Question

Gateway Communications is considering a project with an initial fixed assets cost of $1.68 million that will be depreciated straight-line to a zero book value over the 10-year life of the project. At the end of the project the equipment will be sold for an estimated $226,000. The project will not change sales but will reduce operating costs by $380,500 per year. The tax rate is 35 percent and the required return is 10.1 percent. The project will require $45,000 in net working capital, which will be recouped when the project ends. What is the project's NPV?

Answer 1

Initial Investment

Initial Investment = Initial Fixed Asset Cost + Investment in Net Working Capital

= $16,80,000 + $45,000

= $17,25,000

Annual Cash Inflow

Operating Cash Flow = Pre-Tax Savings(1 – Tax Rate) + (Depreciation x Tax Rate)

= $380,500(1 – 0.35) + [($16,80,000 / 10 Years) x 0.35]

= $247,325 + $58,800

= $306,125

Year 1-9 Cash Flow = $306,125

Year 6 Cash Flow = Annual cash flow + Release of Working Capital + After tax Salvage Value

= $306,125 + $45,000 + [$226,000 x (1 – 0.35)]

= $306,125 + $45,000 + $146,900

= $498,025

Net Present Value (NPV)

Year	Annual Cash Inflows ($)	Present Value factor at 10.10%	Present Value of Cash Inflow ($)
1	3,06,125	0.90827	2,78,042.69
2	3,06,125	0.82495	2,52,536.50
3	3,06,125	0.74927	2,29,370.12
4	3,06,125	0.68054	2,08,328.90
5	3,06,125	0.61811	1,89,217.89
6	3,06,125	0.56140	1,71,860.03
7	3,06,125	0.50990	1,56,094.49
8	3,06,125	0.46313	1,41,775.19
9	3,06,125	0.42064	1,28,769.48
10	4,98,025	0.38206	1,90,273.35
TOTAL			19,46,268.64

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $19,46,268.64 - $17,25,000

= $2,21,268.64

“Hence, the Project’s Net Present Value (NPV) would be $2,21,268.64”

NOTE

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.