Chapter 13, Problem 37P

To determine

Calculate the missing amounts and fill the amounts in the appropriate blanks.

Answer to Problem 37P

Calculate the missing amounts.

Particulars	Division A	Division B	Division C
Sales revenue	$2,000,000	$10,000,000	$800,000
Income	$400,000	$ 2,000,000	$200,000
Average investment	$2,000,000	$2,500,000	$1,000,000
Sales margin	20%	20%	25%
Capital turnover	1	4	0.8
ROI	20%	80%	20%
Residual income	$240,000	$1,800,000	$120,000

Table (1)

Explanation of Solution

Working note (a):

Calculate the amount of sales margin for Division A.

$\begin{array}{c}\text{Sales margin}=\frac{\text{Income}}{\text{Sales revenue}}\\ 20\%=\frac{\$400,000}{\text{Sales revenue}}\\ \text{Sales revenue = }\frac{\$400,000}{\text{20\%}}\\ =\$2,000,000\end{array}$

Thus, the amount of sales margin for Division A is $2,000,000.

Working note (b):

Calculate the amount of capital turnover for Division A.

$\begin{array}{c}\text{Capital turnover}=\frac{\text{Sales revenue}}{\text{Invested capital}}\\ 1=\frac{\$2,000,000}{\text{Invested capital}}\\ =\$2,000,000\end{array}$

Thus, the amount of capital turnover for Division A is $2,000,000.

Working note (c):

Calculate the amount of return on investment (ROI) for Division A.

$\begin{array}{c}\text{Return on investment}=\text{Sales margin}\times \text{Capital turnover}\\ =20\%\times 1\\ =20\%\end{array}$

Thus, the return on investment for Division A is 20%.

Working note (d):

Calculate the amount of residual income for Division A.

$\begin{array}{c}\text{Residual income}=\text{Income}-\left(\text{Inputed interest rate}\right)\left(\text{Invested capital}\right)\\ =\$400,000-\left(8\%\right)\left(\$2,000,000\right)\\ =\$240,000\end{array}$

Thus, the amount of residual income for Division A is $240,000.

Working note (e):

Calculate the amount of sales margin for Division B.

$\begin{array}{c}\text{Sales margin}=\frac{\text{Income}}{\text{Sales revenue}}\\ =\frac{\$2,000,000}{\$10,000,000}\\ =20\%\end{array}$

Thus, the sales margin for Division B is 20%.

Working note (f):

Calculate the amount of capital turnover for Division B.

$\begin{array}{c}\text{Capital turnover}=\frac{\text{Sales revenue}}{\text{Invested capital}}\\ =\frac{\$10,000,000}{\$2,500,000}\\ =4\text{ times}\end{array}$

Thus, the capital turnover for Division B is 4 times.

Working note (g):

Calculate the return on investment for Division B.

$\begin{array}{c}\text{Return on investment}=\text{Sales margin}\times \text{Capital turnover}\\ =20\%\times 4\\ =80\%\end{array}$

Thus, the return on investment for Division B is 80%.

Working note (h):

Calculate the amount of residual income for Division B.

$\begin{array}{c}\text{Residual income}=\text{Income}-\left(\text{Imputed interest rate}\right)\left(\text{Invested capital}\right)\\ =\$2,000,000-\left(\text{8\%}\right)\left(\$2,500,000\right)\\ =\$1,800,000\end{array}$

Thus, the amount of residual income for Division B is $1,800,000.

Working note (i):

Calculate the capital turnover for Division C.

$\begin{array}{c}\text{Return on investment}=\text{Sales margin}\times \text{Capital turnover}\\ 20\%=25\%\times \text{Capital turnover}\\ =0.8\end{array}$

Thus, the capital turnover for Division C is 0.8.

Working note (j):

Calculate the total amount of invested capital for Division C.

Given: The Residual income is $120,000 and the required rate of return on invested capital is 8 percent.

$\begin{array}{c}\text{Residual Income =Income}-\left(\text{Imputed interest rate}\right)\times \left(\text{Invested capital}\right)\\ \text{Income}=\text{Residual Income}-\left(\text{Imputed interest rate}\right)\times \left(\text{Invested capital}\right)\\ =\left[\$120,000-\left(\text{8\%}\right)\times \left(\text{Invested capital}\right)\right]\text{(A)}\end{array}$

The Return on Investment is 20%. So, calculate the amount of invested capital:

$\begin{array}{c}\text{Return on investment}=\frac{\text{Income}}{\text{Invested capital}}\\ 20\%=\frac{\text{Income}}{\text{Invested capital}}\\ \text{Income}=20\%\times \text{Invested capital}\left(\text{B}\right)\end{array}$

Thus, substituting the equations the invested capital is determined as follows:

$\begin{array}{c}\text{Residual Income =Income}-\left(\text{Imputed interest rate}\right)\times \left(\text{Invested capital}\right)\\ \$120,000=\left(20\%\times \text{Invested capital}\right)-\left(\text{8\%}\right)\times \left(\text{Invested capital}\right)\\ \text{\$120,000}=\left(20\%-8\%\right)\times \text{Invested capital}\\ \text{\$120,000}=12\%\times \left(\text{Invested capital}\right)\end{array}$

$\begin{array}{c}\text{Invested capital =}\frac{\$120,000}{12\%}\\ \text{Invested capital }=\$100,000\end{array}$

Thus, the amount of invested capital for Division C is $100,000.

Working note (k):

Calculate the amount of income.

$\begin{array}{c}\text{Retrun on investment}=\frac{\text{Income}}{\text{Invested capital}}\\ 20\%=\frac{\text{Income}}{\text{\$1,000,000}}\\ \text{Income = }20\%\times \text{\$1,000,000}\\ =\$200,000\end{array}$

Thus, the amount of income for Division C is $200,000.

Working note (l):

Calculate the amount of sales revenue for Division C.

$\begin{array}{c}\text{Sales margin}=\frac{\text{Income}}{\text{Sales revenue}}\\ 25\%=\frac{\text{\$200,000}}{\text{Sales revenue}}\\ =\$800,000\end{array}$

Thus, the amount of sales revenue for Division C is $800,000.