Final answer:
To decide if Dot should purchase a new machine, we calculate the NPV by forecasting sales, subtracting costs and depreciation, accounting for taxes, and discounting future cash flows to the present using an 8.20% discount rate. If the NPV is positive, the investment is worthwhile. Otherwise, Dot should not purchase the machine.
Step-by-step explanation:
To determine whether Dot should purchase the new machine with a lifespan of five years that costs $50,000, we need to calculate the net present value (NPV) of the investment. The machine generates $80,000 in sales in year 1, which increases by 5% per annum. The cost of goods sold (COGS) is 60% of the sales, and the machine is depreciated using straight-line depreciation with no salvage value.
Here's the step-by-step calculation:
Calculate the annual sales growth for five years.
Calculate annual expenses based on COGS which is 60% of sales.
Determine the annual depreciation expense, which is $10,000.
Compute the annual profit before tax by subtracting annual expenses and depreciation from sales.
Calculate the annual tax by taking 40% of the profit before tax.
Compute the annual profit after tax by subtracting tax from the profit before tax.
Discount the annual profit after tax back to present value using the discount rate of 8.20%.
Sum up the discounted cash flows over the five years and subtract the initial machine cost to get the NPV.
If the NPV is positive, Dot should go ahead and purchase the machine. If it's negative, Dot should not purchase the machine as it does not cover the cost of capital.