Solution 7.10

a) Calculate the selling price of a bed-night if the numbers sold and profits earned are to remain the same as last year

The approach to this question requires firstly the calculation of last years profit as well as the fixed and variable costs for this year. Once these are calculated then through the use of the CVP formula Profit = P(x) - (a + b(x)) one can get a value for P – required selling price

1. Calculate last years profit
	Profit Statement
	Sales (€50 x 5,000)			250,000
	Less variable costs (€30 x 5000)			150,000
	Total contribution (€20 x 5,000 )			100,000
	Less fixed costs			30,000
	Net profit			70,000


2. Calculate New cost figures
		Variable costs
			Food	15.75
			Direct labour	11
			Variable overhead	6
		Total variabe costs		32.75

		Fixed costs		31,500


	Profit = P(x) - (a + b(x))
	70,000 = P(5,000) - (31,500 + 32.75 (5,000)
	70,000 = 5000P - 195,250
	265,250 = 5000P
	53.05 =	P

The average price per bed-night required to achieve a profit of €70,000 based on sales of 5000 bed-nights is €53.05

b) The number of bed-nights the university needs to sell to maintain last years profit if they decide that price is to remain unchanged from last year.

Again through the use of the CVP formula Profit = P(x) - (a + b(x)) one can get a value for X – number of bed-nights sold

	70,000 = 50(x) - (31,500 + 32.75(x))
	101,500 = 17.25 (x)
	5884.06 =	X

c) Calculate the forecast profit if prices increase by 10 per cent and demand remains the same as last year

The approach here is simply to prepare a profit statement showing the forecast profit based on the above changes

Profit Statement

Sales	€55	X 5,000	275,000
Less variable costs	€32.75	X 5,000	163,750
Contribution	€22.25	x 5,000	111,250

Less fixed costs			31,500
			79,750