Question

Vandalay Industries is considering the purchase of a new machine for the production of latex. Machine A costs $1,810,000 and will last for 4 years. Variable costs are 34 percent of sales, and fixed costs are $147,000 per year. Machine B costs $4,380,000 and will last for 7 years. Variable costs for this machine are 30 percent of sales and fixed costs are $77,000 per year. The sales for each machine will be $8.76 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.

  

Required:

(a)	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.)
	(Click to select)$-3,498,978.25$-7,747,585.91$-3,867,291.75$3,249,862.85$-2,444,137.15

  

(b)	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.)

Answer 1

a) Cost of Machine A = 1810000

Annual depreciation = (Cost - Salvage value) / No of years = (1810000 - 0) / 4 = 452500

Sales = 8.76 million = 8.76 x 1000000 = 8760000

Variable costs = 34% of sales = 34% x 8760000 = 2978400

After tax operating cash flow = (Sales - Variable costs - Fixed Costs - Depreciation)(1-tax rate) + Depreciation = (8760000 - 2978400 - 147000 - 452500)(1-35%) + 452500 = 5182100(1-35%) + 452500 = 3368365 + 452500 = 3820865

First we will find the Present Worth of Machine A

Present Worth of Machine A = -Cost of Machine + Sum of present values of after tax cash flows discounted at 10%

= -1810000 + 3820865 / (1+10%) + 3820865 / (1+10%)² + 3820865 / (1+10%)³ + 3820865 / (1+10%)⁴

= -1810000 + 3473513.64 + 3157739.67 + 2870672.43 + 2609702.21 = 10301627.94

EAC of Machine A = Present Worth of Machine x Capital recovery factor

Capital Recovery Factor = 0.14641 / 0.4641 = 0.315470804

EAC of Machine A = 10301627.93 x 0.315470804 = 3249862.848 = 3249862.85

b) Cost of Machine B = 4380000

Annual depreciation = (Cost - Salvage value) / No of years = (4380000 - 0) / 7 = 625714.28

Sales = 8.76 million = 8.76 x 1000000 = 8760000

Variable costs = 34% of sales = 30% x 8760000 = 2628000

After tax operating cash flow = (Sales - Variable costs - Fixed Costs - Depreciation)(1-tax rate) + Depreciation = (8760000 - 2628000 - 77000 - 625714.28)(1-35%) + 625714.28 = 5429285.72(1-35%) + 625714.28 = 3529035.72 + 625714.28 = 4154750

First we will find the Present Worth of Machine B

Present Worth of Machine B = -Cost of Machine + Sum of present values of after tax operating cash flows discounted at 10%

= -4380000 + 4154750/(1+10%) + 4154750/(1+10%)² + 4154750/(1+10%)³ + 4154750/(1+10%)⁴ + 4154750/(1+10%)⁵ + 4154750/(1+10%)⁶ + 4154750/(1+10%)⁷

= -4380000 + 3777045.45 + 3433677.69 + 3121525.17 + 2837750.15 + 2579772.87 + 2345248.06 + 2132043.69 = 15847063.08

EAC of Machine B = Present Worth of Machine x Capital recovery factor

Capital Recovery Factor = 0.19487171 / 0.9487171 = 0.2054055

EAC of Machine B = 15847063.08 x 0.2054055 = 3255073.915 = 3255073.92