CMA Intermediate · Financial Accounting

Admission of Partner: formula sheet

Full chapter guide

Key formulas

New partner's share: New partner's share = fraction of profit he gets, taken from old partners; The new ratio of all partners must add up to 1.
Sacrificing ratio: Sacrifice = Old share − New share (for each old partner); Sacrificing ratio is the ratio of these sacrifices. If it is not given, assume it equals the old ratio.
Goodwill of the firm (premium-based method): Firm's goodwill = New partner's goodwill premium ÷ his share fraction; Use this when the new partner brings a goodwill premium in cash. For example, a premium of ₹50,000 for a 1/5 share gives firm goodwill of ₹50,000 ÷ 1/5 = ₹2,50,000.
Hidden goodwill: Total firm capital = New partner's capital ÷ his share; Goodwill = Total firm capital − Actual net assets; Actual net assets are the old partners' adjusted capitals (after revaluation and reserves) plus the new partner's capital, excluding goodwill. If total firm capital is more than these net assets, the difference is goodwill.
Goodwill entry (premium brought in cash): Bank A/c Dr (capital + premium); to New Partner's Capital A/c; to Premium for Goodwill A/c; Premium is then shared by old partners in their sacrificing ratio.
Revaluation: Profit or loss on revaluation is shared by old partners in the old ratio; It belongs to the period before admission.
Reserves and accumulated profits: Transfer to old partners' capital accounts in the old ratio; Accumulated losses are debited to old partners in the old ratio.
Sacrifice of an old partner: Sacrifice = Old share − New share; A positive value is a sacrifice. A negative value is a gain.
Sacrificing ratio: Sacrificing ratio = Sacrifice of A : Sacrifice of B : ...; Simplify the fractions to a common denominator and then compare the numerators.
Case 1: new partner's share taken in old ratio: New share of old partner = Old share × (1 − New partner's share); The sacrificing ratio then equals the old ratio. Each partner's sacrifice = Old share × New partner's share.
Case 2: share taken in a stated proportion: Sacrifice of A = New partner's share × A's stated fraction of sacrifice; New share of A = Old share of A − Sacrifice of A.
Check: Sum of all new shares = 1; Also check that the total sacrifice equals the new partner's share.
Gaining ratio (contrast): Gain = New share − Old share; Used when a partner retires or when an old partner increases his share. It is the opposite of sacrifice.
Goodwill by average profit: Goodwill = Average profit × Number of years' purchase; Use adjusted profits (after removing abnormal items). Use a weighted average if weights are given.
Goodwill by super profit: Super profit = Average profit − Normal profit; Goodwill = Super profit × Years' purchase; Normal profit = Capital employed × Normal rate of return ÷ 100.
Capitalisation method: Goodwill = Capitalised value of average profit − Net assets; Capitalised value = Average profit × 100 ÷ Normal rate; Net assets = Assets (excluding goodwill) − outside liabilities.
New partner's share of goodwill: Premium = Total goodwill × New partner's share; This is the amount he brings or is debited.
Sacrificing ratio: Sacrifice = Old share − New share (for each old partner); Premium is credited to old partners in this ratio.
Hidden goodwill: Total firm capital = New partner's capital ÷ His share; Goodwill = Total firm capital − (Net assets of old firm + New partner's capital); Use net assets after revaluation, and after any goodwill already in the books is excluded.
Goodwill not brought in cash: Dr New partner's Capital A/c; Cr Old partners' Capital A/cs (sacrificing ratio); Use this when he cannot pay his share of goodwill.
Existing goodwill written off: Dr Old partners' Capital A/cs (old ratio); Cr Goodwill A/c; Do this before raising or recording new goodwill.
Revaluation Account: debit side: Dr: decrease in assets, increase in liabilities, unrecorded liabilities, expenses of revaluation; These are losses. Each reduces the value of net assets.
Revaluation Account: credit side: Cr: increase in assets, decrease in liabilities, unrecorded assets; These are gains. Each raises the value of net assets.
Result of revaluation: Profit = total credits − total debits (if credits are larger); Loss = total debits − total credits (if debits are larger); Balance is shared in the old ratio, not the new ratio.
Transfer entry on profit: Revaluation A/c Dr; To Old Partners' Capital A/cs (old ratio); On loss, reverse the entry: Old Partners' Capital A/cs Dr; To Revaluation A/c.
Revised book value: New value = Old book value + increase − decrease; Show this in the post-admission Balance Sheet.
Reserve or profit entry: General Reserve A/c (or P&L A/c) Dr. ; To Old partners' Capital A/cs (old ratio); Applies to any credit balance that is not a liability: general reserve, other free reserves, credit balance of P&L A/c.
Accumulated loss entry: Old partners' Capital A/cs (old ratio) Dr. ; To Profit and Loss A/c (debit balance); Also use this for deferred revenue expenditure not yet written off, such as advertisement suspense.
Share of each old partner: Share = Amount × Old ratio share of that partner; Use old ratio only. Never use the new ratio or the sacrificing ratio.
Reserve against a liability: Amount distributed = Reserve balance − Actual liability or claim; Example: Workmen Compensation Reserve ₹50,000 and claim ₹30,000. Distribute ₹20,000 and show the claim as a liability.
Total capital from new partner's capital: Total capital of new firm = New partner's capital ÷ New partner's share; Use when the new partner's capital is given. Share must be a fraction, not a percentage left unconverted.
Total capital from old partners' capital: Total capital of new firm = Total adjusted capital of old partners ÷ (1 − New partner's share); Use when old capitals are to stay as they are and the new partner's capital is to be found.
Required capital of each partner: Required capital = Total capital × Partner's new share; Apply to every partner, including the new one.
Adjusted capital of an old partner: Old capital ± goodwill, revaluation, reserves, profits/losses, other adjustments; Do this before comparing with required capital.
Adjustment: Adjustment = Required capital − Adjusted capital; Positive means cash brought in or credit to current account. Negative means cash withdrawn or debit to current account.
Check: Sum of required capitals = Total capital; Also, cash brought in by the new partner equals the new partner's required capital, apart from any goodwill premium.
Sacrificing ratio: Sacrificing ratio = Old share − New share (for each old partner); A positive result means the partner sacrificed. Goodwill premium is shared in this ratio.
Revaluation profit or loss: Revaluation profit = Increase in assets + Decrease in liabilities − Decrease in assets − Increase in liabilities; Shared by old partners in the old ratio. The new partner has no share, because it relates to the period before admission.
Reserves and accumulated profits: Credit to old partners = Reserve or profit balance × old ratio; Accumulated losses are debited in the same way. The new partner does not share them.
Goodwill already in books: Write off: Dr Old partners' Capital (old ratio), Cr Goodwill; Do this before or along with the new goodwill entry, as the question directs.
Joint life policy with surrender value: Policy shown at surrender value; JLP reserve credited to old partners in old ratio; Any difference between the book value of the policy and its surrender value passes through Revaluation Account.
Cash in new Balance Sheet: New cash = Old cash + Capital brought in + Goodwill premium brought in (− any amount withdrawn by old partners); If goodwill is paid privately to the old partners, it does not enter the firm's cash.
Balance Sheet check: Total assets = Total capitals + Reserves left + Outside liabilities; Use it as the final proof of your solution.

