Question

Spike Inc is considering the purchase of a new machine for the production of computers.  Machine A costs $3,400,000 and will last for 6 years. Variable costs are 20% of sales and fixed costs are $850,000 per year. Machine B costs $5,600,000 and will last for 10 years. Variable costs for the machine are 15% of sales and fixed costs are $1,000,000 per year. The sales for each machine will be $5,000,000 per year. The required rate of return is 8%, the tax rate is 21%, and both machines will be depreciated using straight-line with a no salvage value.

a.) What is the NPV for Machine A?

b.) What is the equivalent annual annuity for Machine B?

c.) Based on the information provided, should the firm:

- purchase machine A because it has a higher equivalent annual annuity

- purchase machine A because it has a higher NPV

- purchase machine B because it has a higher equivalent annual anniuity

- purchase machine B because it has a higher NPV

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

DE Required rate of Return Machine A $3,400,000.00 Machine B $5,600,000.00 Investment Cost Life (years) Sales Variable cost Fixed Cost Depreciation | ЕВТ Tax (21%) Net Income Annual after tax Cash Flow NPV Equivalent Annual Annuity $5,000,000.00 $1,000,000.00 $850,000.00 $566,666.67 $2,583,333.33 $542,500.00 $2,040,833.33 $2,607,500.00 $8,654,158.72 $1,872,027.69 $5,000,000.00 $750,000.00 $1,000,000.00 $560,000.00 $2,690,000.00 $564,900.00 $2,125,100.00 $2,685,100.00 $12,417,239.56 $1,850,534.86 13 14 a) 15 b) 16 17 c) purchase machine A because it has a higher equivalent annual annuity 18 19

Cell reference -

A C D B Required rate of Return 0.08 Machine A Investment Cost 3400000 Life (years) Sales 5000000 Variable cost =C6*0.2 Fixed Cost 850000 Depreciation =C4/C5 EBT =C6-C7-C8-C9 Tax (21%) =C10*0.21 Net Income =C10-C11 Annual after tax Cash Flow =C12+C9 NPV =PV(C1,C5,-C13,,0)-C4 Equivalent Annual Annuity =C14/PV(C1,C5,-1,0) Machine B 5600000 10 5000000 =D6*0.15 1000000 =D4/D5 =D6-D7-D8-D9 =D10*0.21 =D10-D11 =D12+D9 =PV(C1,D5,-D13,,0)-D4 =D14/PV(C1,D5,-1,,0) 12 13 14 a) 15 b) 16 17 c) purchase machine A because it has a higher equivalent annual annuity 18 19

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.