Break-even analysis for a startup

Given

$P = 250$, $V = 150$, $F = 6{,}00{,}000$.

Contribution per unit:

$$C = P - V = 250 - 150 = \text{Rs } 100$$

Contribution margin ratio:

$$\frac{100}{250} = 0.40$$

(a) Break-even

$$Q_{BE} = \frac{F}{P-V} = \frac{6{,}00{,}000}{100} = 6{,}000\ \text{units}$$ $$\text{Break-even sales} = 6{,}000 \times 250 = \text{Rs } 15{,}00{,}000$$

(Check: $6{,}00{,}000 / 0.40 = 15{,}00{,}000$.)

(b) Profit at 9,000 units

$$\text{Profit} = 9{,}000 \times 100 - 6{,}00{,}000 = \text{Rs } 3{,}00{,}000$$

(c) Margin of safety

$$\text{MoS} = \frac{9{,}000 - 6{,}000}{9{,}000} = 0.333 = 33.3\%$$

Sales can fall by one-third before the firm starts losing money.

(d) Units for a profit of Rs 2,00,000

$$Q = \frac{F + \text{Profit}}{P-V} = \frac{6{,}00{,}000 + 2{,}00{,}000}{100} = 8{,}000\ \text{units}$$

 Rs
  |            Total revenue /
  |          /  Total cost /
  |        X <- break-even (6,000 units)
  |   Fixed cost ------------
  +--------------------------- units

Answer: (a) 6,000 units, Rs 15,00,000; (b) Rs 3,00,000; (c) 33.3%; (d) 8,000 units.