Question

You are evaluating two machines. Machine I costs $240,000 and it has a three-year life. It has pre-tax operating costs of $60,000 per year. Machine II costs $450,000 and it has a five-year life. It has pre-tax operating costs of $40,000 per year. For both machines, we use straight-line depreciation to zero over the machine’s life. The pre-tax salvage value of Machine I is $50,000 at the end of its life. The pre-tax salvage value of Machine II is $150,000 at the end of its life. The marginal tax rate is 30% and the appropriate discount rate is 10%.

(1) What is the NPV of investing in each machine?

(2) Should your decision be based on the calculated NPVs in part (1)? If not, which metric you should use to make a decision? Writing down the name of the metric is enough for this part.

(3) What is your decision? Calculate the relevant metric for each machine and do the comparison.

Answer 1

1)	MACHINE I:
	Initial cost	$    -2,40,000.00
	PV of after tax operating costs = -60000*(1-30%)*(1.1^3-1)/(0.1*1.1^3) =	$    -1,04,447.78
	PV of depreciation tax shield = (240000/3)*30%*(1.1^3-1)/(0.1*1.1^3) =	$         59,684.45
	PV of after tax salvage value = 50000*(1-30%)/1.1^3 =	$         26,296.02
	NPV	$    -2,58,467.32
	MACHINE II:
	Initial cost	$    -4,50,000.00
	PV of after tax operating costs = -40000*(1-30%)*(1.1^5-1)/(0.1*1.1^5) =	$    -1,06,142.03
	PV of depreciation tax shield = (450000/5)*30%*(1.1^5-1)/(0.1*1.1^5) =	$      1,02,351.24
	PV of after tax salvage value = 150000*(1-30%)/1.1^5 =	$         65,196.74
	NPV	$    -3,88,594.05
2)	No, the decision should not be based on NPV, as the two machines have unequal lives.
	The decision should be based on 'Equvalent Annual NPV' (can be called Equvalent Annual Cost in this case).
3)	EANPV or EAC - Machine I:
	= -258467.32*0.1*1.1^3/(1.1^3-1) =	$    -1,03,933.54
	EANPV or EAC - Machine II:
	= -388594.05*0.1*1.1^5/(1.1^5-1) =	$    -1,02,510.13
	DECISION:
	As the EAC of Machine II is lower it should be
	chosen.