Chapter 13, Problem 13.3P

To determine

Concept Introduction:

People start their own business and select the form of organization depending upon their need and kind of their business. Partnership is one form of organization. The allocation of profit and loss between the partners is based on the profit-sharing ratio given in the partnership deed and if no priority system is followed then profit and loss will be divided equally.

The best alternative for Mr. R.

Answer to Problem 13.3P

Preparation of the comparative schedule for the two alternatives as follows:

Alternative one		Alternative two
Payment date	Present value	Payment date	Present value
March, $2016$ (for $2015$)	$\$15,78,704$	March, $2016$ (for $2015$)	$\$1,89,815$
March, $2017$ (for $2016$)	$\$1,16,941$	March, $2017$ (for $2016$)	$\$1,03,224$
March, $2018$ (for $2017$)	$\$1,16,941$	March, $2018$ (for $2017$)	$\$14,63,852$
Total	$\$18,12,586$		$\$17,56,891$

The return in alternative one is higher than the return in alternative two. Therefore, Mr. R will have to choose an alternative one.

Explanation of Solution

Alternative$1$:

Mr. R will receive his share of the current year $2015$ on March $31,\text{ 2016}$ with a lump sum payment of $\$15,00,000$ . Mr. R can invest the money at the rate of $8\%$ p.a. compounded annually.

The profit distribution for $2015$ is as follows:

Component	Mr. R	Other partners
Salaries	$\$1,25,000$	$\$3,00,000$
Bonus on income after bonus	$10\%$	$0\%$
% of the remaining profit	$40\%$	$60\%$

The income for the year $2015,\text{ 2016 and 2017}$ is $\$5,50,000,\text{ \$6,50,000 and \$6,82,000}$ respectively.

a. Computation of share of Mr. R in the current year profit $\left(2015\right)$ .

Particulars	Mr. R	Other partners	Total
Income $\left(2015\right)$			$\$5,50,000$
Salaries	$\$1,25,000$	$\$3,00,000$	$\$4,25,000$
Bonus (Note - $1$)	$\$50,000$	-	$\$50,000$
Sub-total	$\$1,75,000$	$\$3,00,000$	$\$4,75,000$
Remaining profit (Note - $2$)	$\$30,000$	$\$45,000$	$\$75,000$
Income allocation	$\$2,05,000$	$\$3,45,000$	$\$5,50,000$

• Note - $1$ : Calculation of bonus:

  $\begin{array}{l}\text{Bonus}=\left(\text{Net income - Bonus}\right)\times 10\%\\ \text{Bonus}=\left(\$5,50,000-\text{Bonus}\right)\times 10\%\\ Bonus\text{ + 10\% of Bonus = \$5,50,000}\times \text{10\%}\\ \text{110\% Bonus = \$55,000}\\ \text{Bonus = }\frac{\text{\$55,000}}{110\%}\\ \text{Bonus = \$50,000}\end{array}$

• Note - $2$ : Calculation of profit share of Mr. R:

The remaining profit is $\$75,000$ and his share is $40\%$ . So, profit is:

  $\begin{array}{c}\text{Profit}=\$75,000\times 40\%\\ =\$30,000\end{array}$

And, another partner’s share is:

  $\begin{array}{c}\text{Share}=\$75,000-\$30,000\\ =\$45,000\end{array}$

Therefore, the total share of income is $\$2,05,000$ of Mr. R in the current year and lump sum compensation is $\$15,00,000$ .

Computation of present value cash flow in the financial year $\text{2016, 2017 and 2018}$ at $8\%$ compound interest as follows:

Component	$2016$	$2017$	$2018$	Total
Total income allocation in the previous year	$\$2,05,000$	-	-	$\$2,05,000$
The lump-sum payment	$\$15,00,000$	-	-	$\$15,00,000$
$8\%$ return on investment (Note - $3$ )	-	$\$1,36,400$	$\$1,47,312$	$\begin{array}{l}\$2,83,712\\ \end{array}$
Total	$\$17,05,000$	$\$1,36,400$	$\$1,47,312$	$\$19,88,712$
Present value index	$0.9259$	$0.8573$	$0.7938$
Net present value	$\$15,78,704$	$\$1,16,941$	$\$1,16,941$	$\$18,12,586$

• Note - $3$ : Computation of return on investment in the subsequent year at $8\%$ compound interest as follows:

Year	Investment	Amount of return
March $31,\text{ 2017}$	$\$17,05,000$	$\$1,36,400$
March $31,\text{ 2018}$	$\begin{array}{l}\$18,41,400\\ \left(\$17,05,000+\$1,36,400\right)\end{array}$	$\$1,47,312$

Therefore, the total income in the alternative one is $\$18,12,586$ .

Alternative$2$:

Mr. R will receive his share of the current year $2015$ . Share of profit of $\text{2016 and 2017}$ on subsequent year in March $31$ . And, as in March $31,\text{ 2018}$ he will receive a lump sum payment of $\$17,00,000$ . Mr. R can invest the money at the rate of $8\%$ p.a. compounded annually.

