Kingsport Container Company makes a single product with wide seasonal variations $in$ demand. The company uses a job order costing system and computes plantwide predetermined overhead rates $on$ a quarterly basis using the number $of$ units $tobe$ produced $as$ the allocation base. Its estimated costs, $by$ quarter, for the coming year are given below.

Quarter

Skipped:

Direct materials

Direct labor

Manufacturing overhead

Total manufacturing costs $(a)$

Number $of$ units $tobe$ produced $(b)$

Estimated unit product cost $(a)+(b)$

$ $200,000$

$80,000$

$230,000$

$510,000$

$120,000$

$4\mathrm{.}25$

Second

$ $100,000$

$40,000$

$206,000$

$ $346,000$

$60,000$

$ $5\mathrm{.}77$

Third

$ $50,000$

$20,000$

$194,000$

$ $264,000$

$30,000$

$ $8\mathrm{.}80$

Fourth.

$ $150,000$

$60,000$

$90,000$

$ $?$

Management finds the variation $in$ quarterly unit product costs $tobe$ confusing. Accordingly, you have been asked $to$ find a more appropriate way $of$ applying manufacturing overhead cost $to$ units $of$ product.

Required:

$1.$ Assuming the estimated variable manufacturing overhead cost per unit $is$ $$0\mathrm{.}40,$ what must $be$ the estimated total fixed manufacturing overhead cost per quarter?

$2.$ Assuming the assumptions about cost behavior from the first three quarters hold constant, what $is$ the estimated unit product cost for the fourth quarter?

$3.$ What $is$ causing the estimated unit product cost $to$ fluctuate from one quarter $to$ the next?

$4.$ Assuming the company computes one predetermined overhead rate for the year rather than computing quarterly overhead rates. calculate the unit product cost for all units produced during the year.