$5-38$ At December $31,2021,$ EarthWear has $$5,890,000$ in a liability account labeled "Reserve for returns." The footnotes to the financial statements contain the following policy: $"$At the time of sale, the company provides a reserve equal to the gross profit on projected merchandise returns, based on prior returns experience." The entity has indicated that returns for sales that are six months old are negligible, and gross profit percentage for the year is $42\mathrm{.}5$ percent. The entity has also provided the following information on sales for the last six months of the year:

$\backslash$table$[[$Month$,$Monthly Sales $(000$s$),$Historical Return Rate$],[$July$,$$$73,300,\mathrm{.}004],[$August$,82,800,\mathrm{.}006],[$September$,93,500,\mathrm{.}010],[$October$,110,200,\mathrm{.}015],[$November$,158,200,\mathrm{.}025],[$December$,202,500,\mathrm{.}032]]$

Required:

a$.$ Using the information given, develop an expectation for the reserve for returns account. Because the rate of return varies based on the time that has passed since the date of sale, do not use an average historical return rate.

b$.$ Determine a tolerable difference for your analytical procedure.

c$.$ Compare your expectation to the book value and determine if it is greater than tolerable difference.

d$.$ Independent of your answer in part $($c$),$ what procedures should the auditor perform if the difference between the expectation and the book value is greater than tolerable misstatement?