Question

The Darlington Equipment Company purchased a machine 5 years ago at a cost of $95,000. The machine had an expected life of 10 years at the time of purchase, and it is being depreciated by the straight-line method by $9,500 per year. If the machine is not replaced, it can be sold for $10,000 at the end of its useful life.

A new machine can be purchased for $170,000, including installation costs. During its 5-year life, it will reduce cash operating expenses by $60,000 per year. Sales are not expected to change. At the end of its useful life, the machine is estimated to be worthless. MACRS depreciation will be used, and the machine will be depreciated over its 3-year class life rather than its 5-year economic life; so the applicable depreciation rates are 33%, 45%, 15%, and 7%.

The old machine can be sold today for $50,000. The firm's tax rate is 40%. The appropriate WACC is 9%.

1. If the new machine is purchased, what is the amount of the initial cash flow at Year 0? Round your answer to the nearest dollar. Negative amount should be indicated by a minus sign.
   $
2. What are the incremental net cash flows that will occur at the end of Years 1 through 5? Round your answers to the nearest dollar.

   Year 1

   Year 2

   Year 3

   Year 4

   Year 5

3. What is the NPV of this project? Round your answer to the nearest cent. Negative amount should be indicated by a minus sign.

Answer 1

Old machine book value

Book value = (purchase price)*remaining life/total life
= (95000)*5/10
= 47500

Time line		0	1	2	3	4	5
Proceeds from sale of existing asset	=selling price* ( 1 -tax rate)	30000
Tax shield on existing asset book value	=Book value * tax rate	19000
Cost of new machine		-170000
=a. Initial Investment outlay		-121000
3 years MACR rate			33.00%	45.00%	15.00%	7.00%	0.00%
Savings			60000	60000	60000	60000	60000
-Depreciation	=Cost of machine*MACR%		-56100	-76500	-25500	-11900	0
=Pretax cash flows			3900	-16500	34500	48100	60000
-taxes	=(Pretax cash flows)*(1-tax)		2340	-9900	20700	28860	36000
+Depreciation			56100	76500	25500	11900	0
=after tax operating cash flow			58440	66600	46200	40760	36000
+Tax shield on salvage book value	=Salvage value * tax rate						0
=Terminal year after tax cash flows							0
b. Total Cash flow for the period		-121000	58440	66600	46200	40760	36000
Discount factor=	(1+discount rate)^corresponding period	1	1.09	1.1881	1.295029	1.4115816	1.538624
Discounted CF=	Cashflow/discount factor	-121000	53614.6789	56055.888	35674.877	28875.412	23397.53
c. NPV=	Sum of discounted CF=	76618.39