Chapter 14, Problem 14.16E

To determine

(a)

Concept Introduction:

Rate of return on investment represents the investment performance. It is beneficial for investor to compare different investments and select best investment. The benefit or return from the original cost of investment is return on investment.

The missing items in return on investment and residual income computations.

Answer to Problem 14.16E

The following table represents various rates of return on investment and residual incomes:

Divisions	Sales	Income from operations	Invested Assets	Return on Investment	Profit Margin	Investment Turnover
California	$\$6,000,000$	$\$1,200,000$	$\$7,500,000$	$16\%$	$20\%$	$8$
Midwest	$\$12,600,000$	$\$1,512,000$	$\$9,000,000$	$16.8\%$	$12\%$	$1.40$
Northwest	$\$13,750,000$	$\$1,925,000$	$\$11,000,000$	$17.5\%$	$14\%$	$1.25$
Texas	$\$5,250,000$	$\$840,000$	$\$3,500,000$	$24\%$	$16\%$	$1.50$

Explanation of Solution

California:

  $\begin{array}{c}\text{Rate of return on investment = }\frac{\text{Income from operation}}{\text{Invested assets}}\\ 16\%=\frac{\text{Sales}\times \text{Profit Margin}}{\text{Invested assets}}\\ 16\%=\frac{\$6,000,000\times 20\%}{\text{Invested assets}}\\ \text{Invested Assets}=\frac{\$1,200,000}{16\%}\\ \text{Invested Assets}=\$7,500,000\end{array}$

Thus, operating income is $\$1,200,000$.

Invested turnover is computed as:

  $\begin{array}{c}\text{Invested Turnover}=\frac{\text{Sales}}{\text{Invested assets}}\\ =\frac{\$6,000,000}{\$7,500,000}\\ =8\end{array}$

Midwest:

  $\begin{array}{c}\text{Income from operations}=\text{Sales}\times \text{Profit margin}\\ \text{Sales}=\frac{\text{Income from operations}}{\text{Profit margin}}\\ =\frac{\$1,512,000}{12\%}\\ =12,600,000\end{array}$

Invested asset is computed as:

  $\begin{array}{c}\text{Invested Turnover}=\frac{\text{Sales}}{\text{Invested assets}}\\ \text{Invested Assets}=\frac{\text{Sales}}{\text{Invested turnover}}\\ =\frac{12,600,000}{1.4}\\ =\$9,000,000\end{array}$

Return on investment is as:

  $\begin{array}{c}\text{Rate of return on investment = }\frac{\text{Income from operation}}{\text{Invested assets}}\\ =\frac{\$1,512,000}{\$9,000,000}\\ =16.8\%\end{array}$

Northwest:

  $\begin{array}{c}\text{Rate of return on investment = }\frac{\text{Income from operation}}{\text{Invested assets}}\\ 17.5\%=\frac{\text{Income from operation}}{\$11,000,000}\\ \text{Income from operations}=\$1,925,000\end{array}$

Invested turnover is computed as:

  $\begin{array}{c}\text{Invested Turnover}=\frac{\text{Sales}}{\text{Invested assets}}\\ =\frac{\$13,750,000}{\$11,000,000}\\ =1.25\end{array}$

  $\begin{array}{c}\text{Income from operations}=\text{Sales}\times \text{Profit margin}\\ \text{Profit Margin}=\frac{\text{Income from operations}}{\text{Sales}}\\ =\frac{\$1,925,000}{\$13,750,000}\\ =14\%\end{array}$

Texas:

  $\begin{array}{c}\text{Rate of return on investment = }\frac{\text{Income from operation}}{\text{Invested assets}}\\ =\frac{\$840,000}{\$3,500,000}\\ =24\%\end{array}$

  $\begin{array}{c}\text{Income from operations}=\text{Sales}\times \text{Profit margin}\\ \text{Profit Margin}=\frac{\text{Income from operations}}{\text{Sales}}\\ =\frac{\$840,000}{\$5,250,000}\\ =16\%\end{array}$

Invested turnover is computed as:

  $\begin{array}{c}\text{Invested Turnover}=\frac{\text{Sales}}{\text{Invested assets}}\\ =\frac{\$5,250,000}{\$3,500,000}\\ =1.5\end{array}$

To determine

(b)

Concept Introduction:

Rate of return on investment represents the investment performance. It is beneficial for investor to compare different investments and select best investment. The benefit or return from the original cost of investment is return on investment.

The residual income assuming the minimum acceptable rate of return is $10\%$.

Answer to Problem 14.16E

The following table represents various rates of return on investment and residual incomes:

Divisions	Sales	Income from operations   $\left(\text{a}\right)$	Invested Assets   $\left(\text{b}\right)$	Minimum rate of return   $\left(\text{c}\right)$	Minimum income   $\left(\text{d}\right)$	Residual income   $\left(\text{e}\right)$
California	$\$6,000,000$	$\$1,200,000$	$\$7,500,000$	$10\%$	$\$750,000$	$\$450,000$
Midwest	$\$12,600,000$	$\$1,512,000$	$\$9,000,000$	$10\%$	$\$900,000$	$\$612,000$
Northwest	$\$13,750,000$	$\$1,925,000$	$\$11,000,000$	$10\%$	$\$1,100,000$	$\$825,000$
Texas	$\$5,250,000$	$\$840,000$	$\$3,500,000$	$10\%$	$\$350,000$	$\$490,000$

Explanation of Solution

The minimum income is computed by multiplying the invested assets with the minimum rate of return.

As in the above table the minimum income i.e. $\left(\text{d}\right)$ is computed by multiplying the invested assets i.e. $\left(\text{b}\right)$ and minimum rate of return i.e. $\left(\text{c}\right)$.

The residual income is calculated by computing the difference between income from operations and minimum income.

As in the above table the residual income i.e. $\left(\text{e}\right)$ is computed by subtracting the minimum income i.e. $\left(\text{d}\right)$ from the income from operations i.e. $\left(\text{a}\right)$.

To determine

(c)

Concept Introduction:

Rate of return on investment represents the investment performance. It is beneficial for investor to compare different investments and select best investment. The benefit or return from the original cost of investment is return on investment.

The profitable division in term of return on investment and residual income.

Answer to Problem 14.16E

The profitable division in term of return on investment is Texas and residual income is Northwest.

Explanation of Solution

The return on investment is highest in the Texas division in comparison to others. So, it is the most profitable division in terms of return.

The residual income is highest in the Northwest division in comparison to others. So, it is the most profitable division in terms of residual income.