Question

Your mother really dislikes the low quality of T-shirts that your company makes. She also dislikes the low-brow sayings and tasteless pictures that you print on them - she won’t let your younger sister wear them. Thus, your mom has been pestering you to expand and produce a higher quality line of T-shirts in addition to your current selection. Below are the details on this project. Cost of new equipment: $80,000 Installation cost of equipment: $40,000 Life of equipment: 5 years, Straight line depreciation Expected sales: $170,000 per year Expected reduction in sales of cheap T-shirts as your few sober customers will probably shift to the new line: $10,000 per year Raw material cost: $90,000 per year New worker salary: $20,000 per year Required Net working capital over the life of the project: $20,000 Expected Salvage value of equipment at the end of 5 year: $30,000 Tax rate: 35%. Assuming a WACC of 15%, what is this project’s NPV? a. -5,098 b. 1,610 c. 8,870 d. 16,742 e. 25,294

Answer 1

Calculating Total initial investment in year 0

Cost of new equipment = 80000, Installation costs = 40000

Total cost of new equipment = Cost of new equipment + installation costs = 80000 + 40000 = 120000

Initial investment in working capital = 20000

Total Initial investment in year 0 = Total cost of new equipment + investment in net working capital = 120000 + 20000 = 1400000

Calculating After tax operating cash flows

Annual Straight line depreciation = D = (Total cost of new equipment - Book value at end of 5 years ) / No of years = (120000 - 0) / 5 = 120000 / 5 = 24000

Incremental sales for the project = S = Expected sales of high quality T-Shirts - Reduction in sale of cheap T-shirts = 170000 - 10000 = 160000

Incremental costs for the project = C = Raw material cost + New worker salary = 90000 + 20000 = 110000

Tax rate = 35%

After tax operating cash flow in year 1 to 5 = (S - C - D)(1- tax rate) + D = (160000 - 110000 - 24000)(1-35%) + 24000 = 26000 x 65% + 24000 = 16900 + 24000 = 40900

Calculating Terminal cash flow

Salvage value at end of 5 years = 30000, Book value at end of 5 years = 0

Terminal cash flow in year 5 = Salvage value at end of 5 years + Recovery of net working capital - tax on gain from sale of equipment = Salvage value at end of 5 years + Recovery of net working capital - tax rate (Salvage value at end of 5 years - Book value at end of 5 years) = 30000 + 20000 - 35%(30000 - 0) = 50000 -10500 = 39500

Calculating net cash flow in year 1 to 5

Year	1	2	3	4	5
After tax operating cash flow (a)	40900	40900	40900	40900	40900
Terminal cash flow (b)					39500
Net Cash flow = (a) + (b)	40900	40900	40900	40900	80400

Calculating NPV of the project

NPV = - Total initial investment in year 0 + Sum of present values of net cash flows for year 1 to 5 discounted at WACC of 15%

= -140000 + 40900 / (1 + 15%) + 40900 / (1 + 15%)² + 40900 / (1 + 15%)³ + 40900 / (1 + 15%)⁴ + 80400 / (1 + 15%)⁵

= -140000 + 35565.2173 + 30926.2759 + 26892.4139 + 23384.7077 + 39973.0095 = 16741.62 = 16742 (rounded to nearest dollar)

Hence NPV of project = $16742

Answer d. $16742