Question

Pearl and Ruby were partners in a firm with a combined capital of \rupee2,50,000. The normal rate of return was 10\%. The profits of the last four years were as follows: \[ \text{2019–2020: \rupee35,000, 2020–2021: \rupee25,000, 2021–2022: \rupee32,000, 2022–2023: \rupee33,000}. \] The closing stock for the year 2022–2023 was overvalued by \rupee5,000. Calculate goodwill of the firm based on three years’ purchase of the last four years’ average super profit.

Hint:

Goodwill based on super profit is calculated by finding the excess of average profit over normal profit and multiplying it by the agreed years of purchase.

Answer 1

Step 1: Calculation of Adjusted Profits \[\text{Profit for 2022–2023 requires adjustment for overvalued stock.}\]\[\text{Adjusted profit for 2022–2023 = \rupee33,000 - \rupee5,000 = \rupee28,000}.\] Profits for the preceding four years (adjusted): \[\text{2019–2020: \rupee35,000, 2020–2021: \rupee25,000, 2021–2022: \rupee32,000, 2022–2023: \rupee28,000}.\] Step 2: Calculation of Average Profit \[\text{Average Profit} = \frac{\text{Total Profits}}{\text{Number of Years}}\]\[\text{Average Profit} = \frac{35,000 + 25,000 + 32,000 + 28,000}{4} = \frac{1,20,000}{4} = \rupee30,000.\] Step 3: Calculation of Normal Profit \[\text{Normal Profit} = \text{Capital Invested} \times \text{Standard Rate of Return}\]\[\text{Normal Profit} = \rupee2,50,000 \times \frac{10}{100} = \rupee25,000.\] Step 4: Calculation of Super Profit \[\text{Super Profit} = \text{Average Profit} - \text{Normal Profit}\]\[\text{Super Profit} = \rupee30,000 - \rupee25,000 = \rupee5,000.\] Step 5: Calculation of Goodwill \[\text{Goodwill} = \text{Super Profit} \times \text{Years of Purchase}\]\[\text{Goodwill} = \rupee5,000 \times 3 = \rupee15,000.\] Final Answer: \[\text{The firm's goodwill is \rupee15,000.}\]