Question

Vandalay Industries is considering the purchase of a new machine for the production of latex. Machine A costs $3,090,000 and will last for six years. Variable costs are 35 percent of sales, and fixed costs are $230,000 per year. Machine B costs $5,292,000 and will last for nine years. Variable costs for this machine are 30 percent of sales and fixed costs are $165,000 per year. The sales for each machine will be $10.8 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. The company plans to replace the machine when it wears out on a perpetual basis. Calculate the EAC for each machine.

Answer 1

Step 1 : Identification of Alternatives

Alternative 1 : Machine A

Alternative 2 : Machine B

Step 2 : Calculation of Net Present Value of Machine A

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

1. Calculation of Cash Outflows:

Particulars	Amount
Cost of Machinery	($3,090,000.00)

2. Calculation of Cash Inflows per year

Particulars	Amount
Sales	$10,800,000.00
Less : Variable Cost ($10.8 million x 35%)	$(3,780,000.00)
Contribution	$7,020,000.00
Less: Fixed Cost	$(230,000.00)
Less: Depreciation (Note 1)	$(515,000.00)
Earnings before tax	$6,275,000.00
Less: Tax @ 35%	$(2,196,250.00)
Earnings after tax	$4,078,750.00
Add: Depreciation	$515,000.00
Future Cash Inflows	$4,593,750.00

Note 1 : Calculation of Depreciation

Cost of Machinery (A)	$3,090,000.00
Life (B)	6 years
Depreciation per year as per SLM (A) /(B)	$515,000.00

3. Calculation of NPV at required rate of return 10%

Particulars	Amount	Period	PVF @10%	Present Value
Cash outflows
Cost of Machinery	($3,090,000.00)	0	1	($3,090,000.00)
Cash Inflows
Future Cash Inflows	$4,593,750.00	1-6	4.355260699	$20,006,978.84
			NPV	$16,916,978.84

NPV of Machine A = $16,916,978.84

Step 3 : Calculation of Net Present Value of Machine B

1. Calculation of Cash Outflows:

Particulars	Amount
Cost of Machinery	($5,292,000.00)

2. Calculation of Cash Inflows per year

Particulars	Amount
Sales	$10,800,000.00
Less : Variable Cost ($10.8 million x 30%)	$(3,240,000.00)
Contribution	$7,560,000.00
Less: Fixed Cost	$(165,000.00)
Less: Depreciation (Note 1)	$(588,000.00)
Earnings before tax	$6,807,000.00
Less: Tax @ 35%	$(2,382,450.00)
Earnings after tax	$4,424,550.00
Add: Depreciation	$588,000.00
Future Cash Inflows	$5,012,550.00

Note 1 : Calculation of Depreciation

Cost of Machinery (A)	$5,292,000.00
Life (B)	9 years
Depreciation per year as per SLM (A) /(B)	$588,000.00

3. Calculation of NPV at required rate of return 10%

Particulars	Amount	Period	PVF @10%	Present Value
Cash outflows
Cost of Machinery	($5,292,000.00)	0	1	($5,292,000.00)
Cash Inflows
Future Cash Inflows	$5,012,550.00	1-9	5.759023816	$28,867,394.83
			NPV	$23,575,394.83

NPV of Machine B = $23,575,394.83

Step 4 : Calculation Of EAC

Equivalent Annual Cost (EAC) = NPV / PVAF(r, t)

Particulars	Machine A	Machine B
NPV	$16,916,978.84	$23,575,394.83
Life	6 years	9 years
PVAF @10%	4.355260699	5.759023816
EAC	$3,884,263.19	$4,093,644.27

Note :

PVAF(r, t) = (1/1+r)^1 + (1/1+r)^2 + ....+ (1/1+r)^n
Where r = required rate of return
t = Time period