Chapter 25, Problem 1BP

a.

To determine

Compute return on investment for each department and use DuPont method to analyze the return on sales and capital turnover.

Explanation of Solution

DuPont model: It is a model which allows the analyst to analyse a company’s performance using the return on sale and capital turnover ratios. This ratio analyses the company’s performance by considering the earnings per sales dollar and the sales generated per capital invested. DuPont model equation is as follows:

$\begin{array}{c}\begin{array}{l}\text{Return on }\\ \text{Investment (ROI)}\end{array}\}=\text{Capital turnover}\times \text{Return on sales}\\ \frac{\text{Operating income}}{\text{Average total assets}}\text{=}\frac{\text{Net sales}}{\text{Average total assets}}\times \frac{\text{Operating earnings}}{\text{Net sales}}\end{array}$

Determine the return on investment for each department.

Particulars	Golf courses	Restaurants	Pro Shops	Complex TCG  (Note 1)
Return On Sales
Operating earnings (A)	$2,000,000	$800,000	$300,000	$3,100,000
Sales revenue (B)	$16,000,000	$2,000,000	$500,000	$18,500,000
Return on sales (1) $\left(\text{A}\right)÷\left(\text{B}\right)$	12.5%	40%	60%	16.8%
Capital Turnover
Sales revenue (A)	$16,000,000	$2,000,000	$500,000	$18,500,000
Average investment (B)	$10,000,000	$3,200,000	$1,000,000	$14,200,000
Capital Turnover (2)$\left(\text{A}\right)÷\left(\text{B}\right)$	160%	62.5%	50%	130%
Return On Investment
Operating earnings (A)	$2,000,000	$800,000	$300,000	$3,100,000
Average investment (B)	$10,000,000	$3,200,000	$1,000,000	$14,200,000
Return on investment $\left(\text{1}\right)\times \left(\text{2}\right)$	20%	25%	30%	21.8%

Table (1)

Note: The ratios of all three departments are added together in Complex TCG column.

As per Table (1), the return on sales for the Department Golf courses is 20% which is the lowest among other departments and the capital turnover for Department Golf course is 160% which is highest among other departments. This is because of the heavy investment made in the assets of Department Golf courses as compared among other departments.

b.

To determine

Determine the ROI of the investment in the new display cases and explain the impact of the investment in the ROI of Department Pro shops. Explain whether the manager of Department Pro shops would be motivated to undertake such investment.

Explanation of Solution

Return on investment (ROI): This financial ratio evaluates how efficiently the assets are used in earning income from operations. So, ROI is a tool used to measure and compare the performance of a units or divisions or a companies. The formula for ROI is as follows:

$\text{Return on investment}\left(\text{ROI}\right)\text{ = }\frac{\text{Operating income }}{\text{Average total investment}}$

Determine the ROI of the new display cases.

$\begin{array}{c}\text{Return on investment}\left(\text{ROI}\right)\text{ = }\frac{\text{Operating income }}{\text{Average total investment}}\\ =\frac{\$6,000}{\$50,000}\\ =12\%\end{array}$

Thus, the ROI of the new display cases is 12%.

Determine the impact of the new display cases on the ROI of Department Pro shops.

$\begin{array}{c}\text{New return on investment}\left(\text{ROI}\right)\text{ = }\frac{\text{Revised operating income }}{\text{Revised average total investment}}\\ =\frac{\$300,000+\$6,000}{\$1,000,000+\$50,000}\\ =\frac{\$306,000}{\$1,050,000}\\ =29.14\%\end{array}$

The new return on investment (ROI) is 29.14%. The manager of Department Pro shops would not be motivated to undertake the investment because the ROI of Department Pro shops would decrease to 29.14%.

c.

To determine

Calculate the residual income for each department if the minimum required return for the Complex TCG is 16 percent and explain the impact of the investment in (b) on the Pro Shop’s residual income.

Explanation of Solution

Residual income: Residual income is the excess of income over the minimum acceptable return on average capital invested. The minimum rate of return shows the opportunity cost of using the invested capital. The formula for residual income is as follows:

$\text{Residual income = Operating earnings}-\left\{\left(\begin{array}{l}\text{Minimum }\\ \text{acceptable }\\ \text{return}\end{array}\right)\times \text{Invested capital}\right\}$

Determine the residual income (loss) for each department.

Particulars	Golf courses	Restaurants	Pro Shops
Operating earnings (A)	$2,000,000	$800,000	$300,000
Minimum acceptable return (B)	16%	16%	16%
Average investment (C)	$10,000,000	$3,200,000	$1,000,000
Minimum acceptable return on average capital invested (D) $\left(\text{B}\right)\times \left(\text{C}\right)$	$1,600,000	$512,000	$160,000
Residual income (E) $\left(\text{A}\right)-\left(\text{D}\right)$	$400,000	$288,000	$140,000

Table (2)

Thus, the residual income (loss) of Department Golf courses, Department Restaurants, and Department Pro Shops are $400,000, $288,000, and $140,000 respectively.

Determine the impact of the new display cases on the residual income of Department Pro Shops.

$\begin{array}{c}\text{Residual income = Operating earnings}-\left\{\left(\begin{array}{l}\text{Minimum }\\ \text{acceptable }\\ \text{return}\end{array}\right)\times \text{Invested capital}\right\}\\ =\$6,000-\left(\text{\$50,000}\times \text{16\%}\right)\\ =\$6,000-\$8,000\\ =(\$2,000)\end{array}$

If the Department Pro Shops buys the new display cases, its residual loss will be reduced by ($2,000).