# Benefit cost ratio for each alternative

Problem 16

A company is considering two alternative methods of producing a new product. The relevant data concerning the alternatives are presented below:

Alternative Alternative

I II

Initial investment $64,000 $120,000

Annual receipts $50,000 $60,000

Annual disbursements $20,000 $12,000

Annual depreciation $16,000 $20,000

Expected life 4 yrs 6 yrs

Salvage value 0 0

At the end of the useful life of whatever equipment is chosen the product will be discontinued. The company's tax rate is 50 percent and its cost of capital is 10 percent.

a. Calculate the net present value of each alternative.

b. Calculate the benefit cost ratio for each alternative.

c. Calculate the internal rate of return for each alternative.

d. If the company is not under capital rationing which alternative should be chosen? Why?

e. Again assuming no capital rationing, suppose the company plans to produce the product indefinitely rather than quit when the equipment wears out. Which alternative should the company select? Why?

f. If the company is experiencing severe capital rationing, and plans to terminate production when the equipment wears out, would any of your answers above change?

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#### Solution Preview

See attached file.

Note on Capital Budgeting

Capital budgeting involves making decisions about long term mix of the composition of assets of the business. As per Zen Wealth, "Capital Budgeting is the process by which the firm decides which long-term investments to make. Capital Budgeting projects, i.e., potential long-term investments, are expected to generate cash flows over several years. The decision to accept or ...

#### Solution Summary

Solution explains benefit cost ratio for each alternative

Benefit Cost Ratio Analysis

Solutions are provided for questions given below.

See the attached file.

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.