The Hindu Business Line : There is safety in numbers

A COMPANY earned a profit of Rs 2,00,000 on a sale volume of Rs 14,00,000 during the first half of a year, the fixed cost being Rs 5,00,000. However, during the second half of the year, it incurred a loss of Rs 1,00,000 although unit variable cost, selling price and fixed cost remained the same.

Required: i) profit-volume ratio, break-even point and margin of safety for the first half of the year; ii) sales volume for the second-half; iii) break-even point and margin of safety for the whole year.

First half-year: Profit 2 lakh + Fixed cost 5 lakh = Contribution Rs 7 lakh

PV ratio = C/S, that is, 7 lakh/14 lakh = 0.5, that is, 50 per cent

Break-even point = F/PV ratio

5 lakh/50 per cent = Rs 10 lakh

Margin of safety = Sales - BEP

14 lakh - 10 lakh = Rs 4 lakh

Sales for the second-half: Sales = F + P / PV ratio = 5 lakhs + (-1.00 lakh) / 50 per cent

4 lakh / 50 per cent = Rs 8 lakh

For the whole year: Fixed cost = 5 lakh + 5 lakh = Rs 10 lakh

BEP = F/PV ratio, that is, 10 lakh/50 per cent = Rs 20 lakh

Sales for the whole year = 14 lakh + 8 lakh = Rs 22 lakh

Margin of safety = Sales - BEP

22 lakh - 20 lakh = Rs 2 lakh

Ratios and B/S

THE following information is furnished by a company in regard to its working as on March 31, 2003:

Capital and reserves — Rs 28,00,000; net working capital — Rs 2,80,000;

current ratio — 2.4; liquid ratio — 1.6; inventory turnover (based on cost of sales) — eight; gross profit on sale — 20 per cent; and credit allowed — one-and-a-half months

Reserves amount to 40 per cent of share capital. All sales are on credit.

Current assets consist of stock, debtors and cash only.

Prepare the balance-sheet of the company as on March 31, 03.

Solution: WN1: Reserves amount to 40 per cent of share capital

100 per cent share capital + 40 per cent reserves

Total (140 per cent) = Rs 28 lakh, then share capital (100 per cent) = Rs 20 lakh

Therefore, reserves (40 per cent) = Rs 8 lakh

WN2: Current ratio = CA/CL = 2.4, that is, 2.4/1.0

Net working capital = CA - CL, that is, 2.4 - 1.0 = 1.4

This is Rs 2,80,000. Then, CA (2.4) = Rs 4,80,000.

Likewise, CL (1.0) = Rs 2,00,000

Net working capital — Rs 2,80,000

WN3: Liquid ratio = LA/CL = 1.6, that is, 1.6/1.0

When CL (1.0) is Rs 2,00,000, liquid assets (1.6) = Rs 3,20,000

WN4: Inventory = CA - LA

Rs 4,80,000 - Rs 3,20,000 = Rs 1,60,000

Inventory turnover = Cost of sales / inventory

Eight = Cost of sales / 1,60,000

Cost of sales = 8 x 1,60,000 = 12,80,000

WN5: Gross profit on sales (20 per cent), that is, 25 per cent on cost of sales

Cost of sales = Rs 12,80,000

Add gross profit (25 per cent) = Rs 3,20,000

Sales = Rs 16,00,000

(GP 20 per cent on 16,00,000 = 3,20,000)

WN6: Assumption: Opening stock and closing stock are same, at Rs 1,60,000

Trading A/c is presented in Table 4.

Note: In such case, cost of sales will be equal to purchases.

WN7: All sales are on credit.

Debtors = 16 lakh x 1.5 months / 12 = 2 lakh

WN8: It is assumed that all purchases are credit purchases.

Creditors = 12,80,000 x 1.5/12 = 1,60,000

WN9: Current assets: Closing stock — 1,60,000; debtors — 2,00,000;

cash (B/F) — 1,20,000; total — 4,80,000

Solution: The balance-sheet (in Rs lakh) as on March 31, 2003, is shown in Table 5.

Variance analysis

RAW materials `A' and `B' having standard costs of Rs 20/kg and Rs 30/kg are mixed in the standard ratio of 60 per cent; 40 per cent to manufacture `Z'.

During a particular week 1,200 kg of `A' costing Rs 25,000 and 1,000 kg of `B' costing Rs 28,000 were mixed to produce 2,200 kg of `Z'. Calculate all material cost variances.

WN1: During a particular week 1,200 kg of A and 1,000 kg of B (total 2,200 kg input) were mixed to produce 2,200 kg of Z, that is, there is no loss in process.