Question

The average profit for the last five years of a firm was ₹ 20,000. The normal rate of return in a similar business is 8\%. Goodwill of the firm is valued at ₹ 24,000 at the three years' purchase of super profit. Calculate the amount of capital employed by the firm.

Hint:

To calculate goodwill, first calculate the super profit, then multiply it by the number of years’ purchase to find the goodwill. Use the formula for normal profit to find capital employed.

Answer 1

The calculation of capital employed begins with determining the super profit, which is the difference between average profit and normal profit: \[\text{Super Profit} = \text{Average Profit} - \text{Normal Profit}.\] Normal profit is computed as the normal rate of return multiplied by the capital employed: \[\text{Normal Profit} = \frac{\text{Normal Rate of Return}}{100} \times \text{Capital Employed}.\] Let \( C \) represent the capital employed. The super profit can be expressed as: \[\text{Super Profit} = ₹ 20,000 - \frac{8}{100} \times C.\] Goodwill is calculated by multiplying the super profit by 3: \[\text{Goodwill} = 3 \times \text{Super Profit}.\] Substituting the given values yields: \[\text{₹ } 24,000 = 3 \times \left( ₹ 20,000 - \frac{8}{100} \times C \right),\] which simplifies to: \[\text{₹ } 24,000 = 60,000 - \frac{24}{100} \times C.\] To solve for \( C \): \[\frac{24}{100} \times C = 60,000 - 24,000 = 36,000,\] resulting in: \[C = \frac{36,000 \times 100}{24} = ₹ 1,50,000.\]