Question

Vandalay Industries is considering the purchase of a new machine for the production of latex. Machine A costs $3,102,000 and will last for six years. Variable costs are 40 percent of sales, and fixed costs are $245,000 per year. Machine B costs $5,310,000 and will last for nine years. Variable costs for this machine are 35 percent of sales and fixed costs are $180,000 per year. The sales for each machine will be $11.1 million per year. The required return is 11 percent, and the tax rate is 30 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. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places. (e.g., 32.16))

	EAC
Machine A	$
Machine B	$

Answer 1

Calculation of EAC i.e. Equivalent annual cost
EAC = Annual Operating cost + [Initial Investment / PV Annuity Factor @ 11%]
Step 1 - Calculation of annuity factor
PV Annuity factor = [1 - (1+r)^-n]/r where r = discount rate and n = number of years
PV Annuity Factor for Machine A = [1 - (1+0.11)^-6]/0.11 = 4.230538
PV Annuity Factor for Machine B = [1 - (1+0.11)^-9]/0.11 = 5.537048
Step 2 - Calculation of EAC of Machine A
Year	Initial Investment	Annual Cash Operating Cost
Initial Investment	-$3,102,000.00
Variable Cost (40% OF Sales)		-$4,440,000.00
Tax savings @ 30% of variable cost		$1,332,000.00
Fixed Cost		-$245,000.00
Tax savings @ 30% of Fixed cost		$73,500.00
Depreciation tax shield @ 30% of $5,17,000		$155,100.00
Net Cash flow	-$3,102,000.00	-$3,124,400.00
EAC of Machine A= -$31,24,400 + [-$31,02,000 /4.230538 ]
EAC of Machine A= -$38,57,640.10
Step 3 - Calculation of EAC of Machine B
Year	Initial Investment	Annual Cash Operating Cost
Initial Investment	-$5,310,000.00
Variable Cost (40% OF Sales)		-$3,885,000.00
Tax savings @ 30% of variable cost		$1,165,500.00
Fixed Cost		-$180,000.00
Tax savings @ 30% of Fixed cost		$54,000.00
Depreciation tax shield @ 30% of $5,90,000		$177,000.00
Net Cash flow	-$5,310,000.00	-$2,668,500.00
EAC of Machine B= -$26,68,500 + [-$53,10,000 /5.537048 ]
EAC of Machine B= -$36,27,494.84
Working
Depreciation per year using straight line method = [Cost - salvage value]/useful life
Depreciation per year for Machine = [$3102000 - $0] / 6 Years = $5.17,000
Depreciation per year for Mahine B = [$5310000 - $0] / 9 Years = $5,90,000