Question

X and Y are partners sharing profits in the ratio of 3 : 1. Z is admitted as a partner for `1/3`rd share in future profits. Following journal entry is passed at the time of Z's admission:

JOURNAL ENTRIES
Date	Particulars	L.F.	Dr. ₹	Cr. ₹
	Bank A/с   ...Dr.		20,000
	To Premium for Goodwill A/c			20,000
	(Amount brought in by Z towards share of goodwill)
	Premium for Goodwill A/c   ...Dr.		20,000
	Z's Current A/c   ...Dr.		10,000
	To X's Capital A/c			30,000
	(Z's share of goodwill transferred to X's capital account)
	Y's Capital A/c   ...Dr.		7,500
	To X's Capital A/c			7,500
	(Adjustment made due to change in profit sharing ratio)

Ascertain the following:

1. Value of Firm's Goodwill,
2. Sacrifice or Gain by X and Y, and
3. New Profit Sharing Ratio of X, Y and Z.

Answer 1

(i) Value of Firm’s Goodwill

From the journal entries, Z’s total share of goodwill is the sum of what he brought in cash and what is adjusted via his current account:

Z's Share of Goodwill = Premium for Goodwill (Cash) + Z's Current A/c

Z's Share of Goodwill = 20,000 + 10,000 = 30,000

Since Z is admitted for a `1/3`rd share, the total goodwill of the firm is calculated as:

Value of Firm's Goodwill = `30,000 xx 3/1 = 90,000`

(ii) Sacrifice or Gain by X and Y

The share of sacrifice or gain is determined by dividing each partner's respective goodwill adjustment by the total value of the firm's goodwill (90,000)

X’s Sacrifice:

X receives a total credit of 30,000 (from Z) + 7,500 (from Y) = 37, 500.

X’s Sacrifice Share: `(37,500)/(90,000) = 5/12 "(Sacrifice)"`

Y’s Gain:

Y's capital account is debited by 7,500, meaning Y is a gaining partner.

Y’s Gaining Share: `(7,500)/(90,000) = 1/12 "(Gain)"`

(iii) New Profit Sharing Ratio of X, Y, and Z

Using the formula: New Share = Old Share − Sacrifice + Gain

X’s New Share:

`3/4 - 5/12 = (9 - 5)/12 = 4/12`

Y’s New Share:

`1/4 + 1/12 = (3 + 1)/12 = 4/12`

Z’s New Share:

`1/3 = 4/12`

The New Profit Sharing Ratio among X, Y, and Z is 4 : 4 : 4, which implies to:

1 : 1 : 1