Chapter 5, Problem 31P

To determine

(a)

Which of the two alternatives should be selected assuming a 10% rate of interest.

Answer to Problem 31P

The Option to be implemented is Option 2, since it results in a lower cash outflow for a period of 30 years.

Explanation of Solution

Given information:

Option 1:

Install one cable now for 4000 lines. Installation cost $20,000 and annual maintenance costs would be $1,500.

Option 2:

Install one cable for 2000 lines now and one cable for 2000 lines after 10 years. Installation cost $15,000 and annual maintenance costs would be $1,000.

Rate of interest for calculation: 10%.

Based on the above information, the following tables outlines the net present value calculation of the two options.

Option 1:

Year	Particulars	Cash flow	Present value Factor @10%	Present value
0	Installation Cost	$20,000.00	1	$20,000.00
1	Operating costs	$1,500.00	0.9091	$1,363.64
2	Operating costs	$1,500.00	0.8264	$1,239.67
3	Operating costs	$1,500.00	0.7513	$1,126.97
4	Operating costs	$1,500.00	0.6830	$1,024.52
5	Operating costs	$1,500.00	0.6209	$931.38
5	Operating costs	$1,500.00	0.6209	$931.38
6	Operating costs	$1,500.00	0.5645	$846.71
7	Operating costs	$1,500.00	0.5132	$769.74
8	Operating costs	$1,500.00	0.4665	$699.76
9	Operating costs	$1,500.00	0.4241	$636.15
10	Operating costs	$1,500.00	0.3855	$578.31
11	Operating costs	$1,500.00	0.3505	$525.74
12	Operating costs	$1,500.00	0.3186	$477.95
13	Operating costs	$1,500.00	0.2897	$434.50
14	Operating costs	$1,500.00	0.2633	$395.00
15	Operating costs	$1,500.00	0.2394	$359.09
16	Operating costs	$1,500.00	0.2176	$326.44
17	Operating costs	$1,500.00	0.1978	$296.77
18	Operating costs	$1,500.00	0.1799	$269.79
19	Operating costs	$1,500.00	0.1635	$245.26
20	Operating costs	$1,500.00	0.1486	$222.97
21	Operating costs	$1,500.00	0.1351	$202.70
22	Operating costs	$1,500.00	0.1228	$184.27
23	Operating costs	$1,500.00	0.1117	$167.52
24	Operating costs	$1,500.00	0.1015	$152.25
25	Operating costs	$1,500.00	0.0923	$138.44
26	Operating costs	$1,500.00	0.0839	$125.86
27	Operating costs	$1,500.00	0.0763	$114.42
28	Operating costs	$1,500.00	0.0693	$104.02
29	Operating costs	$1,500.00	0.0630	$94.56
30	Operating costs	$1,500.00	0.0573	$85.96
	Net cash outflow			$35,071.75

Option 2:

Year	Particulars	Cash flow	Present value Factor @10%	Present value
0	Installation Cost	$15,000.00	1	$15,000.00
1	Operating costs	$1,000.00	0.9091	$909.09
2	Operating costs	$1,000.00	0.8264	$826.45
3	Operating costs	$1,000.00	0.7513	$751.31
4	Operating costs	$1,000.00	0.6830	$683.01
5	Operating costs	$1,000.00	0.6209	$620.92
5	Operating costs	$1,000.00	0.6209	$620.92
6	Operating costs	$1,000.00	0.5645	$564.47
7	Operating costs	$1,000.00	0.5132	$513.16
8	Operating costs	$1,000.00	0.4665	$466.51
9	Operating costs	$1,000.00	0.4241	$424.10
10	Operating costs	$1,000.00	0.3855	$385.54
10	Installation Cost	$15,000.00	0.3855	$5,783.15
11	Operating costs	$2,000.00	0.3505	$700.99
12	Operating costs	$2,000.00	0.3186	$637.26
13	Operating costs	$2,000.00	0.2897	$579.33
14	Operating costs	$2,000.00	0.2633	$526.66
15	Operating costs	$2,000.00	0.2394	$478.78
16	Operating costs	$2,000.00	0.2176	$435.26
17	Operating costs	$2,000.00	0.1978	$395.69
18	Operating costs	$2,000.00	0.1799	$359.72
19	Operating costs	$2,000.00	0.1635	$327.02
20	Operating costs	$2,000.00	0.1486	$297.29
21	Operating costs	$2,000.00	0.1351	$270.26
22	Operating costs	$2,000.00	0.1228	$245.69
23	Operating costs	$2,000.00	0.1117	$223.36
24	Operating costs	$2,000.00	0.1015	$203.05
25	Operating costs	$2,000.00	0.0923	$184.59
26	Operating costs	$2,000.00	0.0839	$167.81
27	Operating costs	$2,000.00	0.0763	$152.56
28	Operating costs	$2,000.00	0.0693	$138.69
29	Operating costs	$2,000.00	0.0630	$126.08
30	Operating costs	$2,000.00	0.0573	$114.62
	Net cash outflow			$34,113.33

