AB Ltd, which has a fairly full order book, is approached by a customer with the offer of a contract for a model that is a variant, in terms of dimensions and materials used, of one of its existing products.

Though the customer expects to pay a normal price for the model, he wants AB Ltd to take account of an 80 per cent learning curve in its price calculations; this level has been shown to be reasonable in AB Ltd's industry for relevant work.

The prospective contract is for a total of 464 units, made up of an initial order of 160 units, two subsequent orders of 80 units each, and three subsequent orders of 48 units each.

AB Ltd estimates the following costs for the initial order:

Direct materials:

P 8mm Q 12 kg Direct wages:

Dept 1

2 3

hr 4

50 15

$

3.50 perm 1.00 per kg per hr 1.25 1.50 1.00

$

Variable overhead: 20% of direct wages Fixed overhead rates, per hour Dept 1

2 3

$

2.00 1.00 0.80 The nature of the work in the three production departments is as follows:
Dept 1 Uses highly automatic machines Alth9ugh the operators on these machines need to be fairly skilled, their efficiency affects only the quality of the work but can have little impact on the quantity of this department's output which is largely machine controlled Dept 2 Partially mechanised Dept 3 An assembly department.
In both depts 2 and 3, the skill of operators is a major determinant of the volume of output.
The terms of the contract price allow for:
Direct materials cost plus Conversion cost plus REQUIRED

(a) Calculate the price per unit for:
(i) initial order of 160 units % profit margin 2-i 12-i (ii) second, third and fourth orders, if given successively but without guarantee offurther orders (iii) whole contract of six orders if given from the start, but on the same basis of production and delivery

(b) Discuss what factors should be considered in deciding whether the learning curve should be taken into account when setting standards for a standard costing system Note that an 80 per cent learning curve on ordinary graph paper would show the following relationship between the x axis (volume) andy axis (cumulative average price of elements subject to the learning curve):
X y X y % %
1.0 100 2.1 78.9 1.1 96.9 2.2 77.8 1.2 93.3 2.3 76.8 1.3 91.7 2.4 76.0 1.4 89.5 2.5 74.9 1.5 87.6 2.6 74.0 1.6 86.1 3.7 73.2 1.7 84.4 2.8 72.3 1.8 83.0 2.9 71.5 1.9 81.5 3.0 70.0 2.0 80.0 3.1 70.0