Chapter 9, Problem 27P

Following is the current balance sheet for a local partnership of doctors:

Cash and current	Liabilities.................. $ 40,000
assets................... $ 30,000	A, capital.................. 20,000
Land...................... 180,000	B, capital.................. 40,000
Building and equipment	C，capital.................. 90,000
(net)..................... 100,000	D, capital.................. 120,000
Totals................... $310,000	Totals................... $310,000

The following questions represent independent situations:

1. a. E is going to invest enough money in this partnership to receive a 25 percent interest. No goodwill or bonus is to be recorded. How much should E invest?
2. b. E contributes $36,000 in cash to the business to receive a 10 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?
3. c. 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?
4. d. E contributes $55,000 in cash to the business to receive a 20 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?
5. e. C retires from the partnership and, as per the original partnership agreement, is to receive cash equal to 125 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?

To determine

Find the amount that E should invest to receive a 25 percent interest.

Answer to Problem 27P

E should invest $90,000 to receive a 25 percent interest.

Explanation of Solution

Calculate E’s investment

$\begin{array}{c}\text{E's}\text{investment}=25\%\times \left(\text{Original}\text{capital}+\text{E's}\text{investment}\right)\\ =25\%\times \left(\$20,000+\$40,000+\$90,000+\$120,000+\text{E's}\text{investment}\right)\\ =25\%\times \left(\$270,000+\text{E's}\text{investment}\right)\\ =\$67,500+25\%\text{E's}\text{investment}\end{array}$

Now, further calculation

$\begin{array}{c}1-0.25\text{E's}\text{investment}=\$67,500\\ 0.75\text{E's}\text{investment}=\$67,500\\ \text{E's}\text{investment}=\frac{\$67,500}{0.75}\\ \text{E's}\text{investment}=\$90,000\end{array}$

E should invest $90,000 to receive a 25 percent interest.

To determine

Find the individual capital balances after E makes the investment of $36,000.

Explanation of Solution

Individual capital balances after E makes the investment of $36,000

Particulars	A	B	C	D	E
Original Capital	$       20,000	$        40,000	$       90,000	$    120,000	$          0
Goodwill	$       16,200	$          5,400	$       21,600	$      10,800	$          0
Investment	$                 -	$                  -	$                -	$               0	$ 36,000
Capital balance	$       36,200	$        45,400	$     111,600	$    130,800	$ 36,000

Working note

Calculate the implied value of the partnership

$\begin{array}{c}\text{Implied}\text{value}=\frac{\$36,000}{10\%}\\ =\$36,000\times \frac{100}{10}\\ =\frac{\$3,600,000}{10}\\ =\$360,000\end{array}$

Calculate total capital after investment of E

$\begin{array}{c}\text{Total}\text{capital}=\$20,000+\$40,000+\$90,000+\$120,000+\$36,000\\ =\$306,000\end{array}$

Calculate goodwill

$\begin{array}{c}\text{Goodwill}=\text{Implied}\text{value}-\text{Total}\text{capital}\\ =\$360,000-\$306,000\\ =\$54,000\end{array}$

Calculate distribution of goodwill

$\begin{array}{c}\text{Goodwill}\text{share}\text{of}\text{A}=\$54,000\times 30\%\\ =\$16,200\\ \text{Goodwill}\text{share}\text{of}\text{B}=\$54,000\times 10\%\\ =\$5,400\end{array}$

Now, goodwill share of other partners

$\begin{array}{c}\text{Goodwill}\text{share}\text{of}\text{C}=\$54,000\times 40\%\\ =\$21,600\\ \text{Goodwill}\text{share}\text{of}\text{D}=\$54,000\times 20\%\\ =\$10,800\end{array}$

To determine

Find the individual capital balances after E makes the investment of $42,000.

Explanation of Solution

Individual capital balances after E makes the investment of $42,000

Particulars	A	B	C	D	E
Original Capital	$       20,000	$        40,000	$       90,000	$      120,000	$          -
Goodwill	$         6,375	$          6,375	$         6,375	$          6,375	$          -
Investment	$                 -	$                  -	$                -	$                 0	$ 42,000
Capital balance	$       26,375	$        46,375	$       96,375	$      126,375	$ 42,000

Working note

Calculate the implied value of the partnership

$\begin{array}{c}\text{Implied}\text{value}=\frac{\$42,000}{20\%}\\ =\$42,000\times \frac{100}{20}\\ =\frac{\$4,200,000}{20}\\ =\$210,000\end{array}$

