Class 12 Accountancy Chapter 2 Reconstitution of a Partnership Firm – Admission of a Partner

Key Concept: Goodwill Concept

Solution: c) Value of the firm’s intangible benefits like reputation.

[Solution Description] Goodwill refers to the monetary value associated with a firm’s reputation, brand, and customer relationships. During admission, it is often valued and adjusted in the accounts to reflect its impact on the partnership’s worth.

Key Concept: Sacrifice Identification

Solution: a) Alex

[Solution Description] According to the problem statement, David acquires his entire share from Alex. Therefore, Alex is the partner who is sacrificing his share to accommodate the new partner, David.

Key Concept: Basic Calculation

Solution: c) Rs. 18,000

[Solution Description] To find the average profit, sum the profits and divide by the number of years:

\[
\text{Average Profit} = \frac{15,000 + 18,000 + 21,000}{3}
\]

\[
= \frac{54,000}{3} = 18,000
\]

So, the average profit is Rs. 18,000.

Key Concept: Concept Identification

Solution: c) Valuation of goodwill

[Solution Description] When a new partner is admitted to a partnership firm, one of the aspects requiring adjustment is the valuation of goodwill. This involves determining how much the new partner must compensate the existing partners for their sacrifice in profit share and any goodwill they have built up over the years.

Key Concept: Concept Application

Solution: c) To ensure the new partner pays for previous efforts of existing partners

[Solution Description]

The valuation of goodwill is important during the admission of a new partner because it ensures that the incoming partner compensates the existing partners for their share of the firm’s reputation and success which has been built up over time. Without valuing goodwill, the new partner may benefit from this without providing due compensation.

Key Concept: Basic Definition

Solution: d) Goodwill not brought by a new partner in cash upon admission.

[Solution Description] Hidden goodwill arises when a new partner is admitted into the partnership but does not bring in his or her share of goodwill in cash. In such cases, the goodwill is adjusted among existing partners according to their sacrificing ratio.

Key Concept: Profit Sharing Impact

Solution: c) It requires recalculation of goodwill

[Solution Description] When a new partner is admitted, goodwill must be recalculated to account for changes in profit-sharing ratios among partners, ensuring fair distribution of benefits associated with the firm’s reputation.

Key Concepts:

Key Concept: Super Profits Method

Solution: d) Rs. 24,000

[Solution Description] Goodwill using the Super Profits Method is calculated as follows:

$$\text{Goodwill} = \text{Super Profits} \times \text{Number of Years’ Purchase} = 4,000 \times 6 = 24,000\, \text{Rs.}$$

Key Concept: Method Recognition

Solution: c) Average Profits Method

[Solution Description] The methods of valuation of goodwill include the Average Profits Method, Super Profits Method, and Capitalisation Method.

Key Concept: Formula Application

Solution: b) Rs. 200,000

[Solution Description] To find the goodwill, use the formula:

$$\text{Goodwill} = \text{Capitalized Value of Average Profits} – \text{Net Assets}$$

Substitute the given values into the formula:

$$\text{Goodwill} = 900,000 – 700,000$$

Simplify the expression:

$$\text{Goodwill} = 200,000$$

Therefore, the goodwill is Rs. 200,000.

Key Concept: Formula Application

Solution: c) Rs. 16,000

[Solution Description] To calculate the normal profit, we use the formula:

$$\text{Normal Profit} = \frac{\text{Firm’s Capital} \times \text{Normal Rate of Return}}{100}$$

Substituting the given values:

$$\text{Normal Profit} = \frac{200000 \times 8}{100} = 16000$$

Therefore, the normal profit is Rs. 16,000.

Key concept: Complex Adjustments, Change in Profit Sharing Ratio

Solution: c) \$18,409.09

[Solution Description]

To find D’s share in the accumulated reserve, we first need to compute the new profit-sharing ratio. With D’s admission, his share is $\frac{1}{6}$, leaving $\frac{5}{6}$ for A, B, and C.

Calculate each partner’s new share:

For A:
\[
\begin{align*}
\text{New share for A} &= \frac{4}{4+3+2} \times \frac{5}{6} \\
&= \frac{4}{9} \times \frac{5}{6} = \frac{20}{54} = \frac{10}{27}
\end{align*}
\]

For B:
\[
\begin{align*}
\text{New share for B} &= \frac{3}{9} \times \frac{5}{6} = \frac{15}{54} = \frac{5}{18}
\end{align*}
\]

For C:
\[
\begin{align*}
\text{New share for C} &= \frac{2}{9} \times \frac{5}{6} = \frac{10}{54} = \frac{5}{27}
\end{align*}
\]

New ratio becomes $10:15:10:9$ after converting fractions to have common denominators.

D’s share of accumulated reserve:

$\text{D’s share} = \frac{9}{44} \times 90000 = 18409.09 \text{ (rounded)}$

Thus, option c) \$18,409.09.

