TWO SEPARATE QUESTIONS (Break-Even-Analysis) 1. At a volume of 125,000 units a c
ID: 362108 • Letter: T
Question
TWO SEPARATE QUESTIONS (Break-Even-Analysis)
1. At a volume of 125,000 units a company’s variable costs are $600,000, fixed costs are $50,000 and profits are $15,000. What is the B.E.P.? How much sales volume does it take to produce profits equal to cost reduction of $500?
2. A company has capacity to produce 600,000 units of a product per year. At present it is operating at 65% of capacity and has an annual income of $425,000. Fixed costs are $200,000; variable costs are $0.60 per unit. What is the company’s profit or loss? What is the B.E.P.? What would the profit be at 80% of capacity?
Explanation / Answer
Answer to question 1 :
Given , Volume of sales = 125,000
Total sales value of the company
= Profit + Total fixed cost + Total variable cost
= 15000 + 50,000 + 600,000
= $665,000
Also, Unit variable cost
= Total variable cost/ Number of units produced
= 600,000/ 125,000
= $4.8/unit
Price per unit = Total sales value/ Sales volume = 665,000/ 125,000 = $5.32 / unit
Let break even volume ( B.E.P) = N
At B.E.P, Total sales = Total cost = Fixed cost + Variable cost/ unit x Number of units
Total sales = Unit Price x Number of units sold = $5.32.N
Total cost = Fixed cost + Unit variable cost/ unit x Number of units = 50,000 + 4.8.N
Therefore at B.E.P
5.32N = 50,000 + 4.8.N
Or, 0.52.N = 50,000
N = 96153.84 ( 96154 ROUNDED TO NEAREST WHOLE NUMBER )
Contribution per unit = Unit price – Unit variable cost = $5.32 - $4.8 = $0.52
Therefore , required increase in sales volume to make profit of $500
= 500 / 0.52
= 961.53 ( 962 rounded to nearest whole number )
B.E.P = 96154
REQUIRED INCREASE IN SALES VOLUME = 962
Answer to question #2 :
Actual production of the company = 65% of capacity 600,000 = 390,000
Thus total cost of the company at volume of 390,000
= Fixed cost + Variable cost /unit x Actual production
= $ 200,000 + 0.60 x 390,000
= $200,000 + $234,000
= $434,000
Total cost of the company = $434,000
Total annual income of the company = $425,000
Since , Income < Total cost , it will lead to a loss situation.
Thus, annual loss for the company = Total cost – Annual income = $434,000 - $425,000 = $9,000
Let Break even Point ( B.E.P) volume = N
At break even point , Total sales = Total cost
Also,
At 65% of capacity i.e. at a volume of 390,000 units its annual income is $425,000
Therefore , Price per unit = $ 425,000 / 390,000 = $1.089 / unit
Therefore, total sales at volume of N = 1.089.N
Total cost = Fixed cost + Variable cost/ unit x Number of units = $200,000 + 0.60.N
Since at B.E.P , Total sales = Total cost ,
Therefore ,
1.089.N = 200,000 + 0.6.N
Or, 0.489.N = 200,000
Or, N = 200,000/ 0.489 = 408997.95 ( 408998 ROUNDED TO NEAREST WHOLE NUMBER )
B.E.P = 408,998
Production at 80% capacity = 80% of 600,000 units = 480,000
Thus total cost for producing 480,000 units
= Fixed cost + Total variable cost
= $200,000 + $ 0.60 x 480,000
= 200,000 + 288,000
= $488,000
Total annual income = Price per unit ( $1.089 / unit ) x Production volume ( 480,000)
= $1.089 x 480,000
= $522720
Profit at 80% of the capacity = Total income – Total cost = $522720 - $488,000 = - $34,720
LOSS AT 65% CAPACITY = $9000
B.E.P = 408,998
PROFIT AT 80% CAPACITY = $34,720
B.E.P = 96154
REQUIRED INCREASE IN SALES VOLUME = 962
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.