Initial investment: Basic calculation Cushing Partners is considering the purchase of a new grading machine to replace the existing one. The existing machine was purchased $3$ years ago at an installed cost of $$20,000$; it was being depreciated under MACRS, using a $5-$year recovery period. $($See Table $4\mathrm{.}2$ for the applicable depreciation percentages.$)$ The existing machine is expected to have a usable life of at least $5$ more years. The new machine costs $$35,000$ and requires $$5,000$ in installation costs; it will be depreciated using a $5-$year recovery period under MACRS. The existing machine can currently be sold for $$25,000$ without incurring any removal or cleanup costs. The firm is subject to a $40\%$ tax rate. Calculate the initial investment associated with the proposed purchase of a new grading machine.

Table $4\mathrm{.}2$

Percentage by recovery year Tax rate

Recovery year $3$ years $5$ years $7$ years $10$ years $40\%$

$133\%20\%14\%10\%$

$245\%32\%25\%18\%$

$315\%19\%18\%14\%$

$47\%12\%12\%12\%$

$512\%9\%9\%$

$65\%9\%8\%$

$79\%7\%$

$84\%6\%$

$96\%$

$106\%$

$114\%$

Totals $100\%100\%100\%100\%$