Chapter 11, Problem 43P

Return on Investment and Economic Value Added Calculations with Varying Assumptions

Knitpix Products is a division of Parker Textiles Inc. During the coming year, it expects to earn income of $310,000 based on sales of $3.45 million. Without any new investments, the division will have average operating assets of $3 million. The division is considering a capital investment project—adding knitting machines to produce gaiters—that requires an additional investment of $600,000 and increases net income by $57,500 (sales would increase by $575,000). If made, the investment would increase beginning operating assets by $600,000 and ending operating assets by $400,000. Assume that the actual cost of capital for the company is 7%. (Note: Round all answers to four decimal places.)

Required:

1. 1. Compute the ROI for the division without the investment.
2. 2. Compute the margin and turnover ratios without the investment. Show that the product of the margin and turnover ratios equals the ROI computed in Requirement 1.
3. 3. CONCEPTUAL CONNECTION Compute the ROI for the division with the new investment. Do you think the divisional manager will approve the investment?
4. 4. CONCEPTUAL CONNECTION Compute the margin and turnover ratios for the division with the new investment. How do these compare with the old ratios?
5. 5. CONCEPTUAL CONNECTION Compute the EVA of the division with and without the investment. Should the manager decide to make the knitting machine investment?

To determine

Calculate ROI for the division without investment.

Answer to Problem 43P

The percentage of ROI is 0.1033 or 10.33%.

Explanation of Solution

Return on Investment (ROI):

Return on investment can be defined as the amount of profit earned by the company on per dollar of investment. It can be computed by dividing operating income by the average operating assets.

Use the following formula to calculate ROI for division without investment:

$\text{ROI}=\frac{\text{Operating Income}}{\text{Average operating assets}}$

Substitute $310,000 for operating income and $3,000,000 for average operating assets in the above formula.

$\begin{array}{c}\text{ROI}=\frac{\$310,000}{\$3,000,000}\\ =0.1033\end{array}$

Therefore, the percentage of ROI is 0.1033 or 10.33%.

To determine

Calculate margin and turnover ratios without investment. Also, describe the product of margin and turnover is equal to the ROI computed.

Answer to Problem 43P

The margin and turnover without investment is 8.99% and 1.15 respectively.

Explanation of Solution

Margin:

The Proportion of operating income to the amount of sales revenue is known as margin. It represents the proportion of sales revenue left, to cover taxes, interest, and profit.

Turnover:

Turnover can be defined as the amount of dollar sales earned by the company from investing every dollar in the operating assets. It is computed by dividing the amount of sales by the average operating assets.

Use the following formula to calculate the margin without investment:

$\text{Margin}=\frac{\text{Operating income}}{\text{Sales}}$

Substitute $310,000 for operating income and $3,450,000 for sales in the above formula.

$\begin{array}{c}\text{Margin}=\frac{\$310,000}{\$3,450,000}\\ =0.0899\end{array}$

Therefore, the percentage of margin is 0.0899 or 8.99% of sales.

Use the following formula to calculate the turnover without investment:

$\text{Turnover}=\frac{\text{Sales}}{\text{Average operating assets}}$

Substitute $3,450,000 for sales and $3,000,000 for average operating assets in the above formula.

$\begin{array}{c}\text{Turnover}=\frac{\$3,450,000}{\$3,000,000}\\ =1.15\end{array}$

Therefore, the turnover is 1.15.

Use the formula to calculate ROI by multiplying turnover and margin:

$\text{ROI}=\text{Margin}\times \text{Turnover}$

Substitute 8.99% for margin and 1.15 for turnover in the above formula.

$\begin{array}{c}\text{ROI}=8.99\%\times 1.15\\ =10.33\%\end{array}$

Therefore, the ROI is 10.33%. It is confirmed that product of margin and turnover is ROI, same as proportion of operating income to average operating assets.

To determine

Calculate ROI with new investment. Also, describe whether the manager should approve the investment.

Answer to Problem 43P

The percentage of ROI is 0.105 or 10.5%.

Explanation of Solution

Use the following formula to calculate ROI for division with investment:

$\text{ROI}=\frac{{\text{Operating Income}}^{\text{1}}}{{\text{Average operating assets}}^{\text{2}}}$

Substitute $367,500 for operating income and $3,500,000 for average operating assets in the above formula.

$\begin{array}{c}\text{ROI}=\frac{\$367,500}{\$3,500,000}\\ =0.105\end{array}$

Therefore, the percentage of ROI is 0.105 or 10.5%.

Manager should approve the investment as ROI with investment of 10.5% is slightly higher than ROI without investment, which is 10.33%.

Working Notes:

1. Calculation of operating income:

$\begin{array}{c}\text{Operating income}=\text{Division income}+\text{Investment income}\\ =\$310,000+\$57,500\\ =\$367,500\end{array}$

Hence, the operating income with investment is $367,500.

