Question

US Auto Company would like to offer rebates to its customers in order to increase sales. If it lowers prices sales will increase.    This will depend on the price elasticity of demand. Assume that the price elasticity of demand is 1.5. This firm is considering a $400 rebate on its cars. Also assume the following information on prices and costs before the rebates:

          Average price per car                                   $9,000 per car

          Expected sales volume at $9,000) per car     1,000,000 cars

          Average total costs per car                           $8,200 per car

          Total variable cost                                         $6,400,000,000

• Calculate the present total fixed costs, average variable costs and average fixed costs.
• What is the present breakeven point?
• What is the change in revenue resulting from the $400 price reduction?
• What is the effect on the cost per car after the change? In other words what is the average cost per car after the change?
• Should the change be made?

Please show the calculation. Thank you.

Answer 1

1. Calculation of present total fixed costs, average variable costs and average fixed costs:
   • Sales =1,000,000 cars
   • Average total cost per car = 8200
   • Total cost at current level of sales = Average total cost per car x Sales
     • Total cost at current level of sales = 8200 x 1,000,000
     • Total cost at current level of sales =  $8,200,000,000.00
   • Total Variable cost = $6,400,000,000
   • Total cost at current level of sales = Total Variable cost +Total fixed cost
     • $8,200,000,000.00 = $6,400,000,000 + Total fixed cost
     • Total fixed cost =  $1,800,000,000.00
   • Average variable costs = Total Variable cost/Sales​​​​​​​
     • Average variable costs = $6,400,000,000/$1,000,000
     • Average variable costs = $6,400
   • Average fixed costs = Total fixed cost/Sales
     • Average fixed costs = $1,800,000,000.00/$1,000,000
     • Average fixed costs = $1,800
2. ​​​​​​​​​​​​​​Present breakeven point calculation:
   • (Sale Price - Average variable cost) x BEP units = Total fixed cost
     • (9000 - 6400) x BEP units = $1,800,000,000.00
     • BEP units = 692307.6923
     • as the car units cant be in decimals, we round it up to next highest integer so the BEP units is 692308 cars
3. ​​​​​​​​​​​​​​The change in revenue resulting from the $400 price reduction is as follows:
   • We need to find out the change in the number of cars that can be sold at a lower price. This can be calculated using the price elasticity of demand.
   • 
   • 
   • 
   • 
   • So the % increase in number of cars is 6.67% of original sales of 1,000,000, which is 66667 cars
   • So new sales is 1,00,00,00 + 66,667 = 1,066,667 cars
   • So the new revenue = new sales x new price
     • 1,066,667 x 8600 =  $9,173,336,200.00
   • Old revenue = old sales x old price
     • Old revenue = 1,000,000 x 9000
     • Old revenue = $9,000,000,000.00
   • Change in revenue = New revenue - Old revenue
     • Change in revenue = $9,173,336,200.00-$9,000,000,000.00
     • Change in revenue = $173,336,200.00
4. ​​​​​​​​​​​​​​The effect on the cost per car after the change is as follows:
   • Total cost at new level of sales = Total Variable cost +Total fixed cost
     • Total cost at new level of sales = $1,800,000,000.00 + New sales x Average variable cost
     • Total cost at new level of sales = $1,800,000,000.00 + 1,066,667 x 6400
     • Total cost at new level of sales = $1,800,000,000.00 + 6,826,668,800.00
     • Total cost at new level of sales = $8,626,668,800.00
   • Average total cost = Total cost at new level of sales / New sales
     • Average total cost = $8,626,668,800.00 / 1,066,667
     • Average total cost = $8087.50
   • Change in average total cost = Old average total cost - new average total cost
     • Change in average total cost = $8200 - $8087.50
     • Change in average total cost = $112.50
     • So the average total cost has reduced
5. As the average total cost has reduced and the revenues increased, the change should be made as it will lead to greater profit.