Net present value is the difference of Sum of Present values of cash inflows and Sum of Present values of cash outflows. If the value is positive then the project may be accepted. While evaluation of two or more alternatives takes place, then the proposal with the higher net present value may be selected since it results in a greater cash inflow over the duration of the project.

In the given scenario, Present values are calculated by calculating the present values of cash outflows such as installation cost and operating cost.

Present value factor is calculated as 1/1.10 ^ N where N is the year of operation of the refrigerator.

Deferment of capital expenditure to Year 10 in case of Option 2 results in a lower overall cash outflow despite increase in the annual operating costs from years 11-30. This is owing to the present value factor.

Conclusion:

Hence the Option to be implemented is Option 2 since it results in lower overall cash outflow.

To determine

(b)

Which of the two alternatives should be selected.

Answer to Problem 31P

The Option to be implemented is Option 1, since it results in a lower cash outflow for a period of 30 years.

Explanation of Solution

Given information:

Option 1:

Install one cable now for 4000 lines. Installation cost $20,000 and annual maintenance costs would be $1,500.

Option 2:

Install one cable for 2000 lines now and one cable for 2000 lines after 5 years. Installation cost $15,000 and annual maintenance costs would be $1,000.

Rate of interest for calculation: 10%.

Based on the above information, the following tables outlines the net present value calculation of the two options.

Option 1:

Year	Particulars	Cash flow	Present value Factor @10%	Present value
0	Installation Cost	$ 20,000.00	1.00	$ 20,000.00
1	Operating costs	$ 1,500.00	0.91	$ 1,363.64
2	Operating costs	$ 1,500.00	0.83	$ 1,239.67
3	Operating costs	$ 1,500.00	0.75	$ 1,126.97
4	Operating costs	$ 1,500.00	0.68	$ 1,024.52
5	Operating costs	$ 1,500.00	0.62	$ 931.38
5	Operating costs	$ 1,500.00	0.62	$ 931.38
6	Operating costs	$ 1,500.00	0.56	$ 846.71
7	Operating costs	$ 1,500.00	0.51	$ 769.74
8	Operating costs	$ 1,500.00	0.47	$ 699.76
9	Operating costs	$ 1,500.00	0.42	$ 636.15
10	Operating costs	$ 1,500.00	0.39	$ 578.31
11	Operating costs	$ 1,500.00	0.35	$ 525.74
12	Operating costs	$ 1,500.00	0.32	$ 477.95
13	Operating costs	$ 1,500.00	0.29	$ 434.50
14	Operating costs	$ 1,500.00	0.26	$ 395.00
15	Operating costs	$ 1,500.00	0.24	$ 359.09
16	Operating costs	$ 1,500.00	0.22	$ 326.44
17	Operating costs	$ 1,500.00	0.20	$ 296.77
18	Operating costs	$ 1,500.00	0.18	$ 269.79
19	Operating costs	$ 1,500.00	0.16	$ 245.26
20	Operating costs	$ 1,500.00	0.15	$ 222.97
21	Operating costs	$ 1,500.00	0.14	$ 202.70
22	Operating costs	$ 1,500.00	0.12	$ 184.27
23	Operating costs	$ 1,500.00	0.11	$ 167.52
24	Operating costs	$ 1,500.00	0.10	$ 152.29
25	Operating costs	$ 1,500.00	0.09	$ 138.44
26	Operating costs	$ 1,500.00	0.08	$ 125.86
27	Operating costs	$ 1,500.00	0.08	$ 114.42
28	Operating costs	$ 1,500.00	0.07	$ 104.02
29	Operating costs	$ 1,500.00	0.06	$ 94.56
30	Operating costs	$ 1,500.00	0.06	$ 85.96
	Net cash outflow			35,071.75

