Many times future sums of money will not come in one payment but in a number of periodic payments. For example, imagine that you want to buy a house and know that you will have periodic mortgage payments and you need to know how much you would have to invest today in order to facilitate all of those payments into the future. This is called an ordinary annuity and it says that a certain value today at a stated interest rate is equal to a certain number of future payouts for a given amount per payment. The following timeline displays how an ordinary annuity pays out when distributed in three equal payments at an annually compounded interest rate of 5%. Payment: $6,000 Payment: $6,000 Payment: $6,000 Year 1 Year 2 Year 3 Present Value: ? The most simple and commonly used method of determining the present value of an ordinary annuity is to multiply the incremental payout by the appropriate rate found on the present value of an ordinary annuity table. + Present Value of an Ordinary Annuity Table 2 - Present Value of an Ordinary Annuity of $1 at Compound Interest Period 5% 6% 7% 8% 9% 10% 11% 12% 1 0.952 0.943 0.935 0.926 0.917 0.909 0.901 0.893 2 1.859 1.833 1.808 1.783 1.759 1.736 1.713 1.690 3 2.723 2.673 2.624 2.577 2.531 2.487 2.444 2.402 4 3.546 3.465 3.387 3.312 3.240 3.170 3.102 3.037 5 4.329 4.212 4.100 3.993 3.890 3.791 3.696 3.605 6 5.076 4.917 4.767 4.623 4.486 4.355 4.231 4.111 7 5.786 5.582 5.389 5.206 5.033 4.868 4.712 4.564 8 6.463 6.210 5.971 5.747 5.535 5.335 5.146 4.968 9 7.108 6.802 6.515 6.247 5.995 5.759 5.537 5.328 10 7.722 7.360 7.024 6.710 6.418 6.145 5.889 5.650 11 8.306 7.887 7.499 7.139 6.805 6.495 6.207 5.938 12 8.863 8.384 7.943 7.536 7.161 6.814 6.492 6.194 13 9.394 8.853 8.358 7.904 7.487 7.103 6.750 6.424 14 9.899 9.295 8.745 8.244 7.786 7.367 6.982 6.628 15 10.380 9.712 9.108 8.559 8.061 7.606 7.191 6.811 16 10.838 10.106 9.447 8.851 8.313 7.824 7.379 6.974 17 11.274 10.477 9.763 9.122 8.544 8.022 7.549 7.120 18 11.690 10.828 10.059 9.372 8.756 8.201 7.702 7.250 19 12.085 11.158 10.336 9.604 8.950 8.365 7.839 7.366 20 12.462 11.470 10.594 9.818 9.129 8.514 7.963 7.469 Using the previous table, enter the correct factor for three periods at 5%: Periodic payment x Factor = Present value $6,000 x (0.909, 0.952, 2.723 OR 3.791) = $16,338 The controller at Bolden has determined that the company could save $6,000 per year in engineering costs by purchasing a new machine. The new machine would last 12 years and provide the aforementioned annual monetary benefit throughout its entire life. Assuming the interest rate at which Bolden purchases this type of machinery is 9%, what is the maximum amount the company should pay for the machine? $_ (Hint: This is basically a present value of an ordinary annuity problem as highlighted above.) Assume that the actual cost of the machine is $50,000. Weighing the present value of the benefits against the cost of the machine, should Bolden purchase this piece of machinery? ___ (No, yes, Not enough information)

