Baird Company makes classic Polish sausage. The company uses a standard cost system to help control costs. Manufacturing overhead is applied to production on the basis of standard direct labor$-$hours. According to the company$$s planning budget, the following manufacturing overhead costs should be incurred at an activity level of $12,000$ labor$-$hours $($the denominator activity level$)$:

Variable manufacturing overhead cost $ $15,000$

Fixed manufacturing overhead cost $39,000$

Total manufacturing overhead cost $ $54,000$

During the most recent year, the following operating results were recorded:

Activity:

Actual labor$-$hours worked $9,000$

Standard labor$-$hours allowed for the actual output $10,000$

Cost:

Actual variable manufacturing overhead cost incurred $ $18,000$

Actual fixed manufacturing overhead cost incurred $ $30,000$

At the end of the year, the company$$s Manufacturing Overhead account contained the following data:

Manufacturing Overhead

Debit Credit

Actual $48,000$ Applied $45,000$

$3,000$

Management would like to determine the cause of the $$3,000$ underapplied overhead.

Required:

$1.$ Compute the predetermined overhead rate. Break the rate down into variable and fixed cost elements.

$2.$ Show how the $$45,000$ Applied figure in the Manufacturing Overhead account was computed.

$3.$ Break down the $$3,000$ underapplied overhead into four components: $(1)$ variable overhead rate variance, $(2)$ variable overhead efficiency variance, $(3)$ fixed overhead budget variance, and $(4)$ fixed overhead volume variance.