Question

Following is the current balance sheet for a local partnership of doctors: Cash and current assets $ 50,000 Liabilities $ 90,000 Land 290,000 A, capital 70,000 Building and equipment (net) 220,000 B, capital 90,000 C, capital 140,000 D, capital 170,000 Totals $ 560,000 Totals $ 560,000 The following questions represent independent situations: E is going to invest enough money in this partnership to receive a 20 percent interest. No goodwill or bonus is to be recorded. How much should E invest? E contributes $120,000 in cash to the business to receive a 20 percent interest in the partnership. Goodwill is to be recorded. Profits and losses have previously been split according to the following percentages: A, 30 percent; B, 10 percent; C, 40 percent; and D, 20 percent. After E makes this investment, what are the individual capital balances? E contributes $42,000 in cash to the business to receive a 20 percent interest in the partnership. Goodwill is to be recorded. The four original partners share all profits and losses equally. After E makes this investment, what are the individual capital balances? E contributes $88,000 in cash to the business to receive a 22 percent interest in the partnership. No goodwill or other asset revaluation is to be recorded. Profits and losses have previously been split according to the following percentages: A, 10 percent; B, 30 percent; C, 20 percent; and D, 40 percent. After E makes this investment, what are the individual capital balances? C retires from the partnership and, as per the original partnership agreement, is to receive cash equal to 130 percent of her final capital balance. No goodwill or other asset revaluation is to be recognized. All partners share profits and losses equally. After the withdrawal, what are the individual capital balances of the remaining partners?

Answer 1

Case I).

Total capital of all existing partners = A’s capital + B’s capital + C’s capital + D’s capital

                                                          = $70,000 + $90,000 + $140,000 + $170,000

                                                          = $470,000

E’s investment = 20%*(Total capital + E’s investment)

E’s investment = 20%*($470,000 + E’s investment)

E’s investment = $94,000 + (0.20*E’s investment)

E’s investment – 0.20E’s investment = $94,000

0.80E’s investment = $94,000

E’s investment = $94,000/0.80

E’s investment = $117,500

Case II).

Goodwill = Implied value of partnership – (Total capital + E’s contribution)

                = (E’s contribution/Interest rate) – ($470,000 + $120,000)

                = ($120,000/0.20) – $590,000

                = $600,000 – $590,000

                = $10,000

Share of existing partner’s in goodwill:

A = $10,000*30%

   = $3,000

B = $10,000*10%

   = $1,000

C = $10,000*40%

   = $4,000

D = $10,000*20%

    = $2,000

So,

Individual capital balance of all partners are as follows:

A’s capital = Original balance + Goodwill

                   = $70,000 + $3,000

                   = $73,000

B’s capital = Original balance + Goodwill

                   = $90,000 + $1,000

                   = $91,000

C’s capital = Original balance + Goodwill

                   = $140,000 + $4,000

                   = $144,000

D’s capital = Original balance + Goodwill

                   = $170,000 + $2,000

                   = $172,000

E’s capital = Investment made by E

                  = $120,000

Case III).

E is contributing $42,000 share for the 20% interest in partnership i.e. lower than the interest of partnership and thus E required to bring goodwill in the partnership firm. Thus,

E’s investment = 20%*(Total capital of all partners + E’s investment)

$42,000 + Goodwill = 0.20*[$470,000 + ($42,000 + Goodwill)]

$42,000 + Goodwill = 0.20*($512,000 + Goodwill)

$42,000 + Goodwill = $102,400 + (0.20*Goodwill)

Goodwill – 0.20Goodwill = $102,400 – $42,000

0.80Goodwill = $60,400

Goodwill = $60,400/0.80

Goodwill = $75,500

The capital balances of other partners will remain unchanged as there is no change in profit sharing ratio and E will contribute $42,000 through cash and $75,500 in the form of goodwill. Thus, total investment of E will be $117,500 i.e. $75,500 + $42,000.

Case IV).

Total capital after investment made by E = $470,000 + $88,000

                                                                  = $558,000

Capital balance of E = $558,000*22%

                                 = $122,760

Bonus provided to E = E’s Capital – Payment by E

                                  = $122,760 – $88,000

                                  = $34,760

Individual capital balance of all partners:

A’s capital = Original balance – Investment

                  = $70,000 – ($34,760*10%)

                  = $66,524

B’s capital = Original balance – Investment

                  = $90,000 – ($34,760*30%)

                  = $90,000 – $10,428

                  = $79,572

C’s capital = Original balance – Investment

                  = $140,000 – ($34,760*20%)

                  = $140,000 – $6,952

                  = $133,048

D’s capital = Original balance – Investment

                   = $170,000 – ($34,760*40%)

                   = $170,000 – $13,904

                   = $156,096

Case V).

Total cash amount receives by C = C’s capital balance*130%

                                                     = $140,000*130%

                                                     = $182,000

Bonus received by C = $182,000 – $140,000

                                   = $42,000

The bonus amount is contributed by remaining partners in equal ratio i.e. $42,000/3 = $14,000.

The capital balances of remaining partners are:

A’s capital = Capital balance – Investment

                   = $70,000 – $14,000

                   = $56,000

B’s capital = Capital balance – Investment

                   = $90,000 – $14,000

                   = $76,000

D’s capital = Capital balance – Investment

                   = $170,000 – $14,000

                   = $156,000