Question

"Your company has asked you to consider the purchase of a new machine for a project. Details of this potential purchase are provided below.
-The project life is 3 years.
The machine costs $187,000.
* You have decided your company will pay cash for half of this machine immediately, and will borrow the remaining half at 5% annual rate compounded annually over 3 years.
* The machine will be depreciated using a seven year MACRS approach.
Annual O&M costs (expenses) of the machine are $20,000.
Annual labor savings (revenues) are $84,000.
Salvage value at the end of year 3 will be $42,000.
Working capital requirement is initially $28,000. Any investment in working capital will be recovered at the end of the project.
Assume an income tax rate and gains tax rate of 21%.
Find the NPW of this project based on a MARR of 14%."

Answer 1

Here MARR is directly given and which is used as the discount rate. Interest rate on the loan is already considered here and hence no requirement of separate treatment for the 5% rate of loan (MARR is usually considering the amount to be paid to Equity, preference & Debt capitals)

Calculation of Yearly Cash Flows

No	Particulars	Year 1	Year2	Year 3	Total
1	After Tax Cash Flows (Note 1)	50560	50560	50560
2	Depreciation Tax shield (*Note 2)	5611.683	9617.223	6868.323
3	Net CF from Operating activity(1+2)	56171.683	60177.223	57428.323
4	Net Salvage Value (Note 3)			50,352.77
5	Recapture of Working Capital			28000
6	Yearly after Tax Cash Flows	56171.683	60177.223	135781.094	252130
	(1+2+3+4+5)
7	Present Value Factor @ 14%	0.8772	0.7695	0.6750
8	Discounted Cash Inflows (6*7)	49,273.41	46,304.42	91,648.37	1,87,226.20

	Calculation of NPV
1	PV of Cash Inflow	1,87,226.20
2	PV of Cash Outflow (187000+28000)	215000
3	NPV (1-2)	(27,773.80)

WN 1: Calculation of After Tax Cash Flow
	Year 1	Year 2	Year 3
Annual Labour Savings	84000	84000	84000
Less: Annual O & M Cost	-20000	-20000	-20000
Before Tax CF	64000	64000	64000
Less: Tax @ 21%	13440	13440	13440
After Tax Cash Flows	50560	50560	50560

	WN 2: Calculation of Depreciation Tax Shield
	Particulars	Year 1	Year 2	Year 3
1	Depreciation Rate (MACRS)	14.29%	24.49%	17.49%
2	Asset Value	187000	187000	187000
3	Depreciation (1*2)	26722.3	45796.3	32706.3
4	Tax Rate	21%	21%	21%
5	Depreciation Tax shield (3*4)	5611.683	9617.223	6868.323

	WN 3: Calculation of Net Salvage Value
1	Purchase Price of Asset	187000
2	Less: Accumulated Depreciation	1,05,224.900
	(26722.3+45796.3+32706.3)
3	Book Value Of the Asset	81,775.100
4	Salavage Value	42000	Cash Inflow
5	Loss from Sale of Asset (4-3)	(39,775.10)
6	Tax Savings on Loss	8352.771	Cash Inflow
	(39775.10*21%)
	Cash Flows from Sale of Asset (4+6)	50352.771	Cash Inflow

Note:-

1. Here the depreciation rate is as per the depreciation rate as provided in the 7 year MACRS method

2. Salvage value is not considered while calculating the depreciation. It is assumed that it is an estimated amount. If we consider the salvage value in calculating the depreciation, the result may change.