Your firm is contemplating the purchase of a new $684,500 computer-based order entry system. The system will be depreciated straight-line to zero over its 5-year life. It will be worth $66,600 at the end of that time. You will be able to reduce working capital by $92,500 (this is a one-time reduction). The tax rate is 21 percent and your required return on the project is 21 percent and your pretax cost savings are $203,750 per year. At what level of pretax cost savings would you be indifferent between accepting the project and not accepting it?

total pretax annual savings = $210,941.06

Explanation:

initial outlay (year 0) = -$684,500 (cost of computer system) + $92,500 (reduction of net working capital) = -$592,000

depreciation expense per year = $684,500 / 5 = $136,900

net after tax cash value = $66,600 x (1 - 21%) = $52,614

net cash flows years 1 - 4 = [($203,750 - $136,900) x 79%] + $136,900 = $189,711.50

net cash flow year 5 = $189,711.50 + $52,614 = $242,325.50

using a 21% discount rate, the NPV = -$16,622.15

Since the NPV is negative, that means that the annual cost savings are not high enough to accept the project.

the point where the company would be indifferent between accepting or rejecting the project is when NPV = 0

this means that net cash flows must increase by $16,622.15 / 2.92595 (PV annuity factor, 21%, 5 periods) = $5,680.94

this is an after tax number, but a pretax annual cost saving = $5,608.94 / 0.79 = $7,191.06

total pretax annual savings = $203,750 + $7,191.06 = $210,941.06

net cash flows years 1 - 4 = [($210,941.06 - $136,900) x 79%] + $136,900 = $195,392.44

net cash flow year 5 = $195,392.44 + $52,614 = $248,006.44

NPV = 0

the investment was $14,174.196

explanation:

a lump sum means that the father of the example made one deposit and leave it be.

we need to know the value of a capital that generated at 4.05% per year during 28 years the sum of $48,613.24

now clearing the formula to solve for capital we got:

and we reach the answer investment = $14,174.20