Question

Often a firm will calculate the break-even point for a price. That is, if we set the price at $X, then how many units will we need to sell to cover costs (that is, our break-even point). Work through the following data and questions to gain a better understanding of this approach.

QUESTIONS

1. Start by completing the table below under the assumption that the product will be sold for $20. (It will be easiest to use Excel to complete the table.) How many units need to be sold to break-even at a product price of $20?
2. Now recalculate the table under the assumption that the product will be sold for $13. How many units need to be sold to break-even at a product price of $13?
3. What do you think you would set first: the sales target or the price? Why? Keep in mind that price has an effect on demand.

No. of Units Allocated Variable Fixed Costs Cost/Unit Total Production Cost Average Unit Unit Cost Price Total Sales Revenue Gross Profit 500 750 1,000 1,250 1,500 1,750 2,000 2,250 2,500 2,750 3,000 $7,500 $7,500 $7,500 $7,500 $7,500 $7,500 $7,500 $7,500 $7,500 $7,500 $7,500 $10 $10 $10 $10 $10 $10 $10 $10 $10 $10 $10

Answer 1

If the price is $20

No. of Units, Q	Allocated fixed Cost, FC	Variable Cost/Unit, V	Total Production Cost, TC= FC+V*Q	Average Unit Cost, ATC= TC/Q	Unit Price, P	Total sales revenue=TR=P*Q	Gross profit= TR-TC
500	7500	10	12500	25.00	20	10000	-2500
750	7500	10	15000	20.00	20	15000	0
1000	7500	10	17500	17.50	20	20000	2500
1250	7500	10	20000	16.00	20	25000	5000
1500	7500	10	22500	15.00	20	30000	7500
1750	7500	10	25000	14.29	20	35000	10000
2000	7500	10	27500	13.75	20	40000	12500
2250	7500	10	30000	13.33	20	45000	15000
2500	7500	10	32500	13.00	20	50000	17500
2750	7500	10	35000	12.73	20	55000	20000
3000	7500	10	37500	12.50	20	60000	22500

Breakeven point is the output where profit is equal to zero. Refer to above table, profit is zero at Q=750. So, 750 units should be sold to break even.

If price is $13

No. of Units, Q	Allocated fixed Cost, FC	Variable Cost/Unit, V	Total Production Cost, TC= FC+V*Q	Average Unit Cost, ATC= TC/Q	Unit Price, P	Total sales revenue=TR=P*Q	Gross profit= TR-TC
500	7500	10	12500	25.00	13	6500	-6000
750	7500	10	15000	20.00	13	9750	-5250
1000	7500	10	17500	17.50	13	13000	-4500
1250	7500	10	20000	16.00	13	16250	-3750
1500	7500	10	22500	15.00	13	19500	-3000
1750	7500	10	25000	14.29	13	22750	-2250
2000	7500	10	27500	13.75	13	26000	-1500
2250	7500	10	30000	13.33	13	29250	-750
2500	7500	10	32500	13.00	13	32500	0
2750	7500	10	35000	12.73	13	35750	750
3000	7500	10	37500	12.50	13	39000	1500

Breakeven point is the output where profit is equal to zero. Refer to above table, profit is zero at Q=2500. So, 2500 units should be sold to break even.

If firm has a market power i.e. it can influence market price. It should first select the output at which the goal of the firm can be met. Price depends upon the output. So, we should first estimate the output level.