Question

Vandelay Industries is considering the purchase of a new machine for the production of latex. Machine A costs $3,150,000 and will last for six years. Variable costs are 37 percent of sales and fixed costs are $290,000 per year. Machine B costs $5,377,000 and will last for nine years. Variable costs for this machine are 32 percent of sales and fixed costs are $210,000 per year. The sales for each machine will be $11.8 million per year. The required return is 10 percent and the tax rate is 23 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. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers in dollars, not millions of dollars, rounded to 2 decimal places, e.g., 1,234,567.89.)

Answer 1

Computation of annual cash flow for both machines:

Depreciation = Initial cost/Useful life

For Machine A, annual Depreciation = $ 3,150,000/6 = $ 525,000

For Machine A, annual Depreciation = $ 5,377,000/9 = $ 597,444.4444 or $ 597,444.44

	Machine A	Machine B
Sales revenue	$11,800,000	$11,800,000
Less: Variable cost	$4,366,000	$3,776,000
Contribution	$7,434,000	$8,024,000
Less: Fixed cost	$290,000	$210,000
Gross profit	$7,144,000	$7,814,000
Less: Depreciation	$525,000.00	$ 597,444.44
PBT	$6,619,000.00	$7,216,555.56
Less: Tax @ 23%	$1,522,370.00	$1,659,807.78
Net profit	$5,096,630.00	$5,556,747.78
Add: Depreciation	$ 525,000.00	$ 597,444.44
Annual cash flow	$5,621,630.00	$6,154,192.22

Computation of NPV:

NPV = Annual cash flow x PVIFA (i, n) - Initial cost

i = Rate of interest = 10 %

n = No. of periods, 6 years for machine A and 9 years for Machine B

NPV of Machine A = $ 5,621,630 x [1-(1+0.1)^-6/0.1] - $ 3,150,000

                                 = $ 5,621,630 x [1-(1.1)^-6/0.1] - $ 3,150,000

                                 = $ 5,621,630 x [(1-0.564473930054)/0.1] - $ 3,150,000

                                 = $ 5,621,630 x (0.435526069946/0.1) - $ 3,150,000

                                 = ($ 5,621,630 x 4.355260699462) - $ 3,150,000

                                 = $ 24,483,664.2059166 - $ 3,150,000

                                 = $ 21,333,664.2059166 or $ 21,333,664.21

NPV of Machine B = $ 6,154,192.22 x [1-(1+0.1)^-9/0.1] - $ 5,377,000

                                 = $ 5,621,630 x [1-(1.1)^-9/0.1] - $ 5,377,000

                                 = $ 5,621,630 x [(1-0.424097618372)/0.1] - $ 5,377,000

                                 = $ 5,621,630 x (0.575902381628/0.1) - $ 5,377,000

                                 = ($ 5,621,630 x 5.759023816275) - $ 5,377,000

                                 = $ 35,442,139.5649143 - $ 5,377,000

                                 = $ 30,065,139.5649143 or $ 30,065,139.56

Computation of EAC:

EAC = NPV/PVIFA (i, r)

EAC of Machine A = $ 21,333,664.21 /4.355260699462 = $ 4,898,366.75279515 or $ 4,898,366.75

EAC of Machine B = $ 30,065,139.56/5.759023816275 = $ 5,220,527.04054391 or $ 5,220,527.04

Machine A should be selected as it has lower EAC than Machine B.