Sam is admitted for 1/5 share and brings Rs. 60,000 as capital.
Using Sam's capital contribution to find the total capitalized value of the firm:
If Sam's 1/5 share = Rs. 60,000
Then Total Capital of the firm = Rs. 60,000 × 5 = Rs. 3,00,000
Actual capital in the firm after Sam's admission:
Old partners' capital (Hem + Nem) = Rs. 80,000 + Rs. 50,000 = Rs. 1,30,000
Sam's capital brought in = Rs. 60,000
Total actual capital = Rs. 1,30,000 + Rs. 60,000 = Rs. 1,90,000
Hidden Goodwill of the firm:
Goodwill = Capitalized value - Actual capital
Goodwill = Rs. 3,00,000 - Rs. 1,90,000 = Rs. 1,10,000
Sam's share of goodwill:
Sam's share = 51 × Rs. 1,10,000 = Rs. 22,000
This represents the amount Sam should contribute towards goodwill for acquiring 1/5 share in the accumulated goodwill of the firm, which will be credited to the old partners in their profit-sharing ratio.