# Benefit Cost Ratio Analysis

Solutions are provided for questions given below.

Using benefit-cost ratio analysis, determine which one of the three mutually exclusive alternatives should be selected. Each alternative has a 6-year useful life. Assume a 10% MARR.

A B C

First Cost $560 $340 $120

Uniform annual benefit 140 100 40

Salvage value 40 0 0

1. The benefit cost ratio for alternative A can be calculated with which equation?

B/C = [ 140 (P/A,i,6) + 40 (P/F,I,6) ]/ [ 560 ]

B/C = [ 140 (P/A,i,6) ]/ [ 560 + 40(P/F,i,6)]

B/C = [ 140 (P/A,i,6) - 40 ]/ [ 560 ]

B/C = [ 140 (P/A,i,6) ] / [ 560 - 40(P/F,i,6)]

2. The benefit cost ratio for alternative C is most nearly

1.18

1.29

1.45

1.51

3. The incremental benefit cost ratio for (B-C) is most nearly

-0.17

0.44

0.86

1.19

4. The incremental benefit cost ratio for (A-B) is most nearly

-0.15

0.18

0.88

1.57

5. Which alternative is preferred?

A

B

C

6. F is proportional to x. The equation is F = ax. The numerical value of a is most nearly

Time 0------1------2------3-----4

Cash Flow 4x 3x 2x x

11

12

13

15

If the MARR is 12%, compute the value of X that makes the two alternatives equally desirable.

A B

Cost $150 X

Uniform annual benefit 40 65

Salvage value 100 200

Useful life in years 6 6

7. The value of X is most nearly

140

260

290

300

Fence posts for a particular job cost $10.50 each to install, including the labor cost. They will last 10 years. If the posts are treated with a wood preservative, they can be expected to have a 15-year life. Assuming a 10% interest rate, how much could one afford to pay for wood preservative treatment.

8. This problem can be approached by determining EUAC. At the breakeven point, which defines the value of the maximum treatment cost, EUACtreated = EUACuntreated.

1.60

2.50

2.70

2.90

Consider three alternatives :

A B C

First Cost $50 $150 $110

Uniform annual benefit 28.8 39.6 39.6

Useful life in years* 2 6 4

Rate of return 10% 15% 16.4%

* At the end of its useful life, an identical alternative (with the same cost, benefits, and useful life) may be installed

9. Using the 12 year analysis period (which is the correct procedure), the Net Future Worths of A,B, and C, respectively are most nearly

-18.9, 75.2, 86.6

20.3, -14.4, 46.1

-22.9, 75.2, 46.1

-18.9, 75.2, 63.3

10. Based on Future Worth Analysis, the recommended alternative is

A

B

C

11. The Payback Period (years) for A is most nearly

0.56

0.72

1.13

1.74

12. The Payback Period (years) for B is most nearly

2.4

2.6

3.1

3.8

13. Based on Payback Period, the preferred alternative is

A

B

C

#### Solution Preview

Please refer attached files for complete solutions.

1. Correct option is A i.e. B/C = [ 140 (P/A,i,6) + 40 (P/F,I,6) ]/ [ 560 ]

2. Please refer attached file for calculations

Correct option is C i.e. 1.45

3. Correct option is D. i.e. 1.19

Please refer attached file for calculations

4. Correct option is C i.e. 0.88

Please refer attached file for calculations

5. Correct option is B.

6. ...

#### Solution Summary

Benefit cost ratio plays an important role in project selection process. Solutions to the given problems provide step by step methodology to calculate B/C ratio, payback period, EUAC and future worth.