Question

Need cash flow diagram

04) Three mutually exclusive alternative are being considered Initial Cost Benefit at the end of the first Year Uniform Annual Benefits at end of subsequent years Useful Life in years $500 $200 $100 $400 $200 $125 $300 $200 $100 At the end of its useful life, an alternative is not replaced. If MARR is 10%, which alternatives should be selected? a) Based on the payback period? b) Based on benefit-cost ratio analysis c) Benefit/Costs Analysis using incremental Analysis.

Answer 1

The payback period is time required to recover the initial investment in a project.
Time taken for A for net cash flows to equal 500 = 200*1 + 100*3, therefore payback period is 4years
Time taken for B for net cash flows to equal 400 = 200*1 + 125*1 + 125 *3/5, therefore payback period is 2(3/5)years
Time taken for C for net cash flows to equal 300 = 200*1 + 100*1, therefore payback period is 2years
Based on payback period, project C will be chosen as it has the lowest payback.

To calculate benefit cost ratio, the net present value of costs and benefits is calculated and then the ratio is computed

	A	B	C
Initial cost	-500	-400	-300
1st year benefit	200	200	200
Subsequent annual benefit	100	125	100
Life	8	8	8
Discounted Benefits in first year	200+PV(0.1,7,100)	200+PV(0.1,7,125)	200+PV(0.1,7,100)
	$686.84	$808.55	$686.84
PV of benefits	Benefits in first year/(1.1)
	$624.40	$735.05	$624.40
B/C	1.25	1.84	2.08

We choose the project with highest B/C, hence project C is chosen

For incremental benefit cost analysis, we start with the base project with the least cost, in this case project C, we compute the present value of additional benefits and costs of moving to any other project. In this case, only project B has some additional cash flows!

Incremental cash flow	25
Benefits in first year	$121.71
PV Benefits	$110.65
Can also be computed by 735.05-624.40
Incremental cost	100
Incremental B/C	1.11

Since the ratio is more than 1, we choose project B. There are no incremental cash-flows while moving from B to A, hence B is chosen!

Cash flow diagrams

200 100 100 100 100 100 100 100 -500 0 1 23 4 56 7 8

200 125 125 125 125 125 125 125 400 0 1 23 4 56 7 8

200 100 100 100 100 100 100 100 300 0 1 23 4 56 7 8