Question

Problem 1: Four design alternatives were proposed. Each design alternative has unique costs and benefits. Given the information for the four mutually exclusive in the table below, recommend the best alternative using the incremental B/C ratio analysis method knowing that the MARR is 6%. (Use the PW in your calculation)

Alternative 1 2 3 4
Capital investment cost $ 12500 11000 12500 16800
Annual operating and maintenance cost $ 120 480 450 140
Annual utility savings $ 580 700 950 1300
Annual revenue $ 700 550 200 250
Annual other benefit $ 400 750 150 500
Project life in years 40 40 40 40

Answer 1

Given data:

MARR = 6%

Alternative	1	2	3	4
Capital Investment Cost $	12500	11000	12500	16800
Annual O&M cost $	120	480	450	140
Annual utility savings $	580	700	950	1300
Annual revenue $	700	550	200	250
Annual other benefit $	400	750	150	500
Project life in years	40	40	40	40

Required formula to use:

where P = present worth

          A = annual worth

          i= rate of interest

          n = project life in years

FROM THE COMPOUND INTEREST TABLES OR THE SUBSTITUTION OF VALUES.

Equivalent Cost (in PW) of alternative 1:

Equivalent Benefits of alternative 1:

Equivalent cost for alternative 2:

Equivalent Benefits of alternative 2:

Equivalent COST of alternative 3:

Equivalent Benefits of alternative 3:

Equivalent COST of alternative 4:

Equivalent Benefits of alternative 4:

Tabulating the calculated values as follows

Alternatives	Equivalent costs	Equivalent Benefits
1	14305.52	25277.28
2	18222.08	30092
3	19,270.7	19559.8
4	18906.44	30,844.3

Now arrange the alternatives in the increasing order of their equivalent costs

EC1   < EC2 < EC4 < EC3

Select first two alternatives from the order.

Alternatives 1 and 2:

Compare 2 to 1:

Incremental Values:

here ,there are no disbenefits specified and hence directly the benfits/cost ratio is considered.

HERE, incremental benefit to cost ratio is greater than 1.

Hence Eliminate alternative 1 and Select alternative 2.

Now , alternatives 2 and 4 are taken into consideration.

Compare alternative 4 to 2:

HERE, incremental benefit to cost ratio is greater than 1.

Hence Select alternative 4 and eliminate alternative 2.

Now, alternatives 4 and 3 are taken into consideration.

Compare alternative 3 to 4

Here the neagative value indicates that the disbenefits are higher than the actual benefits generated. Hence Eliminate alternative 3 and Select alternative 4

Therefore the alternative to be selected among the alternatives is ALTERNATIVE 4.