Problem 16 - Accounting

Question

Data for the North, East, South, and West Divisions of Columbia Wireless Communication Company are as follows: $$ \begin{array}{lcccccc} & \text { Sales } & \begin{array}{c} \text { Income } \\ \text { from } \\ \text { Operations } \end{array} & \begin{array}{c} \text { Invested } \\ \text { Assets } \end{array} & \begin{array}{c} \text { Rate of } \\ \text { Return on } \\ \text { Investment } \end{array} & \begin{array}{c} \text { Profit } \\ \text { Margin } \end{array} & \begin{array}{c} \text { Investment } \\ \text { Turnover } \end{array} \\ \hline \text { North } & \$ 365,000 & (\mathrm{a}) & \text { (b) } & 20 \% & 16 \% & \text { (c) } \\ \text { East } & \text { (d) } & \$ 60,000 & (\mathrm{e}) & (\mathrm{f}) & 12.5 \% & 0.64 \\ \text { South } & \$ 326,000 & (\mathrm{~g}) & \$ 407,500 & 12 \% & \text { (h) } & \text { (i) } \\ \text { West } & \$ 850,000 & \$ 119,000 & \$ 680,000 & (\mathrm{j}) & \text { (k) } & \text { (I) } \end{array} $$ a. Determine the missing items, identifying each by the letters (a) through (1). b. Determine the residual income for each division, assuming that the minimum acceptable rate of return established by management is \(10 \%\). c. Which division is the most profitable in terms of (1) return on investment and (2) residual income?

Step-by-Step Solution

Answer

The North division has the highest ROI at 20%, while the West division has the highest residual income at $51,000.

Step 1: Finding Income from Operations

First, calculate the