Comparing Mutually Exclusive Projects Vandalay Industries is considering the pur

Question

Comparing Mutually Exclusive Projects Vandalay Industries is considering the purchase of a new machine for the production of latex. Machine A costs $3,100,000 and will last for six years. Variable costs are 35 percent of sales, and fixed costs are $204,000 per year. Machine B costs $6,100,000 and will last for nine years. Variable costs for this machine are 30 percent and fixed costs are $165,000 per year . The sales for each machine will be #13.5 million per year. The required return is 10 percent and the tax rate is 35 percent. Both machines will be depreciated on a straight-line basis. If the company plans to replace the machines when it wears out on a perpetual basis, which machine should you choose? Show all steps.

Explanation / Answer

Machine A

Annual depreciation = (cost of asset – salvage value)/ life

                                                = (3,100,000-0) / 6

                                                = 516,666.67

Annual cash flow = (sales – variable cost – fixed cost) x (1-t) + depreciation x t

                                   = ( 13,500,000 – 13,500,000 x 0.35 -204,000) x (1- 0.35) + 516,666.67 x 0.35

                                   = 5,751,983.34

Equivalent Annual Benefit = (Annual cash flow x PVIFA(n,R) - initial investment) / PVIFA(n,R)

                                                    = (5,751,983.34 x PVIFA (6, 10%) – 3,100,000)/PVIFA (6, 10%)

                                                     = (5,751,983.34 x 4.35526 -3,100,000)/ 4.35526

                                                     = 5,040,200.35

MACHINE B

Annual depreciation = (cost of asset – salvage value)/ life

                                                = (6,100,000-0) / 9

                                                = 677,777.78

Annual cash flow = (sales – variable cost – fixed cost) x (1-t) + depreciation x t

                                   = ( 13,500,000 – 13,500,000 x 0.30 -165,000) x (1- 0.35) + 677,777.78 x 0.35

                                   = 6,272,472.22

Equivalent Annual Benefit = (Annual cash flow x PVIFA(n,R) - initial investment) / PVIFA(n,R)

                                                    = (6,272,472.22x PVIFA (9, 10%) – 6,100,000)/PVIFA (9, 10%)

                                                     = (6,272,472.22x 5.759024 -6,100,000)/ 5.759024

                                                     = 5,213,264.97

Since machine B has higher equivalent annual benefit, machine B should be chosen.

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