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 |
4. Project 1 costs A initially, costs B every year, generates C benefits every year and...
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