You have been asked to estimate the optimal working capital, as a percent of revenues, for an auto-parts manufacturing firm that currently maintains a net working capital of 10% of revenues. The firm currently has revenues of $100 million and after-tax operating income of $10 million, and it expects the latter to grow 5% a year in perpetuity. The current cost of capital is 11%. The following table provides estimates of growth and costs of capital at different levels of working capital, ranging from 0% to 100%:

a. Estimate the value of the firm at the current working capital ratio.

b. Estimate the optimal working capital proportion for this firm.

c. What would the optimal working capital proportion for this firm be if the cost of capital were unaffected by the changes in working capital?

Working Capital as % of Revenue 0 10 20 30 40 50 60 70 80 90 100 Expected Growth (%) 4.75 5.00 5.20 5.35 5.45 5.50 5.54 5.55 5.55 5.55 5.55 Cost of Capital (%) 10.90 11.00 11.11 11.23 11.36 11.50 11.65 11.80 11.95 12.10 12.35 the current work