Question

Vandalay Industries is considering the purchase of a new machine for the production of latex. Machine A costs $1,880,000 and will last for 5 years. Variable costs are 35 percent of sales, and fixed costs are $169,000 per year. Machine B costs $4,340,000 and will last for 8 years. Variable costs for this machine are 28 percent of sales and fixed costs are $111,000 per year. The sales for each machine will be $8.68 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 machine when it wears out on a perpetual basis, what is the EAC for machine A? (Do not round your intermediate calculations.) a) -9,283,217.02 b) -2,448,889.26 c) -4,024,597.5 d) -3,641,302.5 e) 3,193,110.74 If the company plans to replace the machine when it wears out on a perpetual basis, what is the EAC for machine B? (Do not round your intermediate calculations.) a) -2,275,542.04 b) -12,139,848.82 c) -8,392,488.68 d) 3,366,457.96 e) -9,275,908.54

Answer 1

Solution 1) Calculation of the Equivalent Annual Cost of Machine A:

Cost of the Machine A $18,80,000

Depreciation as per Straight Line Method = 18,80,000 / 5 = $3,76,000 per year

Calculation of Cash Inflows for Machine A

Particulars	$
Sales	86,80,000
Less: Variable Costs (35% of Sales)	30,38,000
Less: Fixed Costs	1,69,000
Net Profit Before Depreciation and Tax	54,73,000
Less: Depreciation	3,76,000
Net Profit Before Tax	50,97,000
Less: Tax 35%	17,83,950
Net Profit After Tax	33,13,050
Cash Inflows = Net Profit After Tax + Depreciation	36,89,050

                                  

Calculation of Net Present Value of Machine A:

Year	Cash Inflows	Df@10%	Present Value of Cash Inflows
1	36,89,050	0.9091	3353681.818
2	36,89,050	0.8264	3048801.653
3	36,89,050	0.7513	2771637.866
4	36,89,050	0.6830	2519670.788
5	36,89,050	0.6209	2290609.807
		Present Value of Cash Inflows	13984401.93
		Cost of the Machine	18,80,000
		NPV = Present Value of Cash Inflows - Cost of the Machine	1,21,04,402

Therefore, Equivalent Annual Cost = Net Present Value / Annuity Factor

Therefore, Equivalent Annual Cost of Machine A =  1,21,04,402 / 3.7908 = $31,93,110.74

The Correct option is Option E = 3,193,110.74

Solution 2) Calculation of the Equivalent Annual Cost of Machine B:

Cost of Machine B: $4,340,000

Depreciation = 4,340,000 / 8 = $542,000 per year

Calculation of Cash Inflows for Machine B:

Cost of the Machine B: $4,340,000

Depreciation = 4,340,000 / 8 = $542,000 per year

Calculation of Cash Inflows for Machine B:

Particulars	$
Sales	86,80,000
Less: Variable Costs (28% of Sales)	24,30,400
Less: Fixed Costs	1,11,000
Net Profit Before Depreciation and Tax	61,38,600
Less: Depreciation	5,42,500
Net Profit Before Tax	55,96,100
Less: Tax 35%	19,58,635
Net Profit After Tax	36,37,465
Cash Inflows	41,79,965

Calculation of Net Present Value of Machine B:

Year	Cash Inflows	Df@10%	Present Value of Cash Inflows
1	41,79,965	0.9091	3799968.182
2	41,79,965	0.8264	3454516.529
3	41,79,965	0.7513	3140469.572
4	41,79,965	0.6830	2854972.338
5	41,79,965	0.6209	2595429.398
6	41,79,965	0.5645	2359481.271
7	41,79,965	0.5132	2144982.974
8	41,79,965	0.4665	1949984.522
		Present Value of Cash Inflows	22299804.78
		Cost of the Machine	43,40,000
		NPV = Present Value of Cash Inflows - Cost of the Machine	1,79,59,805

Therefore, Equivalent Annual Cost = Net Present Value / Annuity Factor

                                                              = $17959805 / 5.3349

                                                              = $3,366,457.96

The correct option is Option D $3,366,457.96