Chapter 9, Problem 27P

a.

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.

b.

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

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

c.

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

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

d.

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

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

e.

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

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