Chapter 9, Problem 18E

Determining Actual, Standard Costs, and Variances

For each of the following independent cases, fill in the missing amounts:

 

To determine

Concept introduction:

Rate variance:

It is referred to the amount which is computed by multiplying the number of actual hours with the difference between actual rate and standard rate per hour of direct labour.

Time variance:

It is referred to the amount which is computed by multiplying the standard rate per hours with the difference between the number of actual hours and standard hours of direct labour.

Direct labour spending variance:

This is calculated by combining material price variance and material quantity variance.

To compute:

The missing values for direct labor variances.

Answer to Problem 18E

Particulars	Casey Co.	Kevin Inc.	Jess Co.	Valerie Inc.
Unit produced	$2,000$	$1,000$	$120$	$1,500$
Standard hours per unit	$3.5$	$0.9$	$2.5$	$3$
Standard hours	$7,000$	$900$	$300$	$4,500$
Standard rate per hour	$\$14.5$	$\$10.2$	$\$10.50$	$\$7$
Actual hours worked	$6,800$	$975$	$280$	$4,900$
Actual labor cost	$\$96,900$	$\$8,970$	$\$3,090$	$\$31,850$
Direct labor rate variance	$\$1,700\text{F}$	$\$975\text{F}$	$\$150\text{U}$	$\$2,450\text{F}$
Direct labor efficiency variance	$\$2,900\text{F}$	$\$765\text{U}$	$210\text{F}$	$\$2,800\text{U}$

Explanation of Solution

Casey Co.

Calculation of standard hours

Unit produced $=2,000\text{units}$

Standard hours per unit $=3.5\text{hrs}$

Standard hours $=2,000\text{units}\times \text{3}\text{.5hrs}=7,000\text{hrs}$

Calculation of direct labour efficiency variance:

Standard hours $=7,000\text{hours}$

Actual hours $=6,800\text{hours}$

Standard rate per hour $=\$14.50$

$\begin{array}{c}\text{Direct labour efficiency variance=}\left(\text{SH}-\text{AH}\right)\times \text{SR}\\ \text{=}\left(7,000-6,800\right)\times \$14.50\\ =2,900\text{F}\end{array}$

Calculation of Actual Labour cost:

$\begin{array}{c}\text{Direct labour rate variance}=\text{AH}\times \left(\text{SR}-\text{AR}\right)\\ 1,700=6,800\times \left(14.50-\text{X}\right)\\ 1,700=98,600-6,800\text{X}\\ \text{1,700}-98,600=-6,800\text{X}\\ \text{X=}\frac{\$96,900}{6,800\text{hrs}}\\ \text{X}=\$14.25\end{array}$

Labour rate per hour is $\$14.25$.

Where,

$\begin{array}{c}\text{Actual labour cost}=\text{Actual hours worked}\times \text{Actual labour rate per hour}\\ =6,800\text{hrs}\times \text{\$14}\text{.25}\\ =\text{\$}96,900\end{array}$

Kevin Inc.

Calculation of units produced

Standard hours $=900\text{hours}$

Standard hours per unit $=0.9\text{hr}$

Unit produced $=900\text{hrs}÷0.9\text{hr}=1,000\text{units}$

Calculation of standard rate per hour

Standard hours $=900\text{hours}$

Actual hours $=975\text{hours}$

Direct labour efficiency variance $=\$765\text{U}$

Let standard rate per hour = X

$\begin{array}{c}\text{Direct labour efficiency variance}=\left(\text{SH}-\text{AH}\right)\times \text{SR}\\ -765=\left(900-975\right)\times \text{X}\\ -765=900\text{X}-975\text{X}\\ -765=-75\text{X}\\ \text{X=}765÷75\\ \text{X}=10.2\end{array}$

Calculation of Actual Labour cost:

Actual hours $=975\text{hrs}$

Standard rate per hour $=\$10.2$

Direct labour rate variance $=975\text{F}$

Let actual rate per hr be X

$\begin{array}{c}\text{Direct labour rate variance}=\text{AH}\times \left(\text{SR}-\text{AR}\right)\\ 975=975\times \left(10.2-\text{X}\right)\\ 975=9,945-975\text{X}\\ 975-9,945=-975\text{X}\\ -8,970=-975\text{X}\\ \text{X=}\frac{\$8,970}{975\text{hrs}}\\ \text{X}=\$9.2\end{array}$

Labour rate per hour is $\$9.2$.

Where,

$\begin{array}{c}\text{Actual labour cost}=\text{Actual hours worked}\times \text{Actual labour rate per hour}\\ \text{=}975\text{hrs}\times \text{\$}9.2\\ \text{=\$}8,970\end{array}$

Jess co.

Calculation of standard hour per unit:

Units produced $=120\text{units}$

Standard hours $=300\text{hrs}$

$\begin{array}{c}\text{Standard hour per unit}=\frac{\text{Standard hours}}{\text{Number of units produced}}\\ =\frac{300\text{hrs}}{120\text{units}}\\ =2.5\text{hr per unit}\end{array}$

Calculation of actual hours worked:

Direct labour rate variance $=150\text{U}$

Actual labour cost $=\$3,090$

Standard rate per hour $=\$10.50$

Actual hours $=\text{X}$

$\begin{array}{c}\text{Direct labour rate variance}=\text{AH}\times \left(\text{SR}-\text{AR}\right)\\ -150=\text{X}\times 10.50-3,090\\ -150=10.50\text{X}-3,090\\ 2,940\text{=}10.50\text{X}\\ \text{X=}\frac{\$2,940}{10.50\text{hrs}}\\ \text{X}=\$280\end{array}$

So, Actual hour is $\$280$.

Calculation of direct labour efficiency variance:

Standard hours $=300\text{hours}$

Actual hours $=280\text{hours}$

Standard rate per hour $=\$10.50$

$\begin{array}{c}\text{Direct labour efficiency variance=}\left(\text{SH}-\text{AH}\right)\times \text{SR}\\ \text{=}\left(300-280\right)\times \$10.50\\ =210\text{F}\end{array}$

So, direct labour efficiency variance is $210\text{F}$.

Valerie Inc.

Calculation of standard hours:

Actual hours $=4,900\text{hours}$

Standard rate per hour $=\$7$

Direct labour efficiency variance $=\$2,800\text{U}$

Standard hours = X

$\begin{array}{c}\text{Direct labour efficiency variance=}\left(\text{SH}-\text{AH}\right)\times \text{SR}\\ -2,800\text{=}\left(\text{X}-4,900\right)\times 7\\ -2,800=7\text{X}-34,300\\ 7\text{X}=31,500\\ \text{X}=31,500÷7\\ \text{X}=4,500\end{array}$

So, Standard hour is $4,500\text{Hours}$

Calculation of standard hour per unit:

Units produced $=1500\text{units}$

Standard hours $=4,500\text{hrs}$

$\begin{array}{c}\text{Standard hour per unit}=\frac{\text{Standard hours}}{\text{Number of units produced}}\\ =\frac{4,500\text{hrs}}{1500\text{units}}\\ =3\text{hr per unit}\end{array}$

So, Standard hour per unit is $3\text{hr}$

Calculation of direct labour rate variance:

Actual hours $=4,900\text{hours}$

Standard rate per hour $=\$7$

Actual rate per hour $=\$31,850÷4,900=\$6.5$

$\begin{array}{c}\text{Direct labour rate variance}=\text{AH}\times \left(\text{SR}-\text{AR}\right)\\ =4,900\times \left(\$7-\$6.5\right)\\ =\$2,450\text{F}\end{array}$

So, Direct labour rate variance is $\$2,450\text{F}$.