MA – L2 – Q34 – Relevant cost and revenue

KK Enterprises has received an enquiry from a customer for the supply of 500 units of a new product, Product M22. Negotiations on the final price to charge the customer are in progress and the sales manager has asked you to supply relevant cost information.
The following information is available:

(1) Each unit of Product M22 requires the following raw materials:

Raw material type Quantity
X 4 kg
Y 6 kg

(2) The company has 5,000 kg of material X currently in stock. This was purchased last year at a cost of GH¢7 per kg. If not used to make Product M22, this inventory of X could either be sold for GH¢7.50 per kg or converted at a cost of GH¢1.50 per kg, so that it could be used as a substitute for another raw material, material Z, which the company requires for other production. The current purchase price per kilogram for materials is GH¢9.50 for material Z and GH¢8.25 per kg for material X.

(3) There are 10,000 kilograms of raw material Y in inventory, valued on a FIFO basis at a total cost of GH¢142,750. Of this current inventory, 3,000 kilograms were purchased six months ago at a cost of GH¢13.75 per kg. The rest of the inventory was purchased last month. Material Y is used regularly in normal production work. Since the last purchase of material Y a month ago, the company has been advised by the supplier that the price per kilogram has been increased by 4%.

(4) Each unit of Product M22 requires the following number of labour hours in its manufacture:

Type of labour Hours
Skilled 5
Unskilled 3

Skilled labour is paid GH¢8 per hour and unskilled labour GH¢6 per hour.

(5) There is a shortage of skilled labour, so that if production of M22 goes ahead it will be necessary to transfer skilled workers from other work to undertake it. The other work on which skilled workers are engaged at present is the manufacture of Product M16. The selling price and variable cost information for M16 are as follows:

GH¢ per unit
Selling price 100
Less: variable costs of production
Skilled labour (3 hours) 24
Other variable costs 31
55
Contribution 45

(6) The company has a surplus of unskilled workers who are paid a fixed wage for a 37-hour week. It is estimated that there are 900 hours of unused unskilled labour time available during the period of the contract. The balance of the unskilled labour requirements could be met by working overtime, which is paid at time and a half.

(7) The company absorbs production overheads by a machine hour rate. This absorption rate is GH¢22.50 per hour, of which GH¢8.75 is for variable overheads and the balance is for fixed overheads. If production of Product M22 is undertaken, it is estimated that an extra GH¢4,000 will be spent on fixed costs. Spare machining capacity is available and each unit of M22 will require two hours of machining time in its manufacture using the existing equipment. In addition, special finishing machines will be required for two weeks to complete the M22. These machines will be hired at a cost of GH¢2,650 per week, and there will be no overhead costs associated with their use.

(8) Cash spending of GH¢3,250 has been incurred already on development work for the production of M22. It is estimated that before production of the M22 begins, another GH¢1,750 will have to be spent on development, making a total development cost of GH¢5,000.

Required:
Calculate the minimum price that the company should be prepared to accept for the 500 units of Product M22. Explain briefly but clearly how each figure in the minimum price calculation has been obtained.
(Note: The minimum price is the price that equals the total relevant costs of producing the items. Any price in excess of the minimum price will add to total profit).

Workings for relevant costs

Material X
The company has enough kilograms of material X in inventory for the contract. When it is used, the inventory of material X will not be replaced. The relevant cost of the material is therefore its opportunity cost, not its replacement cost. The opportunity cost is the higher of its current sale value (GH¢7.50 per kg) or the net saving obtained if it is used as a substitute for material Z (GH¢9.50 – GH¢1.50 = GH¢8 per kg). The relevant cost of material X is therefore GH¢8 per kg.

Material Y
Material Y is in regular use, so its relevant cost is its current replacement cost.

kg GH¢
Total inventory 10,000 142,750
Purchased six months ago 3,000 41,250
Purchased last month 7,000 101,500

Purchase price last month = GH¢101,500 / 7,000 kg = GH¢14.50 per kg.
Current purchase price = 4% higher = GH¢14.50 × 1.04 = GH¢15.08.

Skilled labour
Skilled labour is in short supply. If it is used to make Product M22, workers will have to be taken off other work. The relevant cost of skilled labour is the wages for the skilled workers for the time spent on M22, plus the lost contribution (net of skilled labour cost) from not being able to make units of Product M16.
Opportunity cost of skilled labour
Skilled labour cost per unit of Product M16 = GH¢24
Number of hours per unit = 3 hours
Contribution per unit of M16 = GH¢45
Contribution per skilled labour hour from M16 = GH¢15
Opportunity cost of skilled labour if it is used to make M22 = (500 × 5) × GH¢15 = GH¢37,500

Unskilled labour
900 unskilled labour hours will be available at no incremental cost to the company (as it is already being paid and is not fully employed). There is no relevant cost for these hours. The additional 600 hours required will involve extra wage payments, including overtime payments. The relevant cost of these 600 hours is GH¢6 per hour × 150% = GH¢9 per hour, including the overtime premium.

Overheads
Variable overheads are included as relevant costs because they will be additional costs if the units of M22 are made. The only incremental fixed costs, however, are the extra cash costs of GH¢4,000. The fixed overhead absorption rate is ignored. The additional costs of hiring special finishing machinery are also included as a relevant cost.

Development costs
Those costs already incurred are past costs (sunk costs) and are not relevant. The future development costs involve additional expenditure and are included as relevant costs.

Minimum price for making 500 units of M22

Materials: GH¢
X (500 units × 4 kg) × GH¢8 16,000
Y (500 units × 6 kg) × GH¢15.08 45,240
Labour:
Skilled wages (500 units × 5 hours) × GH¢8 20,000
Opportunity cost (500 units × 5 hours) × GH¢15 37,500
Unskilled [(500 × 3) – 900] × 6 × 1.5 5,400
Overheads:
Variable (500 units × 2 hours) × GH¢8.75 8,750
Fixed Incremental spending 4,000
Machine hire (2 weeks × GH¢2,650) 5,300
Development costs 1,750
Minimum price 143,940