2. First, calculate average assets of investment in order to calculate overall average assets:

$\begin{array}{c}\text{Average assets of investment}=\frac{\left(\text{Beginning assets}+\text{Ending assets}\right)}{2}\\ =\frac{\left(\$600,000+\$400,000\right)}{2}\\ =\$500,000\end{array}$

Hence, the average asset of investment is $500,000.

Now, calculate the overall average assets:

$\begin{array}{c}\text{Average assets}=\text{Average assets of division}+\text{Average assets of investment}\\ =\$3,000,000+\$500,000\\ =\$3,500,000\end{array}$

Hence, the average asset with investment is $3,500,000.

To determine

Calculate margin and turnover ratios with new investment.

Answer to Problem 43P

The margin and turnover with new investment is 9.13% and 1.15 respectively.

Explanation of Solution

Use the following formula to calculate the margin with new investment:

$\text{Margin}=\frac{\text{Operating income}}{{\text{Sales}}^{\text{3}}}$

Substitute $367,500 for operating income and $4,025,000 for sales in the above formula.

$\begin{array}{c}\text{Margin}=\frac{\$367,500}{\$4,025,000}\\ =0.0913\end{array}$

Therefore, the percentage of margin is 0.0913 or 9.13% of sales.

Use the following formula to calculate the turnover with new investment:

$\text{Turnover}=\frac{\text{Sales}}{\text{Average operating assets}}$

Substitute $4,025,000 for sales and $3,500,000 for average operating assets in the above formula.

$\begin{array}{c}\text{Turnover}=\frac{\$4,025,000}{\$3,500,000}\\ =1.15\end{array}$

Therefore, the turnover is 1.15.

There is an increase in the margin while considering the new investment whereas, the turnover remains the same.

Working Note:

3. Calculation of sales with new investment:

$\begin{array}{c}\text{Sales}=\text{Sales without investment}+\text{Increase}\\ =\$3,450,000+\$575,000\\ =\$4,025,000\end{array}$

Hence, the amount of sales with new investment is $4,025,000.

To determine

Calculate EVA with and without the division. Describe whether the manager should make the knitting machine investment.

Answer to Problem 43P

The amount of EVA with and without investment is $122,500 and $100,000 respectively.

Explanation of Solution

Economic Value Added (EVA):

Economic value added can be evaluated by deducting the dollar amount of capital employed from the operating income after tax. The dollar amount of capital employed can be calculated by multiplying the capital employed by the percentage of the cost of capital.

Use the following formula to calculate the economic value added without investment:

$\text{EVA}=\text{After tax operating income}-\left(\begin{array}{l}\text{Total capital employed}\times \\ \text{Actual percentage of cost of capital}\end{array}\right)$

Substitute $310,000 for after-tax operating income, $3,000,000 for total capital employed and 7% for the actual percentage of the cost of capital in the above formula.

$\begin{array}{c}\text{EVA}=\$310,000-\left(\$3,000,000\times 7\%\right)\\ =\$310,000-\$210,000\\ =\$100,000\end{array}$

Therefore, the amount of EVA without investment is $100,000. In this case, the operating income will be considered as after-tax operating income and average operating assets as total capital employed.

Use the following formula to calculate the economic value added with new investment:

$\text{EVA}={\text{After tax operating income}}^{\text{4}}-\left(\begin{array}{l}{\text{Total capital employed}}^{\text{5}}\times \\ \text{Actual percentage of cost of capital}\end{array}\right)$

Substitute $367,500 for after-tax operating income, $3,500,000 for total capital employed and 7% for the actual percentage of the cost of capital in the above formula.

$\begin{array}{c}\text{EVA}=\$367,500-\left(\$3,500,000\times 7\%\right)\\ =\$367,500-\$245,000\\ =\$122,500\end{array}$

Therefore, the amount of EVA with new investment is $122,500.

As the amount of economic value added increases with new investment, the manager should invest in the knitting machine.

Working Notes:

4. Calculation of after-tax operating income:

$\begin{array}{c}\text{After-tax operating income}=\text{Division income}+\text{Investment income}\\ =\$310,000+\$57,500\\ =\$367,500\end{array}$

Hence, the after-tax operating income with investment is $367,500.

5. First, calculate average assets of investment in order to calculate total capital employed:

$\begin{array}{c}\text{Average assets of investment}=\frac{\left(\text{Beginning assets}+\text{Ending assets}\right)}{2}\\ =\frac{\left(\$600,000+\$400,000\right)}{2}\\ =\$500,000\end{array}$

Hence, the average asset of investment is $500,000.

Now, calculate the total capital employed:

$\begin{array}{c}\text{Total capital employed}=\text{Average assets of division}+\text{Average assets of investment}\\ =\$3,000,000+\$500,000\\ =\$3,500,000\end{array}$

Hence, the total capital employed with investment is $3,500,000.