Xania Inc. uses a normal job$-$order costing system. Currently, a plantwide overhead rate based on machine hours is used. Xania's plant manager has heard that departmental overhead rates can offer significantly better cost assignments than a plantwide rate can offer. Xania has the following data for its two departments for the coming year:

Department A Department B

Overhead costs $($expected$)$ $$400,000$ $$200,000$

Normal activity $($machine hours$)10,0002,000$

Normal activity $($direct labor hours$)4,0002,000$

Required:

$1.$ Compute a predetermined overhead rate for the plant as a whole based on machine hours.

$2.$ Compute predetermined overhead rates for each department using machine hours for Department A and direct labor hours for Department B$.($Note: Carry your calculations out to the nearest dollar.$)$

$3.$ Job $73$ was composed of $1,000$ units; it has $$5,000$ of prime costs and used $40$ machine hours from Department A and $10$ machine hours from Department B; it used $20$ direct labor hours from Department A and $20$ direct labor hours from Department B$.$ Job $74$ was composed of $1,200$ units; it has $$6,000$ of prime costs and used $20$ machine hours from Department A and $40$ machine hours from Department B; it used $30$ direct labor hours from Department A and $20$ direct labor hours from Department B$.$ Compute the cost per unit from Job $73$ and Job $74$ using a plant$-$wide Overhead rate $($from #$1)$; then compute the cost per unit for Job $73$ and Job $74$ using a departmental Overhead rate $($from #$2).$ Be sure to show work $($hint: don$$t forget when computing cost per unit to include all manufacturing costs; hint $2$: find the total cost of the job under one method, and then divide by number made to find cost$/$unit; repeat for the different parts$).$

Job $73$ Plantwide

Job $73$ Departmental

Job $74$ Plantwide

Job $74$ Departmental

$4.$ Using a Plantwide from #$1,$ if actual machine hours for the year were $13,000$ hours and actual overhead costs were $$620,000,$ how much was overhead under$-$ or over$-$applied for the year and how would that affect Cost of Goods Sold when it is closed to that account.

$$$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_($amount$)$ over$-$applied$/$under$-$applied $($circle one$)$

Cost of Goods Sold increased$/$decreased $($circle one$)$