$(1)$ Using data in the exhibits, determine the cost of a $100-$unit batch of model BAC$-29,$ a month$$s spare parts, and a month$$s work done for other divisions under the present method, Sandy$$s first proposal, and her revised proposal.

$(2)$ Are the cost differences among the methods significant? What causes these differences?

$(3)$ Assume that producing a batch of $100$ model BAC$-29$ injectors requires $126$ hours, distributed by department as shown in Exhibit $3,$ and $$4,200$ worth of materials. BAC sells these carburetors for $$115$ each. Determine if this would be profitable at gross profit level? $($Answer using both the present and Sandy$$s first proposed costing methods$).$

$(4)$ What benefits, if any, do you see to BAC if either of the proposed costing method is adopted? Consider this question from the standpoint of $($a$)$ product pricing, $($b$)$ cost control, $($c$)$ measuring departmental performance, and $($d$)$ diagnostic use of cost data. What do you think BAC should do regarding their costing procedures?

$(5)$ Are there any similarities between either of the proposed costing method and activity based costing? Justify your answers with appropriate explanations.

Exhibits

Exhibit $1$: Calculation of plant$-$wide labour and overhead hourly rates for July

Department Amount $($$$)$ Hours

Labour

Casting and stamping $54,6042,528$

Grinding $38,5202,140$

Machining $191,8767,675$

Custom work $81,6643,712$

Assembly $291,78415,357$

Total labour $658,44831,412$

Overheads $1,099,321$

Total labour and overheads $1,757,769$

Hourly rates $$20\mathrm{.}96$

Overheads $$35\mathrm{.}00$

Total $$55\mathrm{.}96$

Exhibit $2$: Proposed departmental labour and overhead hourly rates

Department Per hour rates $($$$)$ Total

Overheads

Labour Overheads Total

Casting and stamping $21\mathrm{.}6031\mathrm{.}3752\mathrm{.}9779,303$

Grinding $18\mathrm{.}0030\mathrm{.}1448\mathrm{.}1464,500$

Machining $25\mathrm{.}0062\mathrm{.}5287\mathrm{.}52479,841$

Custom work $22\mathrm{.}0040\mathrm{.}4862\mathrm{.}48150,262$

Assembly $19\mathrm{.}0021\mathrm{.}1940\mathrm{.}19325,415$

$1,099,321$

Exhibit $3$: Direct labour$-$hour distribution for three CFI division activities

Department BAC$-29$ Spare parts for inventory Work for other

Divisions

$($Hours per batch of $100$ units$)($Hours per typical month$)($Hours per typical month$)$

Casting and

Stamping

$21$

$304$

$674$

Grinding $12270540$

Machining $581,1152,158$

Custom work $---$

Assembly $35--$

$1261,6893,372$

Exhibit $4$: Departmental Overhead rates based on normal volume

Department Normal volume $($labour hours$)$ Normal overhead cost$*($$$)$ Overhead per direct labour hour $($$$)$

Casting and stamping $2,50078,80031\mathrm{.}52$

Grinding $2,40069,00028\mathrm{.}75$

Machining $8,000492,00061\mathrm{.}50$

Custom work $3,600147,82041\mathrm{.}06$

Assembly $17,500352,45020\mathrm{.}14$

Total $/$

Average $34,0001,140,07033\mathrm{.}53$

$*$ Estimated overhead cost if each department operates at its normal volume

With proper calculations