Noelle's diamond ring was stolen in 2017. She originally paid $13,000 for the ring, but it was worth considerably more at the time of the theft. Noelle filed an insurance claim for the stolen ring, but the claim was denied. Because the insurance claim was denied, Noelle took a casualty loss for the stolen ring on her 2017 tax return. In 2017, Noelle had AGI of $65,000. After Noelle threatened legal action, in early 2019, the insurance company had a "change of heart" and sent Noelle a check for $7,800 for the stolen ring. The per-event floor is $100.

What is the proper tax treatment of the $5,000 Noelle received from the insurance company in 2019?

You are the manager of a large crude-oil refinery. as part of the refining process, a certain heat exchanger (operated at high temperatures and with abrasive material flowing through it) must be replaced every year. the replacement and downtime cost in the first year is $165 comma 000. this cost is expected to increase due to inflation at a rate of 7% per year for six years (i.e. until the eoy 7), at which time this particular heat exchanger will no longer be needed. if the company's cost of capital is 15% per year, how much could you afford to spend for a higher quality heat exchanger so that these annual replacement and downtime costs could be eliminated?