Quick revision

Admission ends the old partnership and creates a new one with a new profit sharing ratio.
Sacrificing ratio = old ratio − new ratio for each old partner. A positive result means a sacrifice.
Goodwill brought in by the new partner is shared by old partners in the sacrificing ratio.
Revaluation profit or loss is shared by old partners in the old ratio.
Reserves and accumulated profits are credited to old partners in the old ratio. Accumulated losses are debited to them in the old ratio.
Increase in an asset or decrease in a liability is a gain on the Revaluation Account. The reverse is a loss.
Existing goodwill appearing in the books is written off to the old partners' capital accounts in the old ratio before the new partner is admitted.
If goodwill is not brought in cash, debit the new partner's capital (or current) account with their share of goodwill and credit the sacrificing partners' capital accounts in the sacrificing ratio.
When the new partner's capital and share are given and the firm's capital is to be fixed on that basis, total firm capital = new partner's capital ÷ new partner's share.
Old partners' new capital = firm's total capital × their new share. The difference from their adjusted capital is cash brought in or withdrawn.
Show every adjustment through the Partners' Capital Accounts and prepare the new balance sheet only after posting them all.
Always give working notes. They earn step marks even when the final figure is wrong.

Common mistakes

Sharing revaluation profit or reserves in the new ratio Fix: Share revaluation result, reserves and accumulated profits among old partners in the old ratio only.
Using the old ratio for goodwill instead of the sacrificing ratio Fix: Goodwill premium goes to the partners who sacrifice, in the ratio of their sacrifice. Always compute old share minus new share.
Writing the new ratio as the old ratio plus the new partner's share. Fix: The old partners' shares fall by the sacrifice. Subtract first, then add the new partner's share. Check that the total is 1.
Calculating sacrifice as new share − old share. Fix: Sacrifice = Old − New. If the answer is negative, the partner has gained.
Crediting the premium to old partners in the old ratio. Fix: The premium compensates for sacrifice, so credit it in the sacrificing ratio unless the question says otherwise.
Taking the whole goodwill as the new partner's premium. Fix: Multiply total goodwill by his share. The rest stays with the firm's old partners.
Sharing the revaluation result in the new ratio. Fix: Revaluation relates to the period before admission. Always use the old ratio and only old partners.
Putting a decrease in an asset on the credit side. Fix: Ask whether the change is a gain or loss to the firm. A loss is always a debit in the Revaluation Account.
Sharing the reserve in the new ratio. Fix: The reserve belongs to the old partners. Use the old ratio only and give the new partner nothing.
Using the sacrificing ratio instead of the old ratio. Fix: Sacrificing ratio is only for goodwill. Reserves and accumulated profits always go in the old ratio.

Exam tips

In MCQs, identify which ratio is asked: old, new, sacrificing or gaining. Most wrong options use the wrong ratio.
In written answers, show the new ratio and sacrificing ratio calculation first, as it earns step marks.
Tag each entry with a clear narration and keep the Revaluation Account in proper T-form.
Read for the phrase 'goodwill not to appear in books' and follow it. It changes the entries.
Check that the Balance Sheet totals match before you finish. A mismatch shows an entry is missing.
Write every share as a fraction, not a decimal. Fractions let you check that the total is 1.
Read the sentence on how the share is acquired. It decides whether the sacrificing ratio equals the old ratio.
Show the check line (total = 1) in written answers. It earns marks and catches arithmetic slips.