Question

Question 3 (1 point) Tucson wants to build a new bypass between two major roads that will cut travel time for commuters. The road will cost $14,000,000 and save 17,500 people $100/year on gas. The road will need to be resurfaced every year at a cost of $7500 The road is expected to be used for 20 years. If the cost of money is 8% was is the BCR? 0.95 1.01 1.22 0.73

Answer 1

BCR = PV of Benifits / PV of Cost

PV of Benifits:

Year	CF	PVF @8%	Disc CF
1	$ 17,50,000.00	0.9259	$     16,20,370.37
2	$ 17,50,000.00	0.8573	$     15,00,342.94
3	$ 17,50,000.00	0.7938	$     13,89,206.42
4	$ 17,50,000.00	0.7350	$     12,86,302.24
5	$ 17,50,000.00	0.6806	$     11,91,020.59
6	$ 17,50,000.00	0.6302	$     11,02,796.85
7	$ 17,50,000.00	0.5835	$     10,21,108.19
8	$ 17,50,000.00	0.5403	$       9,45,470.55
9	$ 17,50,000.00	0.5002	$       8,75,435.69
10	$ 17,50,000.00	0.4632	$       8,10,588.60
11	$ 17,50,000.00	0.4289	$       7,50,545.00
12	$ 17,50,000.00	0.3971	$       6,94,949.08
13	$ 17,50,000.00	0.3677	$       6,43,471.37
14	$ 17,50,000.00	0.3405	$       5,95,806.82
15	$ 17,50,000.00	0.3152	$       5,51,672.98
16	$ 17,50,000.00	0.2919	$       5,10,808.32
17	$ 17,50,000.00	0.2703	$       4,72,970.67
18	$ 17,50,000.00	0.2502	$       4,37,935.80
19	$ 17,50,000.00	0.2317	$       4,05,496.11
20	$ 17,50,000.00	0.2145	$       3,75,459.36
PV of Benefit			$ 1,71,81,757.96

PV of Cost = Initial Cost + PV Resurface Cost

PV of Resurface COst :

Year	CF	PVF @8%	Disc CF
1	$         7,500.00	0.9259	$             6,944.44
2	$         7,500.00	0.8573	$             6,430.04
3	$         7,500.00	0.7938	$             5,953.74
4	$         7,500.00	0.7350	$             5,512.72
5	$         7,500.00	0.6806	$             5,104.37
6	$         7,500.00	0.6302	$             4,726.27
7	$         7,500.00	0.5835	$             4,376.18
8	$         7,500.00	0.5403	$             4,052.02
9	$         7,500.00	0.5002	$             3,751.87
10	$         7,500.00	0.4632	$             3,473.95
11	$         7,500.00	0.4289	$             3,216.62
12	$         7,500.00	0.3971	$             2,978.35
13	$         7,500.00	0.3677	$             2,757.73
14	$         7,500.00	0.3405	$             2,553.46
15	$         7,500.00	0.3152	$             2,364.31
16	$         7,500.00	0.2919	$             2,189.18
17	$         7,500.00	0.2703	$             2,027.02
18	$         7,500.00	0.2502	$             1,876.87
19	$         7,500.00	0.2317	$             1,737.84
20	$         7,500.00	0.2145	$             1,609.11
PV of Benefit			$          73,636.11

PV of Cost = Initial Cost + PV Resurface Cost

= $ 14,000,000 + $ 73,636.11

= $ 14,073,636.11

BCR = PV of Benifits / PV of Cost

= $ 1,71,81,757.96 / $ 14,073,636.11

= 1.22

Option C is correct