Many times future sums of money will not come in one payment but in a number of periodic payments. For example, imagine that you want to buy a house and know that you will have periodic mortgage payments and you need to know how much you would have to invest today in order to facilitate all of those payments into the future. This is called an ordinary annuity and it says that a certain value today at a stated interest rate is equal to a certain number of future payouts for a given amount per payment. The following timeline displays how an ordinary annuity pays out when distributed in three equal payments at an annually compounded interest rate of 5%. Payment: $6,000 Payment: $6,000 Payment: $6,000 Year 1 Year 2 Year 3 Present Value: ? The most simple and commonly used method of determining the present value of an ordinary annuity is to multiply the incremental payout by the appropriate rate found on the present value of an ordinary annuity table. + Present Value of an Ordinary Annuity Table 2 - Present Value of an Ordinary Annuity of $1 at Compound Interest Period 5% 6% 7% 8% 9% 10% 11% 12% 1 0.952 0.943 0.935 0.926 0.917 0.909 0.901 0.893 2 1.859 1.833 1.808 1.783 1.759 1.736 1.713 1.690 3 2.723 2.673 2.624 2.577 2.531 2.487 2.444 2.402 4 3.546 3.465 3.387 3.312 3.240 3.170 3.102 3.037 5 4.329 4.212 4.100 3.993 3.890 3.791 3.696 3.605 6 5.076 4.917 4.767 4.623 4.486 4.355 4.231 4.111 7 5.786 5.582 5.389 5.206 5.033 4.868 4.712 4.564 8 6.463 6.210 5.971 5.747 5.535 5.335 5.146 4.968 9 7.108 6.802 6.515 6.247 5.995 5.759 5.537 5.328 10 7.722 7.360 7.024 6.710 6.418 6.145 5.889 5.650 11 8.306 7.887 7.499 7.139 6.805 6.495 6.207 5.938 12 8.863 8.384 7.943 7.536 7.161 6.814 6.492 6.194 13 9.394 8.853 8.358 7.904 7.487 7.103 6.750 6.424 14 9.899 9.295 8.745 8.244 7.786 7.367 6.982 6.628 15 10.380 9.712 9.108 8.559 8.061 7.606 7.191 6.811 16 10.838 10.106 9.447 8.851 8.313 7.824 7.379 6.974 17 11.274 10.477 9.763 9.122 8.544 8.022 7.549 7.120 18 11.690 10.828 10.059 9.372 8.756 8.201 7.702 7.250 19 12.085 11.158 10.336 9.604 8.950 8.365 7.839 7.366 20 12.462 11.470 10.594 9.818 9.129 8.514 7.963 7.469 Using the previous table, enter the correct factor for three periods at 5%: Periodic payment x Factor = Present value $6,000 x (0.909, 0.952, 2.723 OR 3.791) = $16,338 The controller at Bolden has determined that the company could save $6,000 per year in engineering costs by purchasing a new machine. The new machine would last 12 years and provide the aforementioned annual monetary benefit throughout its entire life. Assuming the interest rate at which Bolden purchases this type of machinery is 9%, what is the maximum amount the company should pay for the machine? $___________ (Hint: This is basically a present value of an ordinary annuity problem as highlighted above.) Assume that the actual cost of the machine is $50,000. Weighing the present value of the benefits against the cost of the machine, should Bolden purchase this piece of machinery? _____________ (No, yes, Not enough information)

Payment: $6,000

Payment: $6,000

Payment: $6,000

Present Value: ?

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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APPLY THE CONCEPTS: Present value of an ordinary annuity

(Please see overview of question in attachment)

The most simple and commonly used method of determining the present value of an ordinary annuity is to multiply the incremental payout by the appropriate rate found on the present value of an ordinary annuity table.

+ Present Value of an Ordinary Annuity

Table 2 - Present Value of an Ordinary Annuity of $1 at Compound Interest
Period	5%	6%	7%	8%	9%	10%	11%	12%
1	0.952	0.943	0.935	0.926	0.917	0.909	0.901	0.893
2	1.859	1.833	1.808	1.783	1.759	1.736	1.713	1.690
3	2.723	2.673	2.624	2.577	2.531	2.487	2.444	2.402
4	3.546	3.465	3.387	3.312	3.240	3.170	3.102	3.037
5	4.329	4.212	4.100	3.993	3.890	3.791	3.696	3.605
6	5.076	4.917	4.767	4.623	4.486	4.355	4.231	4.111
7	5.786	5.582	5.389	5.206	5.033	4.868	4.712	4.564
8	6.463	6.210	5.971	5.747	5.535	5.335	5.146	4.968
9	7.108	6.802	6.515	6.247	5.995	5.759	5.537	5.328
10	7.722	7.360	7.024	6.710	6.418	6.145	5.889	5.650
11	8.306	7.887	7.499	7.139	6.805	6.495	6.207	5.938
12	8.863	8.384	7.943	7.536	7.161	6.814	6.492	6.194
13	9.394	8.853	8.358	7.904	7.487	7.103	6.750	6.424
14	9.899	9.295	8.745	8.244	7.786	7.367	6.982	6.628
15	10.380	9.712	9.108	8.559	8.061	7.606	7.191	6.811
16	10.838	10.106	9.447	8.851	8.313	7.824	7.379	6.974
17	11.274	10.477	9.763	9.122	8.544	8.022	7.549	7.120
18	11.690	10.828	10.059	9.372	8.756	8.201	7.702	7.250
19	12.085	11.158	10.336	9.604	8.950	8.365	7.839	7.366
20	12.462	11.470	10.594	9.818	9.129	8.514	7.963	7.469

Using the previous table, enter the correct factor for three periods at 5%:

Periodic payment	x	Factor	=	Present value
$6,000	x	(0.909, 0.952, 2.723 OR 3.791)	=	$16,338

The controller at Bolden has determined that the company could save $6,000 per year in engineering costs by purchasing a new machine. The new machine would last 12 years and provide the aforementioned annual monetary benefit throughout its entire life.

