Chapter 5, Problem 33P

To determine

Which of the two alternatives should be selected.

Answer to Problem 33P

The Option to be implemented is Cantilever bridge, since it results in a lower cash outflow for a period of 50 years.

Explanation of Solution

Given information: (all costs in $Million)

Installation Cost:

Suspension Bridge $585

Cantilever Bridge $470

Land acquisition Cost:

Suspension Bridge $120

Cantilever Bridge $95

Annual Operation and Maintenance costs:

Suspension Bridge $2

Cantilever Bridge $3

Annual Increase in Operation and Maintenance costs:

Suspension Bridge 4%

Cantilever Bridge 3%

Salvage Value in year 50:

Suspension Bridge $30

Cantilever Bridge $27

Rate of Interest for calculation: 8%.

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

Suspension Bridge:

Year	Particulars (Figures in Million)	Cash flow	Present value Factor @8%	Present value
0	Installation Cost	$585.00	1.0000	$585.00
0	Land Cost	$120.00	1.0000	$120.00
1	Operating Costs	$2.00	0.9259	$1.85
2	Operating Costs	$2.08	0.8573	$1.78
3	Operating Costs	$2.16	0.7938	$1.71
4	Operating Costs	$2.25	0.7350	$1.65
5	Operating Costs	$2.34	0.6806	$1.59
6	Operating Costs	$2.43	0.6302	$1.53
7	Operating Costs	$2.53	0.5835	$1.48
8	Operating Costs	$2.63	0.5403	$1.42
9	Operating Costs	$2.74	0.5002	$1.37
10	Operating Costs	$2.85	0.4632	$1.32
11	Operating Costs	$2.96	0.4289	$1.27
12	Operating Costs	$3.08	0.3971	$1.22
13	Operating Costs	$3.20	0.3677	$1.18
14	Operating Costs	$3.33	0.3405	$1.13
15	Operating Costs	$3.46	0.3152	$1.09
16	Operating Costs	$3.60	0.2919	$1.05
17	Operating Costs	$3.75	0.2703	$1.01
18	Operating Costs	$3.90	0.2502	$0.98
19	Operating Costs	$4.05	0.2317	$0.94
20	Operating Costs	$4.21	0.2145	$0.90
21	Operating Costs	$4.38	0.1987	$0.87
22	Operating Costs	$4.56	0.1839	$0.84
23	Operating Costs	$4.74	0.1703	$0.81
24	Operating Costs	$4.93	0.1577	$0.78
25	Operating Costs	$5.13	0.1460	$0.75
25	Maintenance Cost	$185.00	0.1460	$27.01
26	Operating costs	$5.33	0.1352	$0.72
27	Operating costs	$5.54	0.1252	$0.69
28	Operating costs	$5.77	0.1159	$0.67
29	Operating costs	$6.00	0.1073	$0.64
30	Operating costs	$6.24	0.0994	$0.62
31	Operating costs	$6.49	0.0920	$0.60
32	Operating costs	$6.75	0.0852	$0.58
33	Operating costs	$7.02	0.0789	$0.55
34	Operating costs	$7.30	0.0730	$0.53
35	Operating costs	$7.59	0.0676	$0.51
36	Operating costs	$7.89	0.0626	$0.49
37	Operating costs	$8.21	0.0580	$0.48
38	Operating costs	$8.54	0.0537	$0.46
39	Operating costs	$8.88	0.0497	$0.44
40	Operating costs	$9.23	0.0460	$0.42
41	Operating costs	$9.60	0.0426	$0.41
42	Operating costs	$9.99	0.0395	$0.39
43	Operating costs	$10.39	0.0365	$0.38
44	Operating costs	$10.80	0.0338	$0.37
45	Operating costs	$11.23	0.0313	$0.35
46	Operating costs	$11.68	0.0290	$0.34
47	Operating costs	$12.15	0.0269	$0.33
48	Operating costs	$12.64	0.0249	$0.31
49	Operating costs	$13.14	0.0230	$0.30
50	Operating costs	$13.67	0.0213	$0.29
50	Salvage Value	($30.00)	0.0213	($0.64)
	Net cash outflow			$773.80

Cantilever Bridge:

Year	Particulars (Figures in Million)	Cash flow	Present value Factor @8%	Present value
0	Installation Cost	$470.00	1.0000	$470.00
0	Land Cost	$95.00	1.0000	$95.00
1	Operating Costs	$3.00	0.9259	$2.78
2	Operating Costs	$3.09	0.8573	$2.65
3	Operating Costs	$3.18	0.7938	$2.52
4	Operating Costs	$3.28	0.7350	$2.41
5	Operating Costs	$3.38	0.6806	$2.30
6	Operating Costs	$3.48	0.6302	$2.19
7	Operating Costs	$3.58	0.5835	$2.09
8	Operating Costs	$3.69	0.5403	$1.99
9	Operating Costs	$3.80	0.5002	$1.90
10	Operating Costs	$3.91	0.4632	$1.81
11	Operating Costs	$4.03	0.4289	$1.73
12	Operating Costs	$4.15	0.3971	$1.65
13	Operating Costs	$4.28	0.3677	$1.57
14	Operating Costs	$4.41	0.3405	$1.50
15	Operating Costs	$4.54	0.3152	$1.43
16	Operating Costs	$4.67	0.2919	$1.36
17	Operating Costs	$4.81	0.2703	$1.30
18	Operating Costs	$4.96	0.2502	$1.24
19	Operating Costs	$5.11	0.2317	$1.18
20	Operating Costs	$5.26	0.2145	$1.13
21	Operating Costs	$5.42	0.1987	$1.08
22	Operating Costs	$5.58	0.1839	$1.03
23	Operating Costs	$5.75	0.1703	$0.98
24	Operating Costs	$5.92	0.1577	$0.93
25	Operating Costs	$6.10	0.1460	$0.89
25	Maintenance Cost	$210.00	0.1460	$30.66
26	Operating costs	$6.28	0.1352	$0.85
27	Operating costs	$6.47	0.1252	$0.81
28	Operating costs	$6.66	0.1159	$0.77
29	Operating costs	$6.86	0.1073	$0.74
30	Operating costs	$7.07	0.0994	$0.70
31	Operating costs	$7.28	0.0920	$0.67
32	Operating costs	$7.50	0.0852	$0.64
33	Operating costs	$7.73	0.0789	$0.61
34	Operating costs	$7.96	0.0730	$0.58
35	Operating costs	$8.20	0.0676	$0.55
36	Operating costs	$8.44	0.0626	$0.53
37	Operating costs	$8.69	0.0580	$0.50
38	Operating costs	$8.96	0.0537	$0.48
39	Operating costs	$9.22	0.0497	$0.46
40	Operating costs	$9.50	0.0460	$0.44
41	Operating costs	$9.79	0.0426	$0.42
42	Operating costs	$10.08	0.0395	$0.40
43	Operating costs	$10.38	0.0365	$0.38
44	Operating costs	$10.69	0.0338	$0.36
45	Operating costs	$11.01	0.0313	$0.34
46	Operating costs	$11.34	0.0290	$0.33
47	Operating costs	$11.69	0.0269	$0.31
48	Operating costs	$12.04	0.0249	$0.30
49	Operating costs	$12.40	0.0230	$0.29
50	Operating costs	$12.77	0.0213	$0.27
50	Salvage Value	($27.00)	0.0213	($0.58)
	Net cash outflow			$649.48

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 inflows in the form of salvage value and cash outflows such as installation cost and operating cost.

In case of the suspension bridge, Installation Cost is $575 Million, Land Cost is $120 Million and Annual Operating costs are $2 Million with an increase of 4% each year. There is a maintenance cost of $180 Million in Year 25.Salvage value in year 50 is $30 Million.

In case of the cantilever bridge, Installation Cost is $470 Million, Land Cost is $95 Million and Annual Operating costs are $3 Million with an increase of 3% each year. There is a maintenance cost of $210 Million in Year 25. Salvage value in year 50 is $27 Million.

Present value factor is calculated as 1/1.08 ^ N where N is the year of operation of the bridge.

Conclusion:

Hence the bridge to be constructed is the Cantilever bridge, since it results in lower overall cash outflow over the period of 50 years.