Vandelay Industries is considering the purchase of a new machine for the product
ID: 2773466 • Letter: V
Question
Vandelay Industries is considering the purchase of a new machine for the production of latex. Machine A costs $3,084,000 and will last for six years. Variable costs are 40 percent of sales, and fixed costs are $225,000 per year. Machine B costs $5,283,000 and will last for nine years. Variable costs for this machine are 35 percent of sales and fixed costs are $160,000 per year. The sales for each machine will be $10.7 million per year. The required return is 11 percent, and the tax rate is 30 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. (Enter your answer in dollars, not millions of dollars, e.g. 1,234,567. Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
Vandelay Industries is considering the purchase of a new machine for the production of latex. Machine A costs $3,084,000 and will last for six years. Variable costs are 40 percent of sales, and fixed costs are $225,000 per year. Machine B costs $5,283,000 and will last for nine years. Variable costs for this machine are 35 percent of sales and fixed costs are $160,000 per year. The sales for each machine will be $10.7 million per year. The required return is 11 percent, and the tax rate is 30 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.
Explanation / Answer
Vandelay Enterprises Amts in $ Machine A Details Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Investment (3,084,000) Sales Revenue 10,700,000 10,700,000 10,700,000 10,700,000 10,700,000 10,700,000 Variable costs (4,280,000) (4,280,000) (4,280,000) (4,280,000) (4,280,000) (4,280,000) Fixed costs (225,000) (225,000) (225,000) (225,000) (225,000) (225,000) Depreciation (514,000) (514,000) (514,000) (514,000) (514,000) (514,000) Taxable Income 5,681,000 5,681,000 5,681,000 5,681,000 5,681,000 5,681,000 Income Tax@30% 1,704,300 1,704,300 1,704,300 1,704,300 1,704,300 1,704,300 Net Income 3,976,700 3,976,700 3,976,700 3,976,700 3,976,700 3,976,700 Add Back Depreciation 514,000 514,000 514,000 514,000 514,000 514,000 Total cash flow 4,490,700 4,490,700 4,490,700 4,490,700 4,490,700 4,490,700 Discounting factor@ 11% 0.901 0.812 0.731 0.659 0.593 0.535 PV of cash flow 4,045,676 3,644,753 3,283,561 2,958,163 2,665,012 2,400,912 Total PV 18,998,076 NPV 15,914,076 Present value of annuity facor = [1-1/(1+r)^t]/r =[1-1/1.11^6]/0.11 =4.236 EAB(Equivalent annual benefits) =NPV/4.236 = 3,756,864 Total Cash Outflow (4,505,000) (4,505,000) (4,505,000) (4,505,000) (4,505,000) (4,505,000) PV of cash Out flow (4,058,559) (3,656,359) (3,294,017) (2,967,583) (2,673,498) (2,408,557) Total PV of cash outflow (19,058,573) Net PV of Cash Outflow (22,142,573) PV of Annuity factor @11% for 6 yrs 4.236 EAC = NPV of cash outflow/4.236 =-22,142,573/4.236 = (5,227,236) So EAC of Machine A = (5,227,236) Machine B Details Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Investment (5,283,000) Sales Revenue 10,700,000 10,700,000 10,700,000 10,700,000 10,700,000 10,700,000 10,700,000 10,700,000 10,700,000 Variable costs (3,745,000) (3,745,000) (3,745,000) (3,745,000) (3,745,000) (3,745,000) (3,745,000) (3,745,000) (3,745,000) Fixed costs (160,000) (160,000) (160,000) (160,000) (160,000) (160,000) (160,000) (160,000) (160,000) Depreciation (587,000) (587,000) (587,000) (587,000) (587,000) (587,000) (587,000) (587,000) (587,000) Taxable Income 6,208,000 6,208,000 6,208,000 6,208,000 6,208,000 6,208,000 6,208,000 6,208,000 6,208,000 Income Tax@30% 1,862,400 1,862,400 1,862,400 1,862,400 1,862,400 1,862,400 1,862,400 1,862,400 1,862,400 Net Income 4,345,600 4,345,600 4,345,600 4,345,600 4,345,600 4,345,600 4,345,600 4,345,600 4,345,600 Add Back Depreciation 587,000 587,000 587,000 587,000 587,000 587,000 587,000 587,000 587,000 Total cash flow 4,932,600 4,932,600 4,932,600 4,932,600 4,932,600 4,932,600 4,932,600 4,932,600 4,932,600 Discounting factor@ 11% 0.901 0.812 0.731 0.659 0.593 0.535 0.482 0.434 0.391 PV of cash flow 4,443,784 4,003,409 3,606,675 3,249,256 2,927,258 2,637,169 2,375,828 2,140,386 1,928,276 Total PV 27,312,041 NPV 22,029,041 Present value of annuity facor = [1-1/(1+r)^t]/r =[1-1/1.11^9]/0.11 =5.545 EAB(Equivalent annual benefits) =NPV/5.545 = 3,972,775.59 Total Cash Outflow (3,905,000) (3,905,000) (3,905,000) (3,905,000) (3,905,000) (3,905,000) (3,905,000) (3,905,000) (3,905,000) PV of cash Out flow (3,518,018) (3,169,386) (2,855,302) (2,572,344) (2,317,427) (2,087,772) (1,880,876) (1,694,483) (1,526,561) Total PV of cash outflow (21,622,171) Net PV of Cash Outflow (26,905,171) PV of Annuity factor @11% for 9 yrs =5.545 EAC = NPV of cash outflow/5.545 =-22,142,573/5.545 = (4,852,150) So EAC of Machine B = (4,852,150)
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