The Hindu Business Line : Playing the ad game for sports goods

The percentage of readers for each magazine is known. Exposure in any particular magazine is the number of advertisements placed multiplied by the number of principal buyers.

The data shown in Table 1 may be used. The budgeted amount is Rs 1 lakh for the advertisements.

The owner has already decided that Magazine A should have no more than six advertisements and that B and C must each have at least two advertisements.

Formulate an LP model for the problem. You are not required to solve the LP model.

Exposure = No. of advertisements x No. of buyers / magazines

Maximise exposure (P) = 10,000 x + 9,000 y + 2,800 Z

Subject to constraints

Cost: 5,000 x + 4,500 y + 4,250 z 1,00,000

X is less than or equal to six

Y is greater than or equal to two

Z is greater than or equal to two

Formulation: P = 10000 x + 9000 y + 2800 z

Subject to conditions, 5,000 x + 4,500 y + 4250 z + w1=100,000

x + w2 = 6

y - w3 = 2

z - w4 = 2

where, w1, w2 are slack variables; and w3, w4, surplus variables.

Quitting Q

XYZ Ltd produces and sells three types of products — P, Q and R. The management has decided to discontinue the production of Q, as there is not much profit in it. The information given in Table 3 is available. The overhead absorption rates on the direct wages are given in Table 4.

Find out: i) the profitability of the three products, and ii) the PV ratio of P, Q and R. Also give a short comment on the decision of the management.

The statement of profitability (per unit) is presented in Table 5.

Product Q gives the highest PV ratio. The profit of Product Q per unit (Rs 18) is less because of absorption of fixed overheads. If it is discontinued, those fixed overheads are to be apportioned to products P and R. Then the overall profit of the company will come down because of losing contribution per unit of Rs 121. Hence, the decision of the management to discontinue the production of Q is not correct.

Product Q gives highest PV ratio. Hence, it should not be discontinued.

Note: A similar question was asked in the December 2002 examination.

Trucking problem

THE Bombay Transport Company has trucks available at four difference sites in the following numbers: Site A — five trucks; Site B — 10 trucks; Site C — seven trucks; and Site D — three trucks.

Customer W requires five trucks; Customer X, eight trucks; and Customer Y, 10 trucks.

The variable costs of getting trucks to the customers are as follows:

From A to W — Rs 7, to X — Rs 3, to Y — Rs 6

From B to W — Rs 4, to X — Rs 6, to Y — Rs 8

From C to W — Rs 5, to X — Rs 8, to Y — Rs 4

From D to W — Rs 8, to X — Rs 4, to Y — Rs 3

Solve this transportation problem.

To satisfy run conditions, let us introduce dummy destination Z with two trucks required (see Table 6).

Optimum transportation cost = (5 x 3) + (5 x 4) + (3 x 6) + (2 x 8) + (5 x 4) + (2 x 0) + (3x3) = 15 + 20 + 18+ 16 + 20+ 0 + 9 = Rs 98

For optimum value: No. of allocations = sources + destinations - 1 = 4 + 4 - 1 = 7

As the number of allocations is seven, the solution is optimum.

Right profit

IF THE sales are Rs 2 lakh, fixed cost Rs 30,000 and PV ratio 40 per cent, will the profit be: Rs 50,000, Rs 80,000 or Rs 12,000?

The profit will be Rs 50,000. Profit = (sales x PV ratio) - fixed cost, that is, Rs 2 lakh x 40 per cent - Rs 30,000 = Rs 50,000

Production budget

A COMPANY manufactures two products, X and Y. A forecast of units to be sold in the first five months of the year and other information are given in Tables 7 and 8 respectively. There will be no opening and closing work-in-progress at the end of any month.

Finished product (in units), equal to half of the budgeted sale of the next month, should be in stock at the end of each month (including previous year December).

Prepare: Production budget for January-April, and the summarised production cost budget. What are the basic differences between `forecast' and `budget'?

The production budgets of Products X and Y for January-April (units) are given in Table 9. The summarised production cost budget is presented in Table 10.

Note: The closing stock of December will be opening stock of January. Hence, 50 per cent of 1,000 = 500 units. The closing stock of December will be opening stock of January.

Similarly, the January closing stock will become February's opening stock, and so on.

Transfer pricing

A COMPANY AB Ltd has two divisions — X and Y. Division X manufactures a special type of electrical component and Division Y sells a finished product for which it requires one component per unit from X Division. Division X sells the component in the external market at Rs 180 per unit and Division X is also working at almost its full capacity. The variable cost of manufacturing per component is Rs 102.

Division Y is now operating at 50 per cent capacity. It has received a special order for its product. Division Y is keen to get this order. Division Y will meet the special order at a price of Rs 1,200 per unit and it offers a price of Rs 120 per component to Division X.

The possible cost per unit of Division Y's finished product is as follows:

Other purchased component — Rs 500; component to be supplied by Division X — Rs 120; other variable overheads — Rs 320; fixed overheads — Rs 180; and total cost per unit — Rs 1,120

As a manager of Division X, what decision would you like to take regarding the offer by Division Y for the supplies at Rs 120? Would it be economically advantageous for Division Y to buy at Rs 180?

As a manager of Division X, I will not accept the offer price of Rs 120 by Division Y, because: a) Division X sells the components in the external market at Rs 180 per unit; and b) Division X is working at almost its full capacity.

It will be economic advantage for division y to buy at Rs 180 for the following reasons:

a) The total cost will even then be Rs 1,180 (500 + 180 + 320 + 180), thus leaving a profit of Rs 20 per unit (1200 - 1180).

b) Division Y is now operating at 50 pr cent capacity only.

c) Hence the fixed overheads of Rs 180 per unit is not relevant for decision-making. Then the total cost per unit will become Rs 10,00 only (500 + 180 + 320). Special order price of Rs 1,200 will result into a profit of Rs 200 per unit (1200 - 1000).

d) Even if the fixed overheads are taken into account, it will yield a profit of Rs 20 per unit as mentioned in (a) above. Hence it will be economic advantage for Division Y to buy the component from Division X at Rs 180 and to accept the special order at a price of Rs 1,200 per unit.

(To be concluded)

(Suggested answers to the June 2003 ICWA (Stage II) paper on management accounting and performance management.)

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