$15-8$ WORKING CAPITAL POLICY Rentz Corporation is investigating the optimal level of current assets for the coming year. Management expects sales to increase to approximately $$2$ million as a result of an asset expansion presently being undertaken. Fixed assets total $$1$ million, and the firm plans to maintain a $60\%$ debt ratio. Rentz's interest rate is currently $8\%$ on both short$-$term and longer$-$term debt $($which the firm uses in its permanent structure$).$ Three alternatives regarding the projected current asset level are under consideration: $(1)$ a tight policy where current assets would be only $45\%$ of projected sales, $(2)$ a moderate policy where current assets would be $50\%$ of sales, and $(3)$ a relaxed policy where current assets would be $60\%$ of sales. Earnings before interest and taxes should be $12\%$ of total sales, and the federal$-$plus$-$state tax rate is $40\%.$

a$.$ What is the expected return on equity under each current asset level?

b$.$ In this problem, we assume that expected sales are independent of the current asset policy. Is this a valid assumption? Why or why not?

c$.$ How would the firm's risk be affected by the different policies?