Question

KUMA makes three products X, Y, and Z. All three products must be offered for sale each month in order to provide a complete market service. The products are fragile and their quality deteriorates rapidly once they are manufactured.

The products are produced on two types of machine and worked on by a single grade of direct labour. Five direct employees are paid Ghc 8 per hour for a guaranteed minimum of 160 hours each per month.

All of the products are first molded on a machine type 1 and then finished and sealed on a machine type 2.

The machine hours requirements for each of the products are as follows.

		Produce X	Product Y	Product Z
		Hours per unit	Hours per unit	Hours per unit
Machine type 1		1.5	4.5	3.0
Machine type 2		1.0	2.5	2.0

The capacity of the available machine type 1 and 2 are 600 hours and 500 hours per month respectively.

Details of the selling price, unit cost and monthly demand for the three products are as follows

Product H		Product Y		Product C
Ghc per unit		Ghc per unit		Ghc per unit
Selling price                                       91		174		140
Component cost                                  22		19		16
Other direct material cost                   23		11		14
Direct labour cost at per hour             6		48		36
Overheads                                           24		62		52
Profit                                                   16		34		22
Maximum monthly demand units    120		70		60

Although KUMA uses marginal costing and contribution analysis as the basis for its decisionmaking activities, profits are reported in the monthly management accounts using the absorption costing basis. Finished goods inventories are valued in the monthly management accounts at full absorption cost.

Required:

1. Calculate the machine utilization rate for each machine each month and explain which of the machine is the bottleneck/limiting factor                                           (7 marks)
2. Using the current system of marginal costing and contribution analysis, calculate the profit maximizing monthly output of the three products.                               (8 marks)

Answer 1

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a) Machine utilisation rate:-

	Product H	Product Y	Product C	Totals
Selling Price	91	174	140	in Ghc
Component Cost	22	19	16	in Ghc
Other Direct Material	23	11	14	in Ghc
Direct Labour Cost at per hour	6	48	36	in Ghc
Overheads	24	62	52	in Ghc
Profit	16	34	22	in Ghc
Maximum monthly demand units	120	70	60	units
Direct labour man hours per unit	0.75	6	4.5	Hours
Labour hours at maximum demand	90	420	270	780
Total 780 hours is less than 160 * 5 = 800 minimum hours to be paid.
Hence, Labour cost is fixed and irrelevant for decision making.
Overheads are also based on absorption concept and assumed to be fixed and irrelevant for deicison making
Machine hours for type 1/ unit	1.5	4.5	3
Machine hours at max production	180	315	180	675
Machine utilisation rate is 675/600 = 112.50% which represents a bottleneck as only 600 hours are available
And to fulfill the maximum demand level, we need 675 hours of machine 1 to be available.
Machine hours for type 2/ unit	1	2.5	2
Machine hours at max production	120	175	120	415
Machine utilisation rate is 415/500 = 83% which represents excess capacity available.
b) Contribution Analysis using only relevant costs
Selling Price	91	174	140	in Ghc
Component Cost	22	19	16	in Ghc
Other Direct Material	23	11	14	in Ghc
Contribution	46	144	110	in Ghc
Machine hours for type 1/ unit	1.5	4.5	3
Contribution per hour of machine 1	30.66667	32	36.66667
Ranking for use	3rd rank	2nd rank	1st rank
No. of units to be produced	70	70	60
Total time of Machine 1 used for units produced	105	315	180	600
Contribution (Machine hrs * Contr per hr of mach 1)	3220	10080	6600	19900