Your firm is contemplating the purchase of a new 1443000 com

Your firm is contemplating the purchase of a new $1,443,000 computer-based order entry system. The system will be depreciated straight-line to zero over its 5-year life. It will be worth $140,400 at the end of that time. You will be able to reduce working capital by $195,000 (this is a one-time reduction). The tax rate is 33 percent and your required return on the project is 20 percent and your pretax cost savings are $626,200 per year. What is the NPV of this project? What is the NPV if the pretax cost savings are $450,850 per year? At what level of pretax cost savings would you be indifferent between accepting the project and not accepting it?

Solution

1) Initial Investment -1443000 Assuming the working capital savings would be at the beginning of the year of $195000 Depreciation (1443000-140400)/5 260520 Assuming the computer is sold at the end of 5th year, the income would be 140400*(1-0.33) Year Cash flows Aftertax cost savings Depreciation Tax saving on depreciation Total cost savings Discounting factor @ 20% 0 -1443000 -1443000 1 -1443000 0 195000 195000 1 195000 1 626200 419554 260520 85971.6 505525.6 0.833333 421271.3333 2 626200 419554 260520 85971.6 505525.6 0.694444 351059.4444 3 626200 419554 260520 85971.6 505525.6 0.578704 292549.537 4 626200 419554 260520 85971.6 505525.6 0.482253 243791.2809 5 626200 419554 260520 85971.6 505525.6 0.401878 203159.4007 5 140400 94068 0.401878 37803.81944 The NPV would be $301634.80 301634.8158 2) If the pretax cost savings are $450850 Year Cash flows Aftertax cost savings Depreciation Tax saving on depreciation Total cost savings Discounting factor @ 20% 0 -1443000 -1443000 1 -1443000 0 195000 195000 1 195000 1 450850 302069.5 260520 85971.6 388041.1 0.833333 323367.5833 2 450850 302069.5 260520 85971.6 388041.1 0.694444 269472.9861 3 450850 302069.5 260520 85971.6 388041.1 0.578704 224560.8218 4 450850 302069.5 260520 85971.6 388041.1 0.482253 187134.0181 5 450850 302069.5 260520 85971.6 388041.1 0.401878 155945.0151 5 140400 94068 0.401878 37803.81944 -49715.75611 The NPV would be -$49715.80 3) What should be the pretax income so that the NPV is zero for the project Let the pretax income be x Year Cash flows Aftertax cost savings Depreciation Tax saving on depreciation Total cost savings Discounting factor @ 20% 0 -1443000 -1443000 1 -1443000 0 195000 195000 1 195000 1 x 0.67x 260520 85971.6 0.67x+85971.60 0.833333 0.558333x + 71643 2 x 0.67x 260520 85971.6 0.67x+85971.60 0.694444 0.465278x + 59702.50 3 x 0.67x 260520 85971.6 0.67x+85971.60 0.578704 0.387731x + 49752.08 4 x 0.67x 260520 85971.6 0.67x+85971.60 0.482253 0.32311x + 41460.07 5 x 0.67x 260520 85971.6 0.67x+85971.60 0.401878 0.269258x + 34550.06 5 140400 94068 0.401878 37803.81944 0 (1443000)+195000+257107.7+2.00371x = 0 -990892.3 x= 990892.30/2.00371 494528.7991 The pre tax income should be $494528.80