Question

Vandelay Industries is considering the purchase of a new machine for the production of latex. Machine A costs $3,250,000 and will last for six years. Variable costs are 35 percent of sales, and fixed costs are $390,000 per year. Machine B costs $5,507,000 and will last for nine years. Variable costs for this machine are 30 percent of sales and fixed costs are $260,000 per year. The sales for each machine will be $12.8 million per year. The required return is 10 percent, and the tax rate is 23 percent. Both machines will be depreciated on a straight-line basis. The company plans to replace the machine when it wears out on a perpetual basis.

 

Calculate the EAC for each machine. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers in dollars, not millions of dollars, rounded to 2 decimal places, e.g., 1,234,567.89.)

System A=

System B=

Answer 1

The cost of machine A is $3,250,000, it will last for 6 years. The sales are $12.8 million per year, the variable cost is 35% of sales and the fixed costs are $390,000 per year for 6 years. The cost of machine B is $5,507,000, it will last for 9 years. The sales are $12.8 million per year, the variable cost is 30% of sales and the fixed costs are $260.000 per year for 9 years. The required rate of return is 10% and the tax rate is 23%. The depreciation is on straight line basis. Calculate the equalized annual cost (EAC) of machine A. Particulars Cost of machine Investment Operating costs -$3,250,000.00 Variable cost Fixed cost Depreciation Profit before tax Tax at 23% Net income Add: Depreciation Total cash flows -$4.480.000.00 (12.800.000×35%) -$390,000.00 -$541,666.67 (3,250,000/6) -$5,411,666.67 (-4,480,000+-390,000+-541,666.67) $1.244.683.33 (-5,411,666.67x23%) -$4,166,983.33 (-5,411,666.67+1.244.683.33) $541,666.67 -$3,250,000.00 -$3.625,316.66 (-4,166,983.33+5,411,666.67) - Period rate NPV = -Initial cost + Annual operating costx : 1-(1+rate) 1-1.10-6 = -$3,250,000+-$3,625, 316.66 x 0.10 = -$3,250,000 - $3,625, 316.66 x 4.355261 = -$3,250,000 - $15, 789,200.26 = -$19,039,200.26 NPV EAC = 1-(1+rate) -Period rate -$19,039,200.26 4.355261 =-$4,371 540.59 Thus, the EAC of machine A is -$4,371,540.59.

Calcualte the EAC of machine B. Particulars Cost of machine Investment Operating costs -$5.507,000.00 Variable cost Fixed cost Depreciation Profit before tax Tax at 23% Net income Add: Depreciation -$3,840,000.00 (12,800,000x30%) -$260,000.00 -$611.888.89 (5.507,000/9) -$4,711,888.89 (-3.840,000-260,000-611,888.89) $1,083,734.44 (4,711.888.89x23%) -$3,628,154.44 (-4,711.888.89+1,083,734.44) $611.888.89 Total cash flows -$5,507,000.00 -$3,016,265.55 (-3,628,154.44+611.888.89) - Period 1-(1+rate) NPV = -Initial cost + Annual operating costx. rate 1-1.10-9 = -$5,507,000+-$3,016, 265.55x 0.10 = -$5,507,000 - $3,016, 265.55 x 5.759024 = -$5,507,000 - $17,370, 745.69 = -$22,877,745.69 NPV EAC = - Period 1-(1+rate) rate -$22,877, 745.69 5.759024 = -$3,972,503.97 Thus, the EAC of machine B is -$3,972,503.97.