Certainly! Let's break down the solution step-by-step to calculate the value of goodwill on 1st January 2024.
### Step 1: Identify the Profits and Losses for Last Four Years
Given:
- Year: 2018, 2019, 2020, 2021, 2022
- Profit/Loss:
- 2018: ₹ 3,00,000
- 2019: ₹ 2,00,000
- 2020: ₹ (2,80,000) [this indicates a loss]
- 2021: ₹ 3,20,000
- 2022: ₹ 4,00,000
We are interested in the profits and losses for the last four years (2019, 2020, 2021, and 2022).
### Step 2: List the Profits and Losses for the Last Four Years
- 2019: ₹ 2,00,000
- 2020: ₹ (2,80,000) [this is a loss, so it's -2,80,000]
- 2021: ₹ 3,20,000
- 2022: ₹ 4,00,000
### Step 3: Calculate the Average Profit for the Last Four Years
To find the average profit, sum up the profits and losses for these years and then divide by the number of years.
[tex]\[
\text{Total Profit} = ₹ 2,00,000 + (₹ -2,80,000) + ₹ 3,20,000 + ₹ 4,00,000
= ₹ 2,00,000 - ₹ 2,80,000 + ₹ 3,20,000 + ₹ 4,00,000
= ₹ (2,00,000 - 2,80,000 + 3,20,000 + 4,00,000)
= ₹ 6,40,000
\][/tex]
Number of years = 4
[tex]\[
\text{Average Profit} = \frac{₹ 6,40,000}{4} = ₹ 1,60,000
\][/tex]
### Step 4: Calculate the Value of Goodwill
The goodwill is calculated as 2 years' purchase of the average profit. Hence,
[tex]\[
\text{Goodwill} = 2 \times \text{Average Profit}
= 2 \times ₹ 1,60,000
= ₹ 3,20,000
\][/tex]
Therefore, the value of the goodwill on 1st January 2024 is ₹ 3,20,000.
