5%]
PVAF of 1$	for	4.0%	Interest rate for	10	term payments
PVAF of 1$ [4%	8.111
PV of Interest payments	=	$                 2,415.00	x	8.111	=		$          19,588	B
				Bond Value (A+B)			$          66,232

• Answer:

	Amount	Factor	Present Values
PV of Face Value	$          69,000.00	0.676	$                                    46,644.00
PV of Interest payments	$             2,415.00	8.111	$                                    19,588.07
Present Value of Bonds at Issuance			$                                    66,232.07