Average profit = \(\frac { Total\quad profit }{ Number\quad ofyear } \)
= \(\frac { 40,000+50,000+48,000+46,000 }{ 4 } \)
= \(\frac { 1,84,000 }{ 4 } \)
= Rs. 46,000

Average profit before adjusting fair remuneration of the partner	Rs. 46,000
Less: Fair remuneration of partners	6,000
Average profit	40,000

Goodwill = Average profit \(\times\) Number of years of purchase
= 40,000 \(\times\) 3 = Rs. 1,20,000

The monopoly condition or limited competition enables the concern to earn high profits which leads to higher value of goodwill

If the firm enjoys good reputations for its product's quality, there will be higher sales and the value of its goodwill will increase.

Goodwill cannot be seen and touched. It is invisible. Hence it is treated as intangible asset. But it is not a fictitious asset because goodwill has a value and it can be purchased or sold with any other asset.

Number of years purchase means for how many specific years the business will earn same amount of profits because of its past efforts.

Annuity refers to series of uniform cash flow at regular intervals. The table value gives the present value of annuity of rupee one received at the end of every year for a specified number of years.
Annuity factor=\(=\frac { i{ (1+i) }^{ n } }{ { (1+i) }^{ n }-1 } \)
Where, i = interest rate
n = estimated number of yea

i) When there is a change in the profit Sharing ratio.
ii) When a new partner is admitted into a firm.
iii) When an existing partner retires from the firm or when a partner dies.
iv) When a partnership firm is dissolved.

Normal rate of return refers to the rate at which profit is earned by similar business entities in the industry under normal circumstances.

Super profit is the excess of average profit over the normal profit. Average profit is calculated by dividing the total adjusted actual profit of certain number of years by the total number of such years. Normal profit is the profit earned by the similar business, firms under normal conditions.
Normal profit = Capital employed \(\times\) Normal rate of return.
Capital employed = Fixed assets + Current assets - Current liabilities.

Goodwill acquired by making payment in cash or kind is called acquired or purchased Goodwill when a firm purchase an existing business the price paid for purchase of such business may exceed the net assets (Assets - liabilities) of the business acquired.

Goodwill is the good name or reputation of the business which brings benefit to the business. It enables the business to earn more profit. It is the present value of a firm's future excess earnings. It is an intangible asset as it has no physical existence.

Goodwill = Average profit \(\times\) Number of years of purchase
Average profit \(=\frac{Total\ profit}{Number\ of\ years}\)
\(=\frac{5,000+8,000-3,000+6,000}{4}\)
\(=\frac{16,000}{4}\) = Rs. 4,000
Average profit = Rs. 4,000
Goodwill = Average profit \(\times\) Number of years of purchase
4,000 \(\times\) 3 = 12,000
Goodwill = Rs. 12,000

Goodwill = Average profit \(\times\) Number of years of purchase
Average profit \(=\frac{Total\ profit}{Number\ of\ years}\)
\(\frac{10,000+11,000+12,000+13,000+14,000}{5}\)
\(=\frac{60,000}{5}\) = Rs. 12,000
Average profit = Rs. 12,000
Goodwill Average profit \(\times\) Number of years of purchase
12,000 \(\times\) 2 = 24,000
Goodwill = Rs. 24,000

Total capitalised value of the average profit = \(\frac { Average\ profit }{ Normal\ rate\ of\ return } \)\(\times\) 100
=\(\frac { 60,000 }{ 10 } \) \(\times\) 100
= Rs. 6,00,000
Goodwill = Total capitalised value of the average profit – Capital employed
= 6,00,000 – 4,50,000
= Rs. 1,50,000