Question

Alenza, Inc. plans to issue a 10-year semiannual bond with a face value of $990,000 with a coupon rate of 4%. On the date of issue, it expects the market rate for similar bonds will be 6%. Under these conditions, Alenza would like to know how much this issuance would raise.

What framework will you use to solve this problem?

• Cost-Volume-Profit (CVP)

• Counting - Permutation or Combination

• Time Value of Money (TVM)

• Binomial Probability - B(n, p)

• Normal or Standard Normal Distribution

Complete the table below. For the amounts (PV, PMT, & FV) please enter the number only with no dollar sign or commas. Do not forget to include percent signs, where appropriate.

TVM Data Table

c/y	n	i	PV	PMT	FV
1

[UNGRADED] Before you perform any computation: Based on the relationship between the two given interest rates, do you think this bond will be issued at

• a premium

• par

• a discount

Which type of annuity should you use for this problem?

• ordinary annuity

• annuity due

What is the value of the annuity factor that is used to value the cash flows of the interest payments?  

What is the value of the discount factor, DF(), that is used to discount the maturity value?  

How much does Alenza raise from this issue? $  . You may ignore transaction costs. (round to cents ~ two decimal places).

[UNGRADED On your own] Were you correct about whether the bond was issued at a premium, discount, or at par?

Present Value of 1

n\i	1%	2%	3%	4%	6%	8%	12%	24%
5	0.95147	0.90573	0.86261	0.82193	0.74726	0.68058	0.56743	0.34111
10	0.90529	0.82035	0.74409	0.67556	0.55839	0.46319	0.32197	0.11635
15	0.86135	0.74301	0.64186	0.55526	0.41727	0.31524	0.18270	0.039689
20	0.81954	0.67297	0.55368	0.45639	0.31180	0.21455	0.10367	0.013538
25	0.77977	0.60953	0.47761	0.37512	0.23300	0.14602	0.058823	0.0046180
30	0.74192	0.55207	0.41199	0.30832	0.17411	0.099377	0.033378	0.0015752
40	0.67165	0.45289	0.30656	0.20829	0.097222	0.046031	0.010747	0.00018329
50	0.60804	0.137153	0.22811	0.14071	0.054288	0.021321	0.0034602	0.000021326
60	0.55045	0.30478	0.16973	0.095060	0.030314	0.0098759	0.0011141	0.0000024814

Present Value of an Ordinary Annuity of 1

n\i	1%	2%	3%	4%	6%	8%	12%	24%
5	4.85343	4.71346	4.57971	4.45182	4.21236	3.99271	3.60478	2.74538
10	9.47130	8.98259	8.53020	8.1109	7.36009	6.71008	5.65022	3.68186
15	13.86505	12.84926	11.93794	11.11839	9.71225	8.55948	6.81086	4.00129
20	18.04555	16.35143	14.87747	13.59033	11.46992	9.81815	7.46944	4.11026
25	22.02316	19.52346	17.41315	13.76483	12.78336	10.67478	7.84314	4.14742
30	25.80771	22.39646	19.60044	17.29203	13.76483	11.25778	8.05518	4.16010
40	32.83469	27.35548	23.11477	19.79277	15.04630	11.92461	8.24378	4.16590
50	39.19612	31.42361	25.72976	21.48218	15.76186	12.23348	8.30450	4.16658
60	44.95504	34.76089	27.67556	22.62349	16.16143	12.37655	8.32405	4.16666

Present Value of an Annuity Due of 1

n\i	1%	2%	3%	4%	6%	8%	12%	24%
5	4.90197	4.80773	4.71710	4.62990	4.46511	4.31213	4.03735	3.40428
10	9.56602	9.16224	8.78611	8.43533	7.80169	7.24689	6.32825	4.56550
15	14.00370	13.10625	12.29607	11.56312	10.29498	9.24424	7.62817	4.96160
20	18.22601	16.67846	14.32380	14.13394	12.15812	10.60360	8.36578	5.09672
25	22.24339	19.91393	17.93554	16.24696	13.55036	11.52876	8.78432	5.14281
30	26.06579	22.84438	20.18845	17.98371	14.59072	12.15841	9.02181	5.15853
40	33.16303	27.90259	23.80822	20.58448	15.94907	12.87858	9.23303	5.16657
50	39.58808	32.05208	26.50166	22.34147	16.70757	13.21216	9.30104	5.16656
60	45.40459	35.45610	28.50583	23.52843	17.13111	13.36668	9.32294	5.16665

Answer 1

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Alena, Inc.
Frontier World
Book value of bonds	990,000.00
Coupon rate	4.00%
Semi annual rate	2.00%
Semi annual interest	19,800.00
Market rate	6.00%
Semi annual market rate	3.00%

Issue price of bonds	Principle	Coupon Payment
Future Value	990,000.00	19,800.00
Present value factor	0.55368	14.87747
Present value	548,143.20	294,573.91
Price of bonds	842,717.11

Par value of bonds	990,000.00
Issue value	842,717.11
Unamortized Discount	147,282.89
The bonds will issue at: Discount

ordinary annuity

What is the value of the annuity factor that is used to value the cash flows of the interest payments?

14.87747

What is the value of the discount factor, DF(), that is used to discount the maturity value?

0.55368

How much does Alena raise from this issue?

$842,717.11

Yes the bond was issued at a discount.