Calculate total capital after investment of E

$\begin{array}{c}\text{Total}\text{capital}=\$20,000+\$40,000+\$90,000+\$120,000+\$42,000\\ =\$312,000\end{array}$

Calculate goodwill

$\begin{array}{c}\text{E}\text{investment}+\text{Goodwill}=20\%\times \left(\text{Original}\text{capital}+\text{E's}\text{investment}\right)\\ \$42,000+\text{Goodwill}=20\%\times \left(\$270,000+\$42,000+\text{Goodwill}\right)\\ \$42,000+\text{Goodwill}=\$54,000+\$8,400+\text{Goodwill}\\ \$42,000+\text{Goodwill}=\$62,400+0.20\text{Goodwill}\end{array}$

Now, further calculate goodwill

$\begin{array}{c}\text{Goodwill}-0.20\text{Goodwill}=\$62,400-\$42,000\\ 0.80\text{Goodwill}=\$20,400\\ \text{Goodwill}=\frac{\$20,400}{0.80}\\ \text{Goodwill}=\$25,500\end{array}$

Goodwill is distributed equally among all the partners

$\begin{array}{c}\text{Goodwill}\text{to}\text{partners}\text{=}\$25,500\times 25\%\\ =\$6,375\end{array}$

To determine

Find the individual capital balances after E makes the investment of $55,000.

Explanation of Solution

Individual capital balances after E makes the investment of $55,000

Particulars	A	B	C	D	E
Original Capital	$       20,000	$        40,000	$       90,000	$        120,000	$          -
Investment	$                 -	$                  -	$                -	$                   -	$ 55,000
Bonus	$        (1,000)	$         (3,000)	$       (2,000)	$          (4,000)	$ 10,000
Capital balance	$       19,000	$        37,000	$       88,000	$        116,000	$ 65,000

Working note

Calculate the implied value of the partnership

$\begin{array}{c}\text{Implied}\text{value}=\frac{\$55,000}{20\%}\\ =\$55,000\times \frac{100}{20}\\ =\frac{\$5,500,000}{20}\\ =\$275,000\end{array}$

Calculate total capital after investment of E

$\begin{array}{c}\text{Total}\text{capital}=\$20,000+\$40,000+\$90,000+\$120,000+\$55,000\\ =\$325,000\end{array}$

Calculate E’s share in total capital

$\begin{array}{c}\text{E's}\text{share}\text{in}\text{total}\text{capital}=\$325,000\times 20\%\\ =\$65,000\end{array}$

Capital share of E is $65,000 and he invested $55,000. The difference of $10,000 is bonus invested by all the other partners in their profit sharing ratios.

Calculate distribution of bonus

$\begin{array}{c}\text{Bonus}\text{share}\text{of}\text{A}=\$10,000\times 10\%\\ =\$1,000\\ \text{Bonus}\text{share}\text{of}\text{B}=\$10,000\times 30\%\\ =\$3,000\end{array}$

Now, goodwill share of other partners

$\begin{array}{c}\text{Bonusa}\text{share}\text{of}\text{C}=\$10,000\times 20\%\\ =\$2,000\\ \text{Bonus}\text{share}\text{of}\text{D}=\$10,000\times 40\%\\ =\$4,000\end{array}$

To determine

Find the individual capital balances of the remaining partners after the withdrawal of C.

Explanation of Solution

Calculate individual capital balances of the remaining partners after the withdrawal of C

Particulars	A	B	C	D
Original Capital	$       20,000	$        40,000	$       90,000	$        120,000
Bonus	$        (7,500)	$         (7,500)	$       22,500	$          (7,500)
Payment	$                 -	$                  -		$                   -
Total	$       12,500	$        32,500	$   (112,500)	$        112,500

Capital balance of C is $90,000 and he has to collect cash equal to 125% of final capital, balance.

Working note

Calculate cash to be collected

$\begin{array}{c}\text{Cash}\text{to}\text{be}\text{collected}=\$90,000\times 125\%\\ =\$112,500\end{array}$

No goodwill is recognised means bonus method is followed and bonus amount will be given to C

Calculate bonus

$\begin{array}{c}\text{Bonus}=\$112,500-\$90,000\\ =\$22,500\end{array}$

Profits and losses are equally distributed. Hence, contribution of bonus is also equal.

Calculate distribution of bonus by each partner

$\begin{array}{c}\text{Bonus}\text{contribution}=\frac{\$22,500}{3}\\ =\$7,500\end{array}$