Question

- + Fit to page ID Pageview | A Read aloud Question 4 (25 points) A canning plant is considering purchasing a new tomato-peeling machine. Each choice has a 6- year useful life. с First cost Annual benefit Annual O&M cost $52,000 38,000 1 5,000 $63,000 31,000 9,000 $67,000 37,000 12,000 The MARR is 12%. For parts a)-c), which alternative should be selected? a) Solve the problem by payback period. b) Solve the problem by future worth analysis. c) Solve the problem by benefit-cost ratio analysis. d) What would the first cost for alternative B need to be in order for alternative A and alternative B to be equally desirable? --

please answer all the parts and show the formulas where possible.

Answer 1

Cumulative Cashflow Answer a - Payback Period Machine A Year Benefit | Cost Net Cashflow PVF @ 12% Discounted Cash Flow 1 2 3 4= 2-3 6 = 4*5 1 $ 38,000 $ 15,000 $ 23,000 0.893 $ 20,536 2 $ 38,000 $ 15,000$ 23,000 0.797 $ 18,335 3 $ 38,000$ 15,000$ 23,000 0.712 $ 16,371 4 $ 38,000 $ 15,000 $ 23,000 0.636 $ 14,617 5 $ 38,000 $ 15,000 $ 23,000 0.567 $ 13,051 6 $ 38,000$ 15,000 $ 23,000 0.507 $ 11,653 $ $ $ $ $ $ 20,536 38,871 55,242 69,859 82,910 94,562 Discounted Payback Period = 2 Years 9 Month Note 1 Monthly Collection in Year 3 $ 2 Amont to be recovered in Year 3 $ 3 Time Taken to recover (in months) (2/3) | 1,364 $16,371/12) 13,129 $52,000 - $38,871) 9.62

Machine B Year Benefit 1 2 L 11 $ 31,000$ 2 $ 31,000$ 3 $ 31,000$ 4 $ 31,000$ 5 $ 31,000$ 6 $ 31,000$ Cost Net Cashflow PVF @ 12% Discounted Cash Flow Cumulative Cashflow 3 4= 2-3 6 = 4*5 9,000 $ 22,000 0.893 $ 19,643 $ 19,643 9,000$ 22,000 0.797 $ 17,538 $ 37,181 9,000$ 22,000 0.712 $ 15,659 $ 52,840 9,000$ 22,000 0.636 $ 13,981 $ 66,822 9,000 $ 22,000 0.567 $ 12,483 $ 79,305 9,000 $ 22,000 0.507) s 11,146 $ 90,451 Discounted Payback Period = 3 Years 9 Month Note 1 Monthly Collection in Year 4 2 Amount to be recovered in Year 4 3 Time Taken to recover (in months) (2/3) $ $ 1,165 $13,981/12) 10,160 $63,000 - $52,840) 8.72

Machine C Year Benefit 1 2 1 $ 37,000 $ 2 $ 37,000$ 3 $ 37,000$ 4 $ 37,000$ 5 $ 37,000 $ 6 $ 37,000 $ Cost Net Cashflow PVF @ 12% | Discounted Cash Flow Cumulative Cashflow 3 4= 2-3 6 = 4*5 12,000$ 25,000 0.893 $ 22,321 $ 22,321 12,000S 25,000 0.797 $ 19,930 $ 42,251 12,000$ 25,000 0.712 $ 17,795 $ 60,046 12,000$ 25,000 0.636 $ 15,888 $ 75,934 12,000$ 25,000 0.567 $ 14,186 $ 90,119 12,000$ 25,000 0.507 $ 12,666 $ 102,785 Discounted Payback Period = 3 Years 5 Month Note 1 Monthly Collection in Year 4 2 Amount to be recovered in Year 4 3 Time Taken to recover (in months) (2/3) 1,324 $13,981/12) 6,954 $67,000 - $60046) 5.25