The profit distribution for $2015$ is as follows:

Component	Mr. R	Other partners
Salaries	$\$80,000$	$\$3,00,000$
Bonus on income after bonus	$0\%$	$10\%$
% of the remaining profit	$20\%$	$80\%$

b. Computation of share of Mr. R in the current year profit $2017$ .

Particulars	Mr. R	Other partners	Total
Income $\left(2016\right)$			$\$6,05,000$
Salaries	$\$80,000$	$\$3,50,000$	$\$4,30,000$
Bonus (Note - $4$)	-	$\$55,000$	$\$55,000$
Sub-total	$\$80,000$	$\$4,05,000$	$\$4,85,000$
Remaining profit (Note - $5$)	$\$24,000$	$\$96,000$	$\$1,20,000$
Income allocation	$\$1,04,000$	$\$5,01,000$	$\$6,05,000$

• Note - $4$ : Calculation of bonus:

  $\begin{array}{l}\text{Bonus}=\left(\text{Net income - Bonus}\right)\times 10\%\\ \text{Bonus}=\left(\$6,05,000-\text{Bonus}\right)\times 10\%\\ Bonus\text{ + 10\% of Bonus = \$6,05,000}\times \text{10\%}\\ \text{110\% Bonus = \$60,500}\\ \text{Bonus = }\frac{\text{\$60,500}}{110\%}\\ \text{Bonus = \$55,000}\end{array}$

• Note - $5$ : Calculation of profit share of Mr. R:

The remaining profit is $\$1,20,000$ and his share is $20\%$ . So, profit is:

  $\begin{array}{c}\text{Profit}=\$1,20,000\times 20\%\\ =\$24,000\end{array}$

And, another partner’s share is:

  $\begin{array}{c}\text{Share}=\$1,20,000-\$24,000\\ =\$96,000\end{array}$

Computation of present value of March, $2017$ :

Component	Amount
Share from income allocation	$\$1,04,000$
Return on proceeds (Note - $8$)	$\$16,400$
Total proceeds	$\$1,20,400$
Present value index	$0.8573$
Present value	$\$1,03,224$

Therefore, the present value is $\$1,03,224$ .

c. Computation of share of Mr. R in the current year profit $2018$ .

Particulars	Mr. R	Other partners	Total
Income $\left(2016\right)$			$\$6,82,000$
Salaries	$\$80,000$	$\$3,50,000$	$\$4,30,000$
Bonus (Note - $6$)	-	$\$62,000$	$\$62,000$
Sub-total	$\$80,000$	$\$4,12,000$	$\$4,92,000$
Remaining profit (Note - $7$)	$\$38,000$	$\$1,52,000$	$\$1,90,000$
Income allocation	$\$1,18,000$	$\$5,64,000$	$\$6,82,000$

• Note - $6$ : Calculation of bonus:

  $\begin{array}{l}\text{Bonus}=\left(\text{Net income - Bonus}\right)\times 10\%\\ \text{Bonus}=\left(\$6,82,000-\text{Bonus}\right)\times 10\%\\ Bonus\text{ + 10\% of Bonus = \$6,82,000}\times \text{10\%}\\ \text{110\% Bonus = \$68,200}\\ \text{Bonus = }\frac{\text{\$68,200}}{110\%}\\ \text{Bonus = \$62,000}\end{array}$

• Note - $7$ : Calculation of profit share of Mr. R:

The remaining profit is $\$1,90,000$ and his share is $20\%$ . So, profit is:

  $\begin{array}{c}\text{Profit}=\$1,90,000\times 20\%\\ =\$38,000\end{array}$

And, another partner’s share is:

  $\begin{array}{c}\text{Share}=\$1,90,000-\$38,000\\ =\$1,52,000\end{array}$

Computation of present value of March, $2018$ :

Component	Amount
Share from income allocation	$\$1,18,000$
Duplication of capital investment	$\$17,00,000$
Return on proceeds (Note - $8$)	$\$26,032$
Total proceeds	$\$18,44,032$
Present value index	$0.7938$
Present value	$\$14,63,852$

Therefore, the present value is $\$14,63,852$ .

• Note - $8$ : Computation of return on investment in the subsequent year at $8\%$ compound interest as follows:

Year	Investment	Amount of return
March $31,\text{ 2017}$	$\$2,05,000$	$\$16,400$
March $31,\text{ 2018}$	$\begin{array}{l}\$3,25,000\\ \left(\$2,05,000+\$1,20,000\right)\end{array}$	$\$26,032$

Therefore, the present value in alternative two by adding all these is:

  $\begin{array}{c}\text{PV}=\$1,89,815+\$1,03,224+\$14,63,852\\ =\$17,56,891\end{array}$

So, the total cash flow in alternative two is $\$17,56,891$ .