Brookdale Chemicals: Material Mix and Yield Variances
Brookdale Chemicals blends two materials, A and B, to make a fertiliser. The standard mix for 1,000 kg of input is 600 kg of A at £4 per kg and 400 kg of B at £7 per kg. The standard yield is 90%, so 1,000 kg of input should produce 900 kg of finished fertiliser.
In November, Brookdale produced 4,800 kg of fertiliser. It used 3,300 kg of A, costing £13,530, and 2,100 kg of B, costing £15,120. The production manager is pleased because the actual cost per kg of input was below the standard weighted average. The sales manager is concerned that the yield seems low. The standard mix is set by the technical director and has not been reviewed for two years, despite a change in supplier and a new blending machine. Operators are paid a bonus based on output volume, not input efficiency.
1. Calculate the material price, mix and yield variances for November and reconcile them to the total material cost variance. Show workings.
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Standard cost of 900 kg output = (600 × £4) + (400 × £7) = £2,400 + £2,800 = £5,200. Standard cost per kg output = £5,200 / 900 = £5.7778. Standard input per kg output = 1 / 0.9 = 1.1111 kg. Standard input for 4,800 kg = 4,800 / 0.9 = 5,333.33 kg, split A 3,200 kg and B 2,133.33 kg.
Price variance: A (4.00 − 4.10) × 3,300 = £330 adverse; B (7.00 − 7.20) × 2,100 = £420 adverse; total £750 adverse. Mix variance: actual total input 5,400 kg. Standard mix of 5,400 = A 3,240 kg, B 2,160 kg. (3,300 − 3,240) × £4 + (2,100 − 2,160) × £7 = £240 − £420 = £180 favourable. Yield variance: actual output 4,800 vs standard output from actual input 5,400 × 0.9 = 4,860; shortfall 60 kg × £5.7778 = £346.67 adverse. Or (5,333.33 − 5,400) × £5.20 = £346.67 adverse. Total = £750 adverse + £180 favourable + £346.67 adverse = £916.67 adverse. Check: actual cost £13,530 + £15,120 = £28,650; standard cost of actual output 4,800 × £5.7778 = £27,733.33; difference £916.67 adverse.
2. Interpret the mix and yield variances. What operational or behavioural factors could explain them, and who should be held responsible?
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The mix variance is favourable because Brookdale used more of the cheaper material A (3,300 kg vs 3,240 kg standard) and less of the expensive B. But the yield variance is adverse: the actual input produced only 4,800 kg instead of 4,860 kg. The net effect of mix and yield is £180 favourable − £346.67 adverse = £166.67 adverse. So the cheaper mix did not save money overall.
Possible causes: the higher proportion of A may have reduced the chemical reaction or caused processing problems; the new blending machine may be incorrectly set; the supplier change may have altered material quality; operators may have rushed the blend because their bonus rewards output volume, not yield. Responsibility is shared: production for mix and yield, purchasing for price and quality, technical director for the standard mix and yield assumptions. The standard has not been reviewed for two years, so it may no longer be valid.
3. The production manager argues that the favourable mix variance shows good cost control. Critically evaluate this claim and recommend how Brookdale should measure blending performance.
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The production manager is optimising one sub-variance. A favourable mix variance is not good cost control if it causes an adverse yield and a higher total material cost. The total material cost variance is £916.67 adverse, and the net mix/yield position is £166.67 adverse. The manager should be assessed on total material cost, or on mix and yield together, not on the mix variance alone.
Brookdale should: (1) review the standard mix and yield with engineering and suppliers; (2) report a total material cost variance and a mix/yield reconciliation; (3) link bonuses to yield and quality, not just volume; (4) investigate the new machine and supplier change; (5) separate price responsibility from usage responsibility while recognising joint responsibility for total cost. The claim that the favourable mix variance shows good control is therefore misleading.