Answer b - Based on Future Worth Analysis Machine A Year Benefit Cost Deprecition Net Benefit PVF @ 12% Discounted Cash Flow 1 2 3 4 5= 2-3-4 7 = 6*5 OD 0 $ 52,000$ - $ 52,000) 1.000 $ (52,000) 1 $ 38,000 $ 15,000 $ 8,667 $ 14,333 0.893 $ 12,797 2 $ 38,000 $ 15,000$ 8,667 $ 14,333 | 0.797 $ 11,426 3 $ 38,000$ 15,000$ 8,667 $ 14,333 0.712 $ 10,202 4 $ 38,000$ 15,000 $ 8,667$ 14,333 0.636 $ 9,109 5 $ 38,000 $ 15,000$ 8,667$ 14,333 0.567 $ 8,133 6 $ 38,000$ 15,000 $ 8,667 $ 14,333 0.507 $ 7,262 NET PRESENT VALUE $ 6,929 Machine B Year Benefit | Cost Deprecition Net Cashflow PVF @ 12% Discounted Cash Flow 1 2 3 4 5= 2-3-4 7 = 6*5 0 $ - $ 63,000 $ - $ 63,000) 1.000 $ (63,000) 1 $ 31,000 $ 9,000 $ 10,500 $ 11,500 0.893 $ 10,268 21 $ 31,000$ 9,000 $ 10,500 $ 11,500 0.797 $ 9,168 3 $ 31,000$ 9,000 $ 10,500$ 11,500 0.712 $ 8,185 4 $ 31,000$ 9,000 $ 10,500 $ 11,500 0.636 $ 7,308 5 $ 31,000$ 9,000$ 10,500 $ 11,500 0.567 $ 6,525 6 $ 31,000$ 9,000$ 10,500 $ 11,500 0.507 $ 5,826 NET PRESENT VALUE $ (15,719)

Machine C Year Benefit 1 2 0 $ - $ 1 $ 37,000 $ 2 $ 37,000$ 3 $ 37,000$ 4 $ 37,000 $ 5 $ 37,000 $ 6 $ 37,000$ Cost Deprecition Net Cashflow PVF @ 12% Discounted Cash Flow L 4 5= 2-3-4 7 = 6*5 67,000 S - $ 67,000) 1.000 $ 67,000) 12,000$ 11,167$ 13,833 0.893 $ 12,351 12,000 $ 11,167 $ 13,833 0.797 $ 11,028 12,000$ 11,167 $ 13,833 0.712 $ 9,846 12,000$ 11,167$ 13,833 0.636 $ 8,791 12,000$ 11,167 $ 13,833 0.567 $ 7,849 12,000$ 11,167 $ 13,833 0.507 $ 7,008 NET PRESENT VALUE $ (10,127)

Benefit Cost Ratio 4 = 2/3 Answer C - Benefit Cost Ratio Machine Annual Benefit 2 Machine A $ 38,000 $ Machine B 31,000 $ Machine C 37,000 $ Annual Cost 3 23,667 19,500 23,167

Note: The Annual Cost above includes Annual O&M Cost and depreciation cost

Summary

Answer a - based on payback period, Machine A should be selected since it has the least payback period

Answer b - based on Net Present Value(NPV), Machine A should be selected since it has a positive NPV

Answer c - based on Benefit Cost Ratio, Machine A should be selected since its ratio is the highest

Answer D For Machine A & B to be eucally desirable, we should calculate the first cost of Machine B based on the BC Ratio of Machine A Let Annual Depreciation be "X" 1.61 10,500 Basic Data BC Ratio of Machine A Annual OM Cost Annual Depreciation Annual Benefit Required BC Ratio of Machine B 31,000 1.61) Benefit Cost Ratio 1.61 = 31000 10500+X 1.61X + 16905 = 31000 1.61 X = 31000-16905 1.61X = 14095 X = $8,755 Therefore, Annual Depreciation = $8,755 Useful Life = 6 Years Therefore, First Cost = Annual Depreciation Useful Life $8,755546 First Cost $52,530