Question

Your firm is contemplating the purchase of a new $518,000 computer-based order entry system. The system will be depreciated straight-line to zero over its 5-year life. It will be worth $50,400 at the end of that time. You will be able to reduce working capital by $70,000 (this is a one-time reduction). The tax rate is 24 percent and your required return on the project is 23 percent and your pretax cost savings are $164,550 per year. What is the NPV of this project?

Answer 1

Initial Investment cost

Initial Investment cost = Cost of purchase – Reduction in Working capital

= $518,000 - $70,000

= $448,000

Annual Operating cash flow (OCF)

Annual Operating cash flow (OCF) = [Pre-tax savings x (1 – Tax rate)] + [Depreciation x Tax rate]

= [$164,550 x (1 – 0.24)] + [($518,000 / 5 Years) x 0.24]

= [$164,550 x 0.76] + [$103,600 x 0.24]

= $125,058 + $24,864

= $149,922

Year 1 to Year 4 Cash Flow = $149,922

Year – 5 Cash flow

Year – 5 Cash flow = Annual cash flow – Reduction in working capital + After-tax salvage value

= $149,922 - $70,000 + [$50,400 x (1 – 0.24)]

= $149,922 - $70,000 + [$50,400 x 0.76]

= $149,922 - $70,000 + $38,304

= $118,226

Net Present Value (NPV) of the Project

Year	Annual cash flows ($)	Present Value Factor (PVF) at 23.00%	Present Value of annual cash flows ($) [Annual cash flow x PVF]
1	149,922	0.8130081	121,887.80
2	149,922	0.6609822	99,095.78
3	149,922	0.5373839	80,565.67
4	149,922	0.4368975	65,500.55
5	118,226	0.3552012	41,994.02
TOTAL		409,043.82

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

= $409,043.82 - $448,000

= -$38,956.18 (Negative NPV)

Therefore, the Net Present Value (NPV) of the Project will be -$38,956.18 (Negative NPV)

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.