Assuming the interest rate at which Bolden purchases this type of machinery is 9%, what is the maximum amount the company should pay for the machine? $___________

(Hint: This is basically a present value of an ordinary annuity problem as highlighted above.)

Assume that the actual cost of the machine is $50,000. Weighing the present value of the benefits against the cost of the machine, should Bolden purchase this piece of machinery? _____________ (No, yes, Not enough information)

APPLY THE CONCEPTS: Present value of an ordinary annuity
Many times future sums of money will not come in one payment but in a number of periodic payments. For example, imagine that you want to buy a house and know that you will have periodic mortgage payments and you need to know how much you would have to invest today in order to facilitate all of those
payments into the future. This is called an ordinary annuity and it says that a certain value today at a stated interest rate is equal to a certain number of future payouts for a given amount per payment. The following timeline displays how an ordinary annuity pays out when distributed in three equal payments at
an annually compounded interest rate of 5%.
Payment: $6,000
Payment: $6,000
Payment: $6,000
Year 1
Year 2
Year 3
Present Value: ?
The most simple and commonly used method of determining the present value of an ordinary annuity is to multiply the incremental payout by the appropriate rate found on the present value of an ordinary annuity table.
+ Present Value of an Ordinary Annuity
Table 2 - Present Value of an Ordinary Annuity of $1 at Compound Interest
Period
5%
6%
7%
8%
9%
10%
11%
12%
0.952
0.943
0.935
0.926
0.917
0.909
0.901
0.893
2
1.859
1.833
1.808
1.783
1.759
1.736
1.713
1.690
3
2.723
2.673
2.624
2.577
2.531
2.487
2.444
2.402
3.546
3.465
3.387
3.312
3.240
3.170
3.102
3.037
5
4.329
4.212
4.100
3.993
3.890
3.791
3.696
3.605
5.076
4.917
4.767
4.623
4.486
4.355
4.231
4.111
5.786
5.582
5.389
5.206
5.033
4.868
4.712
4.564
8
6.463
6.210
5.971
5.747
5.535
5.335
5.146
4.968
9
7.108
6.802
6.515
6.247
5.995
5.759
5.537
5.328
10
7.722
7.360
7.024
6.710
6.418
6.145
5.889
5.650
11
8.306
7.887
7.499
7.139
6.805
6.495
6.207
5.938
12
8.863
8.384
7.943
7.536
7.161
6.814
6.492
6.194
13
9.394
8.853
8.358
7.904
7.487
7.103
6.750
6.424
14
9.899
9.295
8.745
8.244
7.786
7.367
6.982
6.628
15
10.380
9.712
9.108
8.559
8.061
7.606
7.191
6.811
16
10.838
10.106
9.447
8.851
8.313
7.824
7.379
6.974
17
11.274
10.477
9.763
9.122
8.544
8.022
7.549
7.120
18
11.690
10.828
10.059
9.372
8.756
8.201
7.702
7.250
19
12.085
11.158
10.336
9.604
8.950
8.365
7.839
7.366
20
12.462
11.470
10.594
9.818
9.129
8.514
7.963
7.469
Using the previous table, enter the correct factor for three periods at 5%:
Periodic
Present
x Factor
payment
value
$6,000
$16,338
The controller at Bolden has determined that the company could save $6,000 per year in engineering costs by purchasing a new machine. The new machine would last 12 years and provide the aforementioned annual monetary benefit throughout its entire life. Assuming the interest rate at which Bolden
purchases this type of machinery is 9%, what is the maximum amount the company should pay for the machine? $
(Hint: This is basically a present value of an ordinary annuity problem as highlighted above.)
Assume that the actual cost of the machine is $50,000. Weighing the present value of the benefits against the cost of the machine, should Bolden purchase this piece of machinery?

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