Question

United Firm is planning to buy a new machine for $200,000. The firm’s tax rate is 40%, and its overall WACC is 10%. The new machine has an economic life of 4 years and the salvage value will be $25,000 after 4 years. United Firm is using MACRS 3-year class to depreciate its assets. (i.e. Year 1, depreciate rate is 33.33%, year 2 depreciate rate is 44.45%, year 3 depreciate rate is 14.81% and year 4 depreciation rate is 7.41%). It costs $40,000 for the shipping and installation. Each year, United Firm expects to get an incremental sale of 1,250 units from the new machine. Cost (excluding depreciation) will be $100 for each unit in the first year. It will then increase by 3% per year. Unit price starts at $200 per unit in the first year and will increase by 3% per year as well. In addition, net working capital would have to increase by an amount equal to 12% of sales revenues.

1. Calculate the annual sales revenues and costs (other than depreciation).
2. Construct annual incremental operating cash flow statements.
3. Estimate the required net working capital for each year, and the cash flow due to investments in net working capital.
4. Calculate the after-tax salvage cash flow.
5. Calculate the net cash flows for each year. Based on these cash flows, what are the project’s NPV, IRR, MIRR, PI, payback, and discounted payback? Do these indicators suggest the project should be undertaken?
6. What is the Equivalent Annual Cost of this project?

Answer 1

Total cost of machine = purchase cost + installation cost

Operating cash flow (OCF) each year = income after tax + depreciation - change in NWC

In year 4, the entire NWC is recovered, and hence the change in NWC is negative

profit on sale of machine at end of year 4 = sale price -book value

book value = original cost - accumulated depreciation

after-tax salvage value = salvage value - tax on profit on sale of machine

Discounted cash flow each year = net cash flow / (1 + WACC)^{number of years}

IRR and MIRR are calculated using the Excel functions

PI = (NPV + initial investment) / initial investment

Payback period is the time taken for the cumulative cash flows to equal zero

Discounted payback period is the time taken for the cumulative discounted cash flows to equal zero

EAC = (NPV * WACC) / (1 - (1 + WACC)^-n) (where n = life of project in years)

The calculations are as below :

These indicators suggest the project should be undertaken because the NPV is positive, PI is higher than 1, and the IRR/MIRR are higher than WACC