Paradox Ltd’s accountant is preparing a budget for sales and profitability of one of the company’s products, the brush. He has available the following data for last year: –

Sales £20,000

Variable costs 60% of sales

Fixed costs £70,000

The accountant is worried that costs will rise next year, and the estimate of inflation that he has prepared is based on a probabilistic approach, as follows :-

Average inflation rate Probability

compared with previous year

4% 0.2

6% 0.5

8% 0.3

Inflation will affect all variable costs and all but the following fixed costs: –

Depreciation – which will remain at £15k a year

Factory rental costs – fixed by lease at £15k a year

The sales manager has informed the accountant that it might be difficult to raise sales prices, despite inflation, and that at most selling prices could be raised by 5% above their current level.

His estimate of demand is as follows: –

a, At Current prices **Sales Probability**

**£**

Pessimistic 200,000 0.3

Most likely 220,000 0.4

Optimistic 260,000 0.3

b, If prices go up 5% **Sales Probability**

**£**

Pessimistic 190,000 0.5

Most likely 210,000 0.4

Optimistic 250,000 0.1

The decision whether or not to raise prices must be made at the beginning of the year, to allow the company to produce and issue a price list for a major advertising campaign.

Analyse the foregoing information in a way which will assist management with its budgeting problem. In your analysis you should do the following:-

**a, **Calculate the following for each price level.

The probability of at least breaking even

The probability of achieving a profit of at least £10,000

The probability of achieving a profit of at least £20,000

**b, **Comment on the validity of the approach to uncertainty analysis that you have used.

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