Question

Your firm is contemplating the purchase of a new $2,164,500 computer-based order entry system. The system will be depreciated straight-line to zero over its 5-year life. It will be worth $210,600 at the end of that time. You will be able to reduce working capital by $292,500 (this is a one-time reduction). The tax rate is 25 percent and your required return on the project is 18 percent and your pretax cost savings are $848,700 per year. a. What is the NPV of this project? b. What is the NPV if the pretax cost savings are $611,050 per year? c. At what level of pretax cost savings would you be indifferent between accepting the project and not accepting it?

Answer 1

Answer (a):

Year 0 Cash flow = - (Purchase cost - Reduction in working capital) = -(2164500 - 292500) = -$1,872,000

Year 1 to Year 5 Operating Cash flows:

Annual depreciation = 2164500 / 5 = $432,900

Annual operating cash flow = Annual pretax cost savings * (1 - Tax rate) + Depreciation tax shield

= 848700 * (1 - 25%) + 432900 * 25%

= $744,750

Year 5 Terminal cash flow = Salvage value * (1 - Tax rate) - Increase in working capital

= 210600 * (1 - 25%) - 292500

= - $134,550

NPV = Annual cash flows * PV of $1 annuity for 5 years at 18% + Terminal cash flow * PV of $1 for 5 years at 18% + Year 0 cash flow

= 744750 * (1 - 1/(1 + 18%)^5)/ 18% - 134550/(1 + 18%)^5 - 1872000

= $398147.57

NPV = $398,147.57

Answer (b):

If pretax cost savings are $611,050 per year

Annual operating cash flow = 611050 * (1 - 25%) + 432900 * 25% = $566,512.50

NPV = Annual cash flows * PV of $1 annuity for 5 years at 18% + Terminal cash flow * PV of $1 for 5 years at 18% + Year 0 cash flow

= 566512.50* (1 - 1/(1 + 18%)^5)/ 18% - 134550/(1 + 18%)^5 - 1872000

= -$159,231.57 or ($159,231.57)

NPV = ($159,231.57)

Answer (c):

At indifference point, NPV = $0

From answer 1, we have when pretax cash saving = $848,700, NPV = $398,147.57

For indifference point:

Reduction in after tax cash saving required = 398147.57 / ((1 - 1/(1 + 18%)^5)/ 18%) = $127,318.77

Reduction in pretax cash savings required = 127318.77/ (1 - 25%) = $169,758.36

Hence:

For indifference point:

Pretax cash savings has to be = 848700 - 169758.36 = 678941.64

Level of pretax cost savings where you would be indifferent between accepting and not accepting it = $678,941.64