Question

Your firm is contemplating the purchase of a new $2,035,000 computer-based order entry system. The system will be depreciated straight-line to zero over its 5-year life. It will be worth $198,000 at the end of that time. You will be able to reduce working capital by $275,000 (this is a one-time reduction). The tax rate is 30 percent and your required return on the project is 17 percent and your pretax cost savings are $575,300 per year. Requirement 1: What is the NPV of this project? Requirement 2: What is the NPV if the pretax cost savings are $799,050 per year? Requirement 3: At what level of pretax cost savings would you be indifferent between accepting the project and not accepting it?

Answer 1

Cost of System = $2,035,000
Useful Life = 5 years

Annual Depreciation = Cost of System / Useful Life
Annual Depreciation = $2,035,000 / 5
Annual Depreciation = $407,000

Salvage Value = $198,000
After-tax Salvage Value = $198,000 * (1 - 0.30)
After-tax Salvage Value = $138,600

Initial NWC reduced = $275,000
NWC recovered = $275,000

Answer 1.

Annual OCF = Pretax Cost Saving * (1 - tax) + tax * Annual Depreciation
Annual OCF = $575,300 * (1 - 0.30) + 0.30 * $407,000
Annual OCF = $524,810

NPV = -$2,035,000 + $275,000 + $524,810 * PVA of $1 (17%, 5) - $275,000 * PV of $1 (17%, 5) + $138,600 * PV of $1 (17%, 5)
NPV = -$2,035,000 + $275,000 + $524,810 * 3.199 - $275,000 * 0.456 + $138,600 * 0.456
NPV = -$143,331.21

Answer 2.

Annual OCF = Pretax Cost Saving * (1 - tax) + tax * Annual Depreciation
Annual OCF = $799,050 * (1 - 0.30) + 0.30 * $407,000
Annual OCF = $681,435

NPV = -$2,035,000 + $275,000 + $681,435 * PVA of $1 (17%, 5) - $275,000 * PV of $1 (17%, 5) + $138,600 * PV of $1 (17%, 5)
NPV = -$2,035,000 + $275,000 + $681,435 * 3.199 - $275,000 * 0.456 + $138,600 * 0.456
NPV = $357,712.17

Answer 3.

NPV of this project will be $0 at indifferent point.

NPV = -$2,035,000 + $275,000 + Annual OCF * PVA of $1 (17%, 5) - $275,000 * PV of $1 (17%, 5) + $138,600 * PV of $1 (17%, 5)
0 = -$2,035,000 + $275,000 + Annual OCF * 3.199 - $275,000 * 0.456 + $138,600 * 0.456
0 = -$1,760,000 + Annual OCF * 3.199 - $62,198.40
Annual OCF * 3.199 = $1,822,198.40
Annual OCF = $569,615.00

Annual OCF = Pretax Cost Saving * (1 - tax) + tax * Annual Depreciation
$569,615.00 = Pretax Cost Saving * (1 - 0.30) + 0.30 * $407,000
$569,615.00 = Pretax Cost Saving * 0.70 + $122,100
Pretax Cost Saving * 0.70 = $447,515
Pretax Cost Saving = $639,307.14