Question

Vandalay Industries is considering the purchase of a new machine for the production of latex. Machine A costs $2,130,000 and will last for 4 years. Variable costs are 37 percent of sales, and fixed costs are $132,000 per year. Machine B costs $4,750,000 and will last for 8 years. Variable costs for this machine are 31 percent of sales and fixed costs are $77,000 per year. The sales for each machine will be $9.5 million per year. The required return is 10 percent and the tax rate is 21 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?

If the company plans to replace the machine when it wears out on a perpetual basis, what is the EAC for machine B?

Answer 1

Machine A

The Annual Variable Cost = 37% of $9.5 million = $3,515,000

Annual Fixed Cost = $132000

Total Operating Cost = $3647000

After tax operating Cost = 3647000* (1-0.21) = $2881130

Less: Depreciation tax benefit = 0.21* 2130000/4 = $111825

Total After tax Cost per year= $2881130-$111825 = $2769305

Present value of All Costs = 2130000+ 2769305/0.1* (1-1/1.1^4) = $10908324.23

So, EAC/0.1* (1-1/1.1^4) = 10908324.23

=> EAC = $3441257.81

The Equivalent Annual Cost (EAC) of machine A is -$3441257.81 (negative sign because it is a cost)

Machine B

The Annual Variable Cost = 31% of $9.5 million = $2945000

Annual Fixed Cost = $77000

Total Operating Cost = $3022000

After tax operating Cost = 3022000* (1-0.21) = $2387380

Less: Depreciation tax benefit = 0.21* 4750000/8 = $124687.50

Total After tax Cost per year = $2387380 - $124687.50 = $2262692.50

Present value of All Costs = 4750000+ 2262692.5/0.1* (1-1/1.1^8) = $16821297.50

So, EAC/0.1* (1-1/1.1^8) = 16821297.50

=> EAC = $3153051.58

The Equivalent Annual Cost (EAC) of machine B is -$3153051.58   (negative sign because it is a cost)

So, machine B is cheaper on a perpetual basis as compared to A as its EAC is less than that of A