The Hindu Business Line : Break-even in merged plants

Two cement plants decide to merge to earn higher profits. The working results of the two plants for last year are as shown in Table 1. After merger, the management wants information on the following:

Capacity at which the combined plant will break even.

Profit likely to be made if the combined plant works at 90 per cent capacity.

Sales required to earn a profit of Rs 60 lakh. If the total fixed costs are reduced by Rs 10 lakh, what sales will yield a profit of Rs 60 lakh?

Answer: WN1: Profit of merged plant at 100 per cent capacity is presented in Table 2.

WN2: PV ratio = C/S = 200/900 = 2/9

Solution: (i) BEP = F/PV ratio = 90 lakh/ 2/9 = Rs 405 lakh

Rs 900 lakh sales — 100 per cent capacity

Rs 405 lakh BEP — ?

The combined plant will break even at 45 per cent capacity.

(ii) Profit = (sales x PV) - F

(90 per cent of 900 = 810 x 2/9) - 90

180 - 90 = Rs 90 lakh profit

(iii) Sales = (80 + 70) / 2/9 = 675 lakh.

If total fixed costs are reduced by Rs 10 lakh,

Sales = F + P / PV ratio = (80 + 60) / 2/9 = Rs 630 lakh

Sales will yield a profit of Rs 60 lakh.

Variance calc

A building can be constructed by engaging a gang of workers as per the details given in Table 3, for 100 working days of eight hours each. Actual completion of the work however took 104-days of eight hours each. This includes 16 hours of stoppages due to heavy rains. The actual number of workers engaged and the actual rates paid are given in Table 4.

Calculate the following variances: labour cost; labour rate; labour efficiency; labour mix; and idle time.

Answer: Working notes 1 and 2, on standard cost (SC) and actual cost (AC), and working note 3 are presented in presented in Tables 5, 6 and 7.

Solution: (a) Labour cost variance = SC - AC (3,24,800 - 3,99,360) = Rs 74,560 A

b) Labour rate variance = AHP (SR - AR)

Skilled: 6656 (25 - 30) = Rs 33,280 A

Semi-skilled: 4992 (20 - 24) = Rs 19,968 A

Unskilled: 4992 (16 - 16) = Nil

Total = Rs 53,248 A

c) Labour efficiency variance = SR (SH - AHW)

Skilled = 25 (4,800 - 6,528) = 43,200 A

Semi-skilled = 20 (6,400 - 4,896) = 30,080 F

Unskilled =16 (4,800 - 4,896) = 1,536 A

Total = 14,656 A

d) Labour mix variance = SR (SPPAU - AHW)

Skilled = 25 (16,320/16,000 x 4,800 - 6,528)

25 (4,896 - 6,528 ) = 40,800 A

Semi-skilled = 20 (16,320/16,000 x 6,400 - 4,896)

20 (6,528 - 4,896) = 32,640 F

Unskilled = 16 (16,320/16,000 x 4,800 - 4,896)

16 (4,896 - 4,896 ) = nil

Total = 8,160 A

e) Idle time variance = SR x idle time

Skilled = 25 x 128 = 3200 A

Semi-skilled = 20 x 96 = 1920 A

Unskilled = 16 x 96 = 1536 A

Total = 6656 A

Note 1: Labour yield variance: The building should have been constructed at a labour cost of Rs 3,24,800 (16,000 man-hours).

SYR = 3,24,800/16,000 man-hours = Rs 20.30

AHW = 16,320 to complete the construction of building.

LYV = 20.30 (16,000 - 16,320 ) = Rs 6,496 A

Reconciliation: LCV — 74560 A

LRV — 53248 A

Idle time variance — 6656 A

LEV — 14656 A

LMV — 8160 A

LYV — 6496 A