Question

Crockett is considering the purchase of an automated sewing machine that will cost $200,000 and is expected to operate for 5 years, after that it has no salvage value. The investment is expected to generate $360,000 revenues for each of the five year of the project’s life. Crockett is expecting to increase it’s accounts receivables by $60,000 and inventories by $36,000. this also will lead to an increase in accounts payable by $18,000.

This project will also result in cost of goods sold equal to 60% of revenues while incurring other
operational expenses of $5,000 per year. In addition, the depreciation expense is one-fifth of the initial
investment. Income tax is 30% and the required rate of return is 20%.

Calculate the following:

The amount of cash needed to invest in working capital (Net working capital for year 0)

Operating cash flow

Comment on this project by calculating the NPV

Perform a sensitivity test assuming the expected revenues will decrease to $300,000 per year.

Perform a sensitivity test assuming the expected operational expenses will rise 50% for every year.

Answer 1

Answer 1:

Cash needed to invest in working capital (Net working capital for year 0) = Increase its accounts receivables + Increase its inventories - Increase in accounts payable

= $60,000 + $36,000 - 18,000

= $78,000

Cash needed to invest in working capital (Net working capital for year 0) = $78,000

Answer 2:

Initial Investment = $200,000

Depreciation expense is one-fifth of the initial investment = $200,000 / 5 = $40,000

Operating cash flow = (Revenue - Cost of goods sold - other operational expenses) * (1 - Tax rate) + Depreciation Tax shield  

= ($360,000 - 60% * $360,000 - $5,000) * (1 - 30%) + $40,000 * 30%

= $109,300

Operating cash flow = $109,300

Answer 3:

PV Factor for a One-Dollar Annuity Discounted at 20% for 5 Periods = [1 - 1/(1 + k) ⁿ] / k = (1 - 1/(1 +20%) ⁵) /6%

PV Factor for One Dollar Discounted at 20% for 5 Periods = 1 / (1 + k) ⁿ = 1/ (1 + 20%) ⁵

NPV = (Annual Operating cash flow * PV factor) + Release of working capital at the end year 5 * PV factor - Initial Investment - Initial investment in working capital

= $109,300 * (1 - 1/(1 +20%) ⁵) /20%+ $78,000 * 1 /(1 + 20%) ⁵ - $200,000 - $78,000

= $80,220.36

NPV = $80220.36

Answer 4:

Assuming the expected revenues will decrease to $300,000 per year:

Reduction in contribution = ($360,000 - $300,000) * (1 - 60%)

= $24,000

NPV will decrease by = (Annual Reduction in contribution * (1 - Tax rate) * PV factor

= $24,000* (1 - 30%) * (1 - 1/(1 +20%) ⁵) /20%

= $50,242.28

Assuming the expected revenues will decrease to $300,000 per year, NPV will decrease by $50,242.28

Answer 4:

Assuming the expected operational expenses will rise 50% for every year:

Increase in operational expense = $5000 * 50% = $2,500

NPV will decrease by = (Annual Increase in operational expense * (1 - Tax rate) * PV factor

= 2500 * (1- 30%) * 1 - 1/(1 +20%) ⁵) /20%

= $5,233.57

Assuming the expected operational expenses will rise 50% for every year, NPV will decrease by $5,233.57