Key Concept: Application of Given Ratios

Solution: c) $$31:41:18$$

[Solution Description]

The existing shares of Joshua and Daniel are $\frac{4}{9}$ and $\frac{5}{9}$ respectively. Sarah takes $\frac{1}{5}$ of the total share, i.e., $\frac{1}{10}$ from each partner.

For Joshua:

$$\text{New Share of Joshua} = \frac{4}{9} – \frac{1}{10} = \frac{40}{90} – \frac{9}{90} = \frac{31}{90}$$

For Daniel:

$$\text{New Share of Daniel} = \frac{5}{9} – \frac{1}{10} = \frac{50}{90} – \frac{9}{90} = \frac{41}{90}$$

Sarah’s Share:

$$\text{Sarah’s Share} = \frac{18}{90}$$

Therefore, the new profit-sharing ratio is $31:41:18$.

Key concept: Impact of Goodwill on Capital

Solution: b) Capital decreases by \$3,000

[Solution Description]

– Each partner bears an equal share of goodwill by reducing their capital.

– Each partner’s share of goodwill = $$\frac{12000}{4} = 3000$$.

– Thus, each partner’s capital reduces by \$3,000.

Key Concept: Basic Definition

Solution: b) An intangible asset

[Solution Description] Goodwill in the context of partnership accounts is an intangible asset. It represents the value of a business above its tangible assets, often due to factors like reputation or customer loyalty.

Key Concept: Profit Sharing Change

Solution: b) Admission of a new partner

[Solution Description] When a new partner is introduced into the partnership or when an existing partner retires, the profit-sharing ratio needs adjustment. Both these events lead to a reallocation of profits, requiring a new agreement on how profits are distributed among remaining partners.

Key Concept: Special Advantages

Solution: c) Import licenses

[Solution Description] Special advantages such as patents, trademarks, or import licenses provide a competitive edge to a business and significantly enhance its goodwill. Among the options given, having exclusive rights like patents or import licenses are considered special advantages.

Key concept: Calculation of Gains/Losses

Solution: d) Rs. 10,000 Gain

[Solution Description] To determine the net gain or loss, subtract the total debit from the total credit in the revaluation account.

$$\text{Net Gain} = \$40,000 – \$30,000 = \$10,000$$

Since the result is positive, there is a net gain of Rs. 10,000.

Key Concept: Mixed Sacrifice

Solution: b) $$33:23:14$$

[Solution Description]

The old profit-sharing ratio between Asha and Meena is 4:3. Therefore, Asha’s share is $\frac{4}{7}$ and Meena’s share is $\frac{3}{7}$.

Rina acquires $\frac{1}{5}$ share equally from Asha and Meena. Thus, each sacrifices $\frac{1}{10}$ $(\frac{1}{5} \div 2 = \frac{1}{10})$.

The new share for Asha is:

$\frac{4}{7} – \frac{1}{10} = \frac{40}{70} – \frac{7}{70} = \frac{33}{70}$

The new share for Meena is:

$\frac{3}{7} – \frac{1}{10} = \frac{30}{70} – \frac{7}{70} = \frac{23}{70}$

Rina’s share is given as $\frac{1}{5}$, or $\frac{14}{70}$.

Hence, the new profit-sharing ratio is $33:23:14$.

Key Concept: Basic Entry

Solution: a) Bank A/c Dr. 15,000; To Premium for Goodwill A/c 15,000

[Solution Description] When a new partner brings goodwill in cash, the entry involves debiting the Bank Account and crediting the Premium for Goodwill Account with the amount brought. Thus, the correct journal entry is:

$$\text{Bank A/c Dr. 15,000} \to \text{Premium for Goodwill A/c 15,000}$$

Key concept: Complex Goodwill Adjustment

Solution: a) \$0

[Solution Description] The sacrifice/gain calculations are initially needed to distribute goodwill.

Original share of Y: $\frac{5}{15}$, New share of Y: $\frac{6}{15}$

Gain for Y: $\frac{6}{15} – \frac{5}{15} = \frac{1}{15}$

Original share of Z: $\frac{3}{15}$, New share of Z: $\frac{4}{15}$

Gain for Z: $\frac{4}{15} – \frac{3}{15} = \frac{1}{15}$

Since both Y and Z gain equal amounts, there is no compensation required between them under this specific scenario.

Key Concept: Ratio Identification

Solution: d) 12:8:5

[Solution Description]

When Dinesh is admitted, he takes a $\frac{1}{5}$ share, leaving the remaining share as:

$$1 – \frac{1}{5} = \frac{4}{5}$$

Akshay and Bharati will share this $\frac{4}{5}$ according to their previous ratio of $3:2$.

Calculate the adjusted shares for Akshay and Bharati:

$$\text{Akshay’s New Share} = \frac{3}{5} \times \frac{4}{5} = \frac{12}{25}$$

$$\text{Bharati’s New Share} = \frac{2}{5} \times \frac{4}{5} = \frac{8}{25}$$

The new profit-sharing ratio becomes:

$$12:8:5$$