Temple Limited has been offered two new contracts, the details of which are as follows:

Question

	(1)	(2)
	£000	£000
Contract price	1000	2100
Direct materials	300	600
Direct labour	300	750
Variable overhead	100	250
Fixed overhead	100	200
800		1800
Profit	200	300
Direct materials required (kilos)	50000	100000
Direct labour hours required	10000	25000

Note:
The fixed overhead has been apportioned on the basis of direct labour cost. Temple is a one-product firm. Its budgeted cost per unit for its normal work for the year to 31 December 2018 is summarised below.

	£
Sales	6000
Direct materials (100 kilos)	700
Direct labour (200 hours)	3000
Variable overhead	300
Fixed overhead	1000
5000
Profit	1000

The company would only have the capacity to accept one of the new contracts.
Unfortunately, materials suitable for use in all of its work are in short supply and the company has estimated that only 200,000 kilos would be available during the year to December 2018. Even more worrying is the shortage of skilled labour, only 100,000 direct labour hours are expected to be available during the year. The good news is that there may be an upturn in the market for its normal contract work.

Required:
Calculate

(a) the contribution per unit of each limiting factor for
(i) the company’s normal work
(ii) Contract 1
(iii) Contract 2.
(b) The company’s maximum contribution for the year to 31 December 2018, assuming that it accepts either Contract 1 or Contract 2.

Accepted Answer

Contributions for Temple Limited:

(a) Calculation of the contribution per unit of limiting factor

(i) Normal work:

	£
Sales	6000
Direct materials (100 kilos)	700
Direct labour (200 hours)	3000
Variable overhead	300
4000
Contribution	2000

Contribution per unit of key factor:

[latex]Direct materials:\frac{£2000}{100 kilos} =£20 per kilo[/latex]

Direct labour:

[latex]\frac{£2000}{200 direct labour hours} =£10 per direct labour hour[/latex]

(ii) and (iii) Calculation of the contribution per unit of limiting factor for each of the proposed two new contracts:

	Contract 1	Contract 2
	£000	£000
Contract price	1000	2100
Less: Variable costs
Direct materials	300	600
Direct labour	300	750
Variable overhead	100	250
700		1600
Contribution	300	500
Contribution per unit of key factor:
Direct materials	£300	£500
	50 kilos	100 kilos
	= £6 per kilo	£5 per kilo
Direct labour	£300	£500
	10 DLH	25 DLH
	= £30 per DLH	£20 per DLH

Summary of contribution per unit of limiting factor:

	Direct materials	Direct labour
	£	£
Normal work	20	10
Contract 1	6	5
Contract 2	30	20

(b) Calculation of the total maximum contribution

Contract 1
If Contract 1 is accepted, it will earn a total contribution of £300,000. This will leave 150,000 kilos of direct material available for its normal work (200,000 kilos maximum available, less the 50,000 used on Contract 1). This means that 1,500 units of ordinary work could be undertaken (150,000 kilos divided by 100 kilos per unit).

However, Contract 1 will absorb 10,000 direct labour hours, leaving 90,000 DLH available (100,000 DLH less 10,000 DLH). As each unit of ordinary work uses 200 DLH, the maximum number of units that could be undertaken is 450 (90,000 DLH divided by 200 DLH). Thus the maximum number of units of ordinary work that could be undertaken if Contract 1 is accepted is 450 and NOT 1500 units if direct materials were the only limiting factor. As each unit makes a contribution of £2000, the total contribution would be £900,000 (450 units × £2000).

The total maximum contribution, if Contract 1 is accepted, is therefore, £1,200,000 (£300,000 + 900,000).

Contract 2
If Contract 2 is accepted, only 100,000 kilos of direct materials will be available for ordinary work (200,000 kilos maximum available less 100,000 required for Contract 2). This means that only 1000 normal jobs could be undertaken (100,000 kilos divided by 100 kilos required per unit).

Contract 2 would absorb 25,000 direct labour hours, leaving 75,000 available for normal work (100,000 maximum DLH less the 25,000 DLH used by Contract 2). As each unit of normal work takes 200 hours, only 375 units could be made (75,000 DLH divided by 200 DLH per unit). If this contract is accepted, 375 is the maximum number of normal jobs that could be undertaken. This would give a total contribution of £750,000 (375 units multiplied by £2000 of contribution per unit).

If Contract 2 is accepted, the total maximum contribution would be £1,250,000, i.e. Contract 2’s contribution of £500,000 plus the contribution of £750,000 from the normal work.

The decision
Accept Contract 2 because the maximum total contribution would be £1,250,000 compared with the £1,200,000 if Contract 1 was accepted.

Tutorial notes
1 The various cost relationships are assumed to remain unchanged at all levels of activity.
2 Fixed costs will not be affected irrespective of which contract is accepted.
3 The market for Temple’s normal sales is assumed to be flexible.
4 Contract 2 will absorb one-half of the available direct materials and one-quarter of the available direct labour hours. Would the company want to commit such resources to work that may be uncertain and unreliable and that could have an adverse impact on its normal customers?

Question 18.TQ.5 : Temple Limited has been offered two new contracts, the detai...

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