Make 15 profit on sales break even sales simple questionSolu

Make 15% profit on sales, break even sales, simple question.

Solution

Total fixed cost (FC) = $34,950

Total variable cost (TVC) = $60,000

(a)

(i) If required selling price be P, then

Breakeven quantity (Q) = FC / (P - Unit variable cost) = FC / [P - (TVC / Q)]

500 = $34,950 / [P - ($60,000 / 500)]

500 = 34,950 / (P - 120)

500P - 60,000 = 34,950

500P = 94,950

P = $189.90

(ii) If required price be P,

Profit = Revenue - FC - TVC

0.15 x P x Q = P x Q - 34,950 - 60,000

P x 500 x (1 - 0.15) = 94,950

P x 0.85 = 189.9

P = $223.41

(b) Now, Q = 600

(i) If required selling price be P, then

Breakeven quantity (Q) = FC / (P - Unit variable cost) = FC / [P - (TVC / Q)]

600 = $34,950 / [P - ($60,000 / 600)]

600 = 34,950 / (P - 100)

600P - 60,000 = 34,950

600P = 94,950

P = $158.25

(ii) If required price be P,

Profit = Revenue - FC - TVC

0.15 x P x Q = P x Q - 34,950 - 60,000

P x 600 x (1 - 0.15) = 94,950

P x 0.85 = 158.25

P = $186.17

(c) P = $170

(i) Breakeven quantity (Q) to make a profit = FC / [P - (TVC / Q)]

Q = 34,950 / [170 - (60,000 / Q)]

Q x [170 - (60,000 / Q)] = 34,950

170Q - 60,000 = 34,950

170Q = 94,950

Q = 558

(ii)

Q = (FC + Required profit) / [P - (TVC / Q)]

Q = (34,950 + 1,000) / [170 - (60,000 / Q)]

Q x [170 - (60,000 / Q)] = 35,950

170Q - 60,000 = 35,950

170Q = 95,950

Q = 564

(d) Maintenance costs appear in both fixed and variable cost categories because this is a mixed cost, so a part of maintenance cost is fixed and the remaining part varies with units of output produced.