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Aryan and Adya were partners in a firm sharing profits and losses in the ratio of 3 : 1. Their Balance Sheet on $31^{\text {st }}$ March, 2024 was as follows:



\begin{table}

\captionsetup{labelformat=empty}

\caption{Balance sheet of Aryan and Adya as at $31^{\text {st }}$ March, 2024}


Liabilities
\begin{tabular}[t]{l}
Amount

(₹)
& Assets &


Amount

(₹)
\\

\hline Capitals : & & Machinery & 3,90,000 \\

\hline Aryan 3,20,000 & & Furniture & 80,000 \\

\hline Adya 2,40,000 & 5,60,000 & Debtors 90,000 & \\

\hline Workmen's & & Less : provision for & \\

\hline Compensation Reserve & 20,000 & doubtful debts 1,000 & 89,000 \\

\hline Bank loan & 60,000 & Stock & 77,000 \\

\hline Creditors & 48,000 & Cash & 32,000 \\

\hline & & \multirow[t]{2}{*}{Profit \& Loss Account} & 20,000 \\

\hline & 6,88,000 & & 6,88,000 \\

\hline

\end{tabular}

\end{table}



Dev was admitted into the firm on $1^{\text {st }}$ April, 2024 for $1 / 5^{\text {th }}$ share in the profits of the firm on the following terms:

(i) Dev will bring capital proportionate to his share in the profits of the firm.

(ii) Goodwill of the firm was valued at ₹ 2,00,000 and Dev will bring his share of goodwill premium in cash.

(iii) Machinery was revalued at ₹ 4,50,000.

(iv) A provision for doubtful debts was to be created at 5\% on debtors.

(v) A liability of ₹ 3,500 included in creditors was not likely to arise.



Prepare Revaluation Account and Partners' Capital Accounts on Dev's admission.

Verified Answer :

  • Revalue assets and liabilities: Increase in machinery (\(₹60,000\)) and reduction in creditors (\(₹3,500\)) minus the increase in PDD (\(₹3,500\)) yields a revaluation profit of \(₹60,000\).
  • Distribute reserves and revaluation profit: Allocate WCR, P&L loss, and revaluation profit among Aryan and Adya (\(3:1\)).
  • Account for Goodwill: Credit the incoming partner's share of goodwill (\(₹40,000\)) to existing partners in their sacrificing ratio.
  • Determine Dev's Capital: Calculate Dev's proportionate share of capital (\(1/5\) of \(₹8,25,000 = ₹1,65,000\)) based on the adjusted capital of the old partners.
  • Final Balances: Aryan: \(\boxed{₹3,95,000}\), Adya: \(\boxed{₹2,65,000}\), Dev: \(\boxed{₹1,65,000}\).

Explanation

  1. Data and Problem Analysis

We are tasked with accounting for the admission of a new partner, Dev, into an existing partnership firm comprising Aryan and Adya, who share profits and losses in a \(3:1\) ratio. The process involves revaluing assets and liabilities, distributing accumulated reserves and losses, adjusting goodwill, and calculating Dev's required proportionate capital.

The initial Balance Sheet data:

  • Capital balances: Aryan \(₹3,20,000\), Adya \(₹2,40,000\)
  • Workmen's Compensation Reserve (WCR): \(₹20,000\)
  • Profit & Loss Account (loss): \(₹20,000\)
  • Machinery: \(₹3,90,000\)
  • Debtors: \(₹90,000\) (with existing PDD of \(₹1,000\))
  • Creditors: \(₹48,000\)
  • Dev's share: \(1/5\) of the profits.
  1. Revaluation Account Calculations

The Revaluation Account tracks changes in assets and liabilities to adjust the partners' capital accounts.

  • Machinery value increases from \(₹3,90,000\) to \(₹4,50,000\), creating a profit of \(₹60,000\).
  • Provision for Doubtful Debts (PDD) must be \(5\%\) of \(₹90,000\), which is \(₹4,500\). Since the existing provision is \(₹1,000\), we need to create an additional provision of \(₹3,500\) (Loss).
  • Liability of \(₹3,500\) included in creditors is not likely to arise, creating a profit of \(₹3,500\).

The net profit on revaluation is \(₹60,000 + ₹3,500 - ₹3,500 = ₹60,000\).
This profit is distributed between Aryan and Adya in their old ratio of \(3:1\):

  • Aryan's share: \(₹60,000 \times \frac{3}{4} = ₹45,000\)
  • Adya's share: \(₹60,000 \times \frac{1}{4} = ₹15,000\)
  1. Capital Account Adjustments and Dev's Capital

Next, we distribute the existing reserves and accumulated losses and adjust the capital accounts.

  • WCR (\(₹20,000\)) is distributed to Aryan and Adya in ratio \(3:1\):

Aryan: \(₹20,000 \times \frac{3}{4} = ₹15,000\); Adya: \(₹20,000 \times \frac{1}{4} = ₹5,000\).

  • Profit & Loss Account loss (\(₹20,000\)) is distributed in ratio \(3:1\):

Aryan: \(₹20,000 \times \frac{3}{4} = ₹15,000\); Adya: \(₹20,000 \times \frac{1}{4} = ₹5,000\).

  • Goodwill of the firm is \(₹2,00,000\). Dev's share for \(1/5\) is \(₹40,000\). This premium is credited to old partners in their sacrificing ratio (\(3:1\)):

Aryan: \(₹40,000 \times \frac{3}{4} = ₹30,000\); Adya: \(₹40,000 \times \frac{1}{4} = ₹10,000\).

Calculating closing balances (before Dev's entry):

  • Aryan: \(₹3,20,000 + ₹15,000 - ₹15,000 + ₹45,000 + ₹30,000 = ₹3,95,000\)
  • Adya: \(₹2,40,000 + ₹5,000 - ₹5,000 + ₹15,000 + ₹10,000 = ₹2,65,000\)

Combined Capital = \(₹3,95,000 + ₹2,65,000 = ₹6,60,000\).

  1. Conclusion and Final Capital Balances

Dev's capital is proportionate to his \(1/5\) share. The old partners' combined capital represents the remaining \(4/5\) of the firm's capital.
Total Capital of the Firm = \(\frac{₹6,60,000}{4/5} = ₹8,25,000\).
Dev's Capital = \(₹8,25,000 \times \frac{1}{5} = ₹1,65,000\).

Final Capital Balances:

  • Aryan: \(₹3,95,000\)
  • Adya: \(₹2,65,000\)
  • Dev: \(₹1,65,000\)

Examples

In a real-life business, when a new partner joins, it is vital to fairly value the current assets and liabilities to ensure that the existing partners are compensated for their historical efforts, and the incoming partner starts on a clean slate. Calculating the proportionate capital ensures that the investment of all partners is in balance with their profit-sharing rights, promoting fairness and long-term partnership stability. This accounting process is a standard procedure in corporate restructuring and expansion, helping maintain transparency and trust between all parties involved.

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