Final answer:
The firm would realize an increase in income by reducing its accounts receivable to 50 days. The annual increase would be the interest earned from investing the increase in cash at 7.5 percent.
Step-by-step explanation:
To calculate the annual increase in income, we need to find the difference in the number of days of accounts receivable. Currently, the firm has 90 days of net revenues, and it wants to reduce it to 50 days. So, the reduction in days is 90 - 50 = 40 days. Assuming the firm has 365 days in a year, the firm would realize an increase in income for 40/365 of its net revenues.
The increase in income would be calculated as:
Income increase = (40/365) * $45.0 million
To find how much the firm would earn if the increase in cash is invested at 7.5 percent, we need to calculate the interest earned:
Interest earned = 7.5% * Income increase
Therefore, the annual increase in income would be the interest earned from investing the increase in cash at 7.5 percent.