$3)$ In March $2023,$ Paul purchased for $$83,500$ a new machine to use in an existing production line of his manufacturing business. Assume that the machine is a unit of property and is not a material or supply. Paul pays $$5,775$ to install the machine, and after the machine is installed, he pays $$2,750$ to perform a critical test on the machine to ensure that it will operate in accordance with quality standards. On November $2023,$ the machine fails the critical test, and another critical test is done. He pays $$3,000$ for that test. On January $2024$ the machine finally passes the test. On January $15,$ Paul pays $$2,400$ to insure the machine for the year. On the same date, he also pays $$2,400$ for a maintenance service contract for the machine. In February $2024,$ Paul places the machine in service on the production line.

a$)$ How much will Paul be required to capitalize on the cost of the machine?

b$)$ When can Paul start depreciating the machine? Why?

c$)$ Paul decides to sell the machine March $2026$ for $$70,000.$ What is the amount of Paul$$s taxable gain$/$loss on the sale of the asset. Assume the Machine is $7$ year property.

d$)$ What is the character of the gain$/$loss$?$ Why?