Question

4. Project 1 costs A initially, costs B every year, generates C benefits every year and D disbenefits every year with a life of 5 years. Project 2 costs E initially, cost Fevery year, generates G benefits every year and H disbenefits every year with a life of 6 years. Project 3 costs I initially, costs) every year, generates K benefits every year and L disbenefits every year with a life of 10 years. Use an annual rate of R to conduct incremental B/C ratio analyses to select one of the alternatives. "Do Nothing" is not an option. Must show your procedures.TR = 12.00% A = 128 B = 60 C = 60 D= 10 160 E = F- 62 G= 69 15 H= 340 50 K = 83 L = Final Selection Have to Use Conventional B/C Ratio Analysis

Answer 1

We will first create a table of all the costs and benefits. next, we will calculate the present worth of all the cash flows by the discount factor of 12%.
However, projects have unequal lives so we will have to calculate the equivalent annual value by using the PV annuity factor for respective project life.
The benefit to cost ratio should be more than 1 to be accepted.
However, all three projects have a BC ratio of less than 1 so actually all should be rejected.
If that is not possible then the project with the highest BC ratio should be selected.
Project 3 should be selected in this case.

Project 1
PV of annual cost
=PV(12%,5,-60)
=216.29

BC Ratio = Total Benefits / Total Costs

	Option 1	PW @ 12%	Option 2	PW @ 12%	Option 3	PW @ 12%
Initial Cost	128	128	160	160	340	340
Annual Cost	60	216.29	62.00	254.91	50	282.51
Disbenefits	10	36.05	15.00	61.67	20	113.00
Benefits	60	216.29	69.00	283.69	83	468.97
Life	5		6		10
Interest Rate	0.12		0.12		0.12
Total Benefits		216.29		283.69		468.97
Total Cost		380.3343		476.5784		735.5156
PV Annuity Factor		3.6048		4.1114		5.6502
Equivalent Annual	Benefits	60		69		83
Equivalent Annual	Costs	105.5084		115.9161		130.1746
Benefits to Cost Ratio		0.5687		0.5953		0.6376