Kingsport Containers Company makes a single product that is subject to 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 to be produced as the allocation base. Its estimated costs, by quarter, for the coming year are given below:

Quarter

First Second Third Fourth

Direct materials $ $200,000$ $ $100,000$ $ $50,000$ $ $150,000$

Direct labor $80,00040,00020,00060,000$

Manufacturing overhead $230,000206,000194,000?$

Total manufacturing costs $($a$)$ $ $510,000$ $ $346,000$ $ $264,000$ $ $?$

Number of units to be produced $($b$)120,00060,00030,00090,000$

Estimated unit product cost $($a$)-$: $($b$)$ $ $4\mathrm{.}25$ $ $5\mathrm{.}77$ $ $8\mathrm{.}80$ $ $?$

Management finds the variation in quarterly unit product costs to be confusing. It has been suggested that the problem lies with manufacturing overhead because it is the largest element of total manufacturing cost. Accordingly, you have been asked to find a more appropriate way of assigning 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.