Question

Hi,

Can you please solve this correctly?

With interest at 10%, what is the benefit-cost ratio for this government project?

Initial Cost	$205454
Additional costs at the end of year 1 and year 2	$34758/year
Benefits at end of year 1 and year 2	$0/year
Annual benefits at end of year 3 through year 10	$103447/year

Enter your answer as follow: 12.34

Answer 1

Benefit cost ratio = sum of the present value of the benefits associated with a project / sum of the present value of the costs associated with a project.
Calculation of sum of the present value of the benefits associated with a project								Calculation of sum of the present value of the benefits associated with a project
Year	Benefits	Discount factor @ 10%	Present Value					Year	Costs	Discount factor @ 10%	Present Value
0	$0.00	1	$0.00					0	$205,454.00	1	$205,454.00
1	$0.00	0.909091	$0.00					1	$34,758.00	0.909091	$31,598.18
2	$0.00	0.826446	$0.00					2	$34,758.00	0.826446	$28,725.62
3	$103,447.00	0.751315	$77,721.26					3	$0.00	0.751315	$0.00
4	$103,447.00	0.683013	$70,655.69					4	$0.00	0.683013	$0.00
5	$103,447.00	0.620921	$64,232.45					5	$0.00	0.620921	$0.00
6	$103,447.00	0.564474	$58,393.13					6	$0.00	0.564474	$0.00
7	$103,447.00	0.513158	$53,084.67					7	$0.00	0.513158	$0.00
8	$103,447.00	0.466507	$48,258.79					8	$0.00	0.466507	$0.00
9	$103,447.00	0.424098	$43,871.63					9	$0.00	0.424098	$0.00
10	$103,447.00	0.385543	$39,883.30					10	$0.00	0.385543	$0.00
Sum of the present value of the benefits associated with a project			$456,100.92					Sum of the present value of the costs associated with a project			$265,777.80
Benefit cost ratio = $4,56,100.92 / $2,65,777.80 = 1.72