Accounts receivable changes without bad debts Tara's Textiles currently has credit sales of $$360$ million per year and an average collection period of $59$ days. Assume that the price of Tara's products is $$60$ per unit and that the variable costs are $$55$ per unit. The firm is considering an accounts receivable change that will result in a $20\mathrm{.}4\%$ increase in sales and a $19\mathrm{.}9\%$ increase in the average collection period. No change in bad debts is expected. The firm's equal$-$risk opportunity cost on its investment in accounts receivable is $13\mathrm{.}5\%.($Note: Use a $365-$day year.$)$

a$.$ Calculate the additional profit contribution from new sales that the firm will realize if it makes the proposed change.

b$.$ What marginal investment in accounts receivable will result?

c$.$ Calculate the cost of the marginal investment in accounts receivable.

d$.$ Should the firm implement the proposed change? What other information would be helpful in your analysis?