Option 2:

Year	Particulars	Cash flow	Present value Factor @10%	Present value
0	Installation Cost	$ 15,000.00	1.00	$ 15,000.00
1	Operating costs	$ 1,000.00	0.91	$ 909.09
2	Operating costs	$ 1,000.00	0.83	$ 826.45
3	Operating costs	$ 1,000.00	0.75	$ 751.31
4	Operating costs	$ 1,000.00	0.68	$ 683.01
5	Operating costs	$ 1,000.00	0.62	$ 620.92
5	Operating costs	$ 1,000.00	0.62	$ 620.92
5	Installation Cost	$ 15,000.00	0.62	$ 9,313.82
6	Operating costs	$ 2,000.00	0.56	$ 1,128.95
7	Operating costs	$ 2,000.00	0.51	$ 1,026.32
8	Operating costs	$ 2,000.00	0.47	$ 933.01
9	Operating costs	$ 2,000.00	0.42	$ 848.20
10	Operating costs	$ 2,000.00	0.39	$ 771.09
11	Operating costs	$ 2,000.00	0.35	$ 700.99
12	Operating costs	$ 2,000.00	0.32	$ 637.26
13	Operating costs	$ 2,000.00	0.29	$ 579.33
14	Operating costs	$ 2,000.00	0.26	$ 526.66
15	Operating costs	$ 2,000.00	0.24	$ 478.78
16	Operating costs	$ 2,000.00	0.22	$ 435.26
17	Operating costs	$ 2,000.00	0.20	$ 395.69
18	Operating costs	$ 2,000.00	0.18	$ 359.72
19	Operating costs	$ 2,000.00	0.16	$ 327.02
20	Operating costs	$ 2,000.00	0.15	$ 297.29
21	Operating costs	$ 2,000.00	0.14	$ 270.26
22	Operating costs	$ 2,000.00	0.12	$ 245.69
23	Operating costs	$ 2,000.00	0.11	$ 223.36
24	Operating costs	$ 2,000.00	0.10	$ 203.05
25	Operating costs	$ 2,000.00	0.09	$ 184.59
26	Operating costs	$ 2,000.00	0.08	$ 167.81
27	Operating costs	$ 2,000.00	0.08	$ 152.56
28	Operating costs	$ 2,000.00	0.07	$ 138.69
29	Operating costs	$ 2,000.00	0.06	$ 126.08
30	Operating costs	$ 2,000.00	0.06	$ 114.62
	Net cash outflow			39,997.78

Net present value is the difference of Sum of Present values of cash inflows and Sum of Present values of cash outflows. If the value is positive then the project may be accepted. While evaluation of two or more alternatives takes place, then the proposal with the higher net present value may be selected since it results in a greater cash inflow over the duration of the project.

In the given scenario, Present values are calculated by calculating the present values of cash outflows such as installation cost and operating cost.

Present value factor is calculated as 1/1.10 ^ N where N is the year of operation of the refrigerator.

Deferment of capital expenditure to Year 5 in case of Option 2 results in a higher overall cash outflow due to increase in the annual operating costs from years 6-30. This is owing to the present value factor.

Conclusion:

Hence the Option to be implemented is Option 1 since it results in lower overall cash outflow.