Question

A corporation is considering a proposal for the purchase of a machine that will save $250,000 per year before taxes. The cost of operating the machine, including maintenance, is $35,000 per year. The machine will be needed for five years after which it will have a zero salvage value. MACRS depreciation will be used, assuming a three‐year class life. The marginal income‐tax rate is 24%. If the firm wants 15% IRR after taxes, how much can it afford to pay for this machine?

Answer 1

For finding out the maximum that can be paid for
the machine the NPV should be set at 0 with a
discount rate of 15%.
That is,
0 = -x+(250000-35000)*(1-24%)*PVIFA(15,5]+PV of Depreciation tax shield
where x = cost of machine.
The PV of depreciation tax shield can be expressed as a function of x.
Year	Depreciation %	Tax shield %	PVIF at 15%	PV of % tax shield on depreciation
1	33.33	9.999	0.86957	8.69
2	44.45	13.335	0.75614	10.08
3	14.81	4.443	0.65752	2.92
4	7.41	2.223	0.57175	1.27
				22.97
PV of depreciation tax shield = 22.97% of the cost of the machine.
Inputting this into the NPV equation, we have
0 = -x+215000*0.76*3.35216+x*0.2297
x*0.7703 = 547743
x = 547743/0.7703 =	$            7,11,078
Answer: The maximum that can be paid for the machine =	$            7,11,078