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 4 years. Variable costs are 36 percent of sales, and fixed costs are $153,000 per year. Machine B costs $4,310,000 and will last for 7 years. Variable costs for this machine are 28 percent of sales and fixed costs are $93,000 per year. The sales for each machine will be $8.62 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? (b) 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

Cost of Machine A = $1,880,000

Life of machine A = 4 years

Annual depreciation = Cost of machine/ Life of machine

Annual depreciation of machine A = 1,880,000/4

= $470,000

Calculation of annual cash inflows

Sales	8,620,000
Less: Variable cost @ 36%	- 3,103,200
Contribution	5,516,800
Less: Fixed cost	- 153,000
EBIT	5,363,800
Less: Depreciation	- 470,000
Earnings before tax	4,893,800
Less : Tax @ 35%	- 1,712,830
Earnings after tax	3,180,970
Add : Depreciation	470,000
Annual cash flows after tax	3,650,970

Present value of cash inflows = Annual cash flows after tax x PVAF(_{10% , 4} )

= 3,650,970 x 3.170

= $11,573,575

NPV of machine A = Present value of cash inflows - Present value of cash outflows

= 11,573,575 - 1,880,000

= $ 9,693,575

EAC of machine A = NPV of a project/PVAF(_{10%, 4} )

= 9,693,575/3.170

= $3,057,910

Machine b

Cost of Machine B = $4,310,000

Life of machine B = 7 years

Annual depreciation = Cost of machine/ Life of machine

Annual depreciation of machine B = 4,310,000/7

= $615,714

Calculation of annual cash inflows

Sales	8,620,000
Less: Variable cost @ 28%	- 2,413,600
Contribution	6,206,400
Less: Fixed cost	- 93,000
EBIT	6,113,400
Less: Depreciation	- 615,714
Earnings before tax	5,497,686
Less : Tax @ 35%	- 1,924,190
Earnings after tax	3,573,496
Add : Depreciation	615,714
Annual cash flows after tax	4,189,210

Present value of cash inflows = Annual cash flows after tax x PVAF(_{10% , 7} )

= 4,189,210 x 4.868

= $20,393,074

NPV of machine B = Present value of cash inflows - Present value of cash outflows

= 20,393,074 - 4,310,000

= $16,083,074

EAC of machine B = NPV of a project/PVAF(_{10%, 7})

= 16,083,074/4.868

= $3,303,836