Question Two

Sandy Lands Ltd carries an item of inventory in respect of which the following data apply:

The fixed cost of ordering per batch is $10$;

The expected steady quarterly volume of sales is $3125$ units;

The cost of holding one unit stock for one year is $1.$

You are required to:

$($a$)$ Calculate the minimum annual cost of ordering and stocking the item.

$($b$)$ Calculate to the nearest whole number of units the optimal batch size if the expected steady quarterly

volume of sales:

first falls to $781$ units and second rises to $6250$ units

and to state the relationship between the rates

of change of sales and the optimal batch size.

$(5$ marks$)$

$($c$)$ Explain the basis of the derivation of the formula for the optimal batch size given below:

EBS$=\sqrt[\phantom{2}]{2C_o\frac{D}{Ch}}$

Question Three

A company had a budget of $200000$ direct labour hours for a period. This was used as the basis for

establishing standard factory overhead absorption rates. Fixed factory overhead was budgeted to be

$400000,$ and variable factory overhead $200000.$ Output was budgeted at $400000$ units.

In the period $420000$ units were completed in $202000$ direct labour hours, at a labour cost of $787800.$

No labour rate variance occurred. The factory overhead incurred during the period was $620000.$

Required:

$($a$)$ Calculate the following variances:

i$.$ labour efficiency;

ii$.$ overhead expenditure;

iii. fixed overhead volume;

iv$.$ variable overhead efficiency.

$($b$)$ Explain the meaning and significance of the fixed overhead volume variance. How may the fixed overhead

volume variance be further analyzed?

$($c$)($i$)$ Calculate the efficiency ratio in the situation outlined above.

$($ii$)$ What are the implications for both unit costs and profit of such efficiency?