Question 10.3: We are considering the purchase of a $200,000 computer-based...
We are considering the purchase of a $200,000 computer-based inventory management system. It will be depreciated straight-line to zero over its four-year life. It will be worth $30,000 at the end of that time. The system will save us $60,000 before taxes in inventory-related costs.
The relevant tax rate is 39 percent. Because the new setup is more efficient than our existing one, we will be able to carry less total inventory and thus free up $45,000 in net working capital. What is the NPV at 16 percent? What is the DCF return (the IRR) on this investment?
We can first calculate the operating cash flow. The aftertax cost savings are $60,000 × (1 – .39) = $36,600. The depreciation is $200,000/4 = $50,000 per year, so the depreciation tax shield is $50,000 × .39 = $19,500. Operating cash flow is thus $36,600 + 19,500 = $56,100 per year.
The capital spending involves $200,000 up front to buy the system. The aftertax salvage is $30,000 × (1 – .39) = $18,300. Finally, and this is the somewhat tricky part, the initial investment in net working capital is a $45,000 inflow because the system frees up working capital. Furthermore, we will have to put this back in at the end of the project’s life. What this really means is simple: while the system is in operation, we have $45,000 to use elsewhere.
To finish our analysis, we can compute the total cash flows:
| Year | |||||
| 0 | 1 | 2 | 3 | 4 | |
| Operating cash flow | $56,100 | $56,100 | $56,100 | $56,100 | |
| Change in NWC | $ 45,000 | – 45,000 | |||
| Capital spending | \underline{- 200,000} | \underline{18,300} | |||
| Total cash flow | -\$\underline{\underline{155,000}} | $\underline{\underline{56,100}} | $\underline{\underline{56,100}} | $\underline{\underline{56,100}} | $\underline{\underline{29,400}} |
At 16 percent, the NPV is –$12,768, so the investment is not attractive. After some trial and error, we find that the NPV is zero when the discount rate is 11.48 percent, so the IRR on this investment is about 11.5 percent.