3 A breakeven graph for an investment on the sales of a new

3. A breakeven graph for an investment on the sales of a new computer is given to the right. The y-axis is the amount in thousands of dollars. Answer (estimate) the following: 2,500 2,000 a) Give the equation for total revenue in terms of volume of sales. b) Give the equation for total costs in terms of volume of sales c) What is the breakeven level of sales? d) If you sell 22,000 new computers this year, will you have a profit Break-even point S 1,500 1,000 500 5,000 10,000 15,000 20,000 25,000 30,00i0 or loss? e) At 22,000 computers, what are your marginal and average costs?

Solution

(a) Equation of total revenue: TR = P x where TR: Total revenue, P: Unit price and Q: Sales volume (quantity)

When Q = 0, TR = 0 and when Q = 20,000, TR = $1,500,000

P = TR / Q = $1,500,000 / 20,000 = $75

Therefore,

TR ($) = 75Q

(b) Equation of total cost (TC) = F + V x Q where F: Fixed cost, V: Unit variable cost & Q: Quantity

When Q = 0, TC = $500,000

$500,000 = F + V x 0

F = $500,000

When Q = 20,000, TC = $1,500,000

$1,500,000 = $500,000 + V x 20,000

20,000 x V = $1,000,000

V = $50

Therefore,

TC ($) = 500,000 + 50Q

(c) In break-even, TR = TC which holds true when Q = 20,000 units

(d) When Q = 22,000:

TR ($) = 75 x 22,000 = 1,650,000

TC ($) = 500,000 + 50 x 22,000 = 500,000 + 1,100,000 = 1,600,000

Since TR > TC, there is a profit equal to $50,000 (= $1,650,000 - $1,600,000).

(d) When Q = 22,000:

Marginal cost = V = $50

Average cost = TC / Q = $1,600,000 / 22,000 = $72.73