Question

Your firm is contemplating the purchase of a new $480,000 computer-based order entry system. The system will be depreciated straight-line to zero over its five-year life. It will be worth $30,000 at the end of that time. You will be able to reduce working capital by $35,000 at the beginning of the project. Working capital will revert back to normal at the end of the project. Assume the tax rate is 35 percent.

Requirement 1:

Suppose your required return on the project is 10 percent and your pretax cost savings are $155,000 per year. What is the NPV of the project? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

NPV

$

Requirement 2:

Suppose your required return on the project is 10 percent and your pretax cost savings are $125,000 per year. What is the NPV of the project? (Do not round intermediate calculations. Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places (e.g., 32.16).)

NPV

$

Answer 1

Answer 1:

Working:

Year 0 cash outflow:

Initial investment = Cost of new system - Reduction in working capital

= 480000 - 35000

= $445,000

Year 0 to Year 5 Cash flow:

Pretax cost savings per year = $155,000

Post tax cost saving per year = 155000 * (1 - 35%) = $100,750

Annual depreciation = (Cost of system - salvage value) /useful life = (480000 - 0) / 5 = $96,000

Annual depreciation tax shield = 96000 * 35% = $33,600

Annual cash flow = Post tax cost saving per year + Annual depreciation tax shield = 100750 + 33600 = $134,350

Terminal cash flow:

Salvage value net of tax = 30000 * (1 - 35%) = $19,500

Requirement of working capital (back to normal) = $35,000

Terminal cash flow = 19500 - 35000 = - $15,500

NPV:

NPV = Annual cash flow * PV of $1 annuity for 5 years at 10% rate + Terminal cash flow * PV of $1 for 5 years at 10% rate - Initial investment

= 134350 * (1 - 1 / (1 + 10%) ⁵) / 10% - 15500 * 1/ (1 + 10%) ⁵ - 445000

= $54,667.92

Answer 2:

Working:

Year 0 cash outflow:

Initial investment = Cost of new system - Reduction in working capital

= 480000 - 35000

= $445,000

Year 0 to Year 5 Cash flow:

Pretax cost savings per year = $125,000

Post tax cost saving per year = 125000 * (1 - 35%) = $81,250

Annual depreciation = (Cost of system - salvage value) /useful life = (480000 - 0) / 5 = $96,000

Annual depreciation tax shield = 96000 * 35% = $33,600

Annual cash flow = Post tax cost saving per year + Annual depreciation tax shield = 81250 + 33600 = $114,850

Terminal cash flow:

Salvage value net of tax = 30000 * (1 - 35%) = $19,500

Requirement of working capital (back to normal) = $35,000

Terminal cash flow = 19500 - 35000 = - $15,500

NPV:

NPV = Annual cash flow * PV of $1 annuity for 5 years at 10% rate + Terminal cash flow * PV of $1 for 5 years at 10% rate - Initial investment

= 114850 * (1 - 1 / (1 + 10%) ⁵) / 10% - 15500 * 1/ (1 + 10%) ⁵ - 445000

= - $19252.42