Question

A security team for a local high school contemplates replacing their current contract security system with a new and improved version. It will cost $450,000 to get the new system and the cost will be depreciated straight-line to 0 over the system’s 4-year expected life. The system is expected to be worth $250,000 at the end of 4 years. The security team believes that the new system will save them $125,000 per year (before taxes) in contract security costs. The tax rate is 34%, the required rate of return is 17%.

What is the NPV (Net Present Value) for buying the new system? SHOW EBIT, OCF, CS, and PROJECT CASH FLOW for each year of the project’s life.

Answer 1

Cost of new system = $450000

Initial Cash outflow in year 0 = - Cost of New system = - 450000

Annual Straight line depreciation = (Cost of system - Book value at end of 4 years) / 4 = (450000 - 0) / 4 = 112500

Since the system will save costs, therefore incremental costs for year 1 to 4 = - 125000

Incremental revenue for year 1 to 4 = 0

EBIT for year 1 to 4 = (Incremental Revenue - Incremental costs - Depreciation) = [ 0 - (-125000) - 112500] = 125000 - 112500 = 12500

Operating cash flow for year 1 to 4 = OCF = EBIT(1-tax rate) + Depreciation = 12500(1-34%) + 112500 = 12500 x 66% + 112500 = 8250 + 112500 = 120750

Salvage value of system at end of 4 years = 250000

Terminal cash flow for year 4 = Salvage value of system at end of 4 years - tax on gain from sale of system = Salvage value of system at the end of 4 years - tax rate (Salvage value of system at end of 4 years - Book value of system at end of 4 years) = 250000 - 34%(250000 - 0) = 250000 - 85000 = 165000

Cash Flow Projections:

Year	0	1	2	3	4
Initial Cash Outflow (a)	-450000
Operating Cash Flow (b)		120750	120750	120750	120750
Terminal Cash Flow (c)					165000
Net Cash Flow = (a) + (b) + (c)	-450000	120750	120750	120750	285750

Net Present value of buying new system = Initial cash outflow + Sum of present values of Net cash flows for year 1 to 4 discounted at 17%

= -450000 + 120750 / (1 + 17%) + 120750 / (1 + 17%)² + 120750 / (1 + 17%)³ + 285750 / (1 + 17%)⁴

= -450000 + 103205.1282 + 88209.5112 + 75392.7446 + 152490.5012 = -30702.1148 = -30702.11

Hence the Net present value of buying new system = -30702.11