Final answer:
The initial investment for the new high-powered microscopy machine is calculated as the sum of the cost of the new machine and installation expenses, minus the net proceeds from the sale of the old equipment after taxes, adjusted by the net change in working capital. The resulting initial investment amounts to $328,400.
Step-by-step explanation:
To calculate the initial investment in the high-powered microscopy machine, we need to incorporate various costs and proceeds from the sale of the old equipment. The initial cost of the new machine is $385,000 and installation expenses are $31,600. The old equipment can be sold for $116,200, but this sale will incur $42,900 in taxes due to the gain on the sale. Additionally, current assets will increase by $20,000 and current liabilities by $5,100 due to this transaction.
The initial investment is hence the cost of the new machine and installation, minus the proceeds from the sale of the old equipment after taxes, adjusted for the changes in working capital. Therefore, the calculation would be: Initial cost of new machine ($385,000) plus installation expenses ($31,600) minus net proceeds from the sale of old equipment ($116,200 - $42,900) minus the net increase in working capital ($20,000 - $5,100).
The initial investment for the new microscopy machine would then be $385,000 + $31,600 - ($116,200 - $42,900) - ($20,000 - $5,100) = $385,000 + $31,600 - $73,300 - $14,900 = $328,400.