The labs department of a local hospital is debating on whether or not to purchase a new centrifuge with a larger capacity than the current one they own. The new centrifuge costs $31,000, but it will save the hospital an average of $4,500 each year. The centrifuge has an expected lifespan of 8 years. The savings are to be realized at the end of each year. Using a 4% discount factor, perform a cost-benefit analysis to determine if the hospital should purchase the new centrifuge. Would your answer change if the discount factor is increased to 6%?