Vandelay Industries is considering the purchase of a new machine for the product
ID: 2712472 • Letter: V
Question
Vandelay Industries is considering the purchase of a new machine for the production of latex. Machine A costs $3,120,000 and will last for six years. Variable costs are 40 percent of sales, and fixed costs are $260,000 per year. Machine B costs $5,337,000 and will last for nine years. Variable costs for this machine are 35 percent of sales and fixed costs are $195,000 per year. The sales for each machine will be $11.4 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.)
EAC:
Machine A $
Machine B $
Explanation / Answer
Vandelay Enterprises Amts in $ Details Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Investment (second investment after 6 year considering same equivalent cost) (3,102,000) (3,102,000) PV of Investments (6,204,000) Sales Revenue 11,100,000 11,100,000 11,100,000 11,100,000 11,100,000 11,100,000 11,100,000 11,100,000 11,100,000 Variable costs (4,440,000) (4,440,000) (4,440,000) (4,440,000) (4,440,000) (4,440,000) (4,440,000) (4,440,000) (4,440,000) Fixed costs (245,000) (245,000) (245,000) (245,000) (245,000) (245,000) (245,000) (245,000) (245,000) Depreciation (517,000) (517,000) (517,000) (517,000) (517,000) (517,000) (517,000) (517,000) (517,000) Taxable Income 5,898,000 5,898,000 5,898,000 5,898,000 5,898,000 5,898,000 5,898,000 5,898,000 5,898,000 Income Tax@30% 1,769,400 1,769,400 1,769,400 1,769,400 1,769,400 1,769,400 1,769,400 1,769,400 1,769,400 Net Income 4,128,600 4,128,600 4,128,600 4,128,600 4,128,600 4,128,600 4,128,600 4,128,600 4,128,600 Add Back Depreciation 517,000 517,000 517,000 517,000 517,000 517,000 517,000 517,000 517,000 Total cash flow 4,645,600 4,645,600 4,645,600 4,645,600 4,645,600 4,645,600 4,645,600 4,645,600 4,645,600 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 4,185,225 3,770,473 3,396,823 3,060,201 2,756,937 2,483,727 2,237,592 2,015,849 1,816,080 Total PV 25,722,908 NPV 19,518,908 Present value of annuity facor = 5.537 EAB(Equivalent annual benefits) $ 3,525,177.54 = Total Cash Outflow (6,204,000) (4,685,000) (4,685,000) (4,685,000) (4,685,000) (4,685,000) (4,685,000) (4,685,000) (4,685,000) (4,685,000) PV of cash Out flow (4,220,721) (3,802,451) (3,425,632) (3,086,155) (2,780,319) (2,504,792) (2,256,570) (2,032,946) (1,831,483) Total PV of cash outflow (32,145,068) PV of Annuity factor @11% for 9yrs 5.537 EAC = NPV of cash outflow/5.537 (5,805,503) - So EAC of Machine A = $ (5,805,502.56) Machine B Details Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Investment (5,310,000) Sales Revenue 11,100,000 11,100,000 11,100,000 11,100,000 11,100,000 11,100,000 11,100,000 11,100,000 11,100,000 Variable costs (3,885,000) (3,885,000) (3,885,000) (3,885,000) (3,885,000) (3,885,000) (3,885,000) (3,885,000) (3,885,000) Fixed costs (180,000) (180,000) (180,000) (180,000) (180,000) (180,000) (180,000) (180,000) (180,000) Depreciation (590,000) (590,000) (590,000) (590,000) (590,000) (590,000) (590,000) (590,000) (590,000) Taxable Income 6,445,000 6,445,000 6,445,000 6,445,000 6,445,000 6,445,000 6,445,000 6,445,000 6,445,000 Income Tax@30% 1,933,500 1,933,500 1,933,500 1,933,500 1,933,500 1,933,500 1,933,500 1,933,500 1,933,500 Net Income 4,511,500 4,511,500 4,511,500 4,511,500 4,511,500 4,511,500 4,511,500 4,511,500 4,511,500 Add Back Depreciation 590,000 590,000 590,000 590,000 590,000 590,000 590,000 590,000 590,000 Total cash flow 5,101,500 5,101,500 5,101,500 5,101,500 5,101,500 5,101,500 5,101,500 5,101,500 5,101,500 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 4,595,946 4,140,492 3,730,173 3,360,516 3,027,492 2,727,470 2,457,180 2,213,676 1,994,303 Total PV 28,247,248 NPV 22,937,248 Present value of annuity facor = 6 EAB(Equivalent annual benefits) =NPV/5.537 = $ 4,142,540.72 Total Cash Outflow (4,065,000) (4,065,000) (4,065,000) (4,065,000) (4,065,000) (4,065,000) (4,065,000) (4,065,000) (4,065,000) PV of cash Out flow (3,662,162) (3,299,245) (2,972,293) (2,677,741) (2,412,380) (2,173,315) (1,957,941) (1,763,911) (1,589,109) Total PV of cash outflow (22,508,098) Net PV of Cash Outflow (27,818,098) PV of Annuity factor @11% for 9 yrs 5.537 EAC = NPV of cash outflow/5.537 (5,024,038) So EAC of Machine B = $ (5,024,037.97) So EAC of Machine A = $ (5,805,502.56) So EAC of Machine B = $ (5,024,037.97) Based on this Machine B should be purchased
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