Question

Anu, Benu and Sara are partners in a firm sharing profits and losses in the ratio of `4/9:2/9:1/3`. Anu retires from the firm on 1st April, 2024. She gives half of her share to Benu and the remaining half to Sara.

On Anu’s retirement, it is decided that goodwill of the firm be valued at two years’ purchase of the average profits of the preceding four years which were as follows:

Year	Profit
2020-21	₹ 40,000 (including gain from speculation ₹ 4,000)
2021-22	₹ 80,000 (excluding repairs of machinery ₹ 6,000)
2022-23	₹ 1,10,000
2023-24	₹ 40,000 (loss)

You are required to calculate:

1. The new profit-sharing ratio of the remaining partners in the reconstituted firm.
2. The firm’s goodwill on the date of Anu’s retirement. 
   (Show the workings clearly with the formula)

Answer 1

i. Old Ratio of Anu, Benu and Sara `= 4/9 : 2/9:1/3`

`= (4:2:3)/9`

= 4 : 2 : 3

Anu retires [Anu’s share = `4/9`]

Half of Anu’s share = `1/2 xx 4/9 = 2/9`

Benu’s new share = `2/9 + 2/9 = 4/9`

Sara’s new share = `3/9 + 2/9 = 5/9`

New profit sharing ratio of Benu and Sara = `4/9:5/9`

= 4 : 5

ii. Adjusted profit for 2020-21 = 40,000 – 4,000 (abnormal gain)

= ₹ 36,000

Adjusted profit for 2021-22 = 80,000 – 6,000 (repair of machinery)

= ₹ 74,000

2022-23 = ₹ 1,10,000

2023-24 = ₹ 40,000 (Loss)

Average profit of the preceding four years 

`= (36000+74000 + 110000 + (40000))/4`

= ₹ 45,000

Goodwill = Average profit × No. of year’s purchase

= 45,000 × 2

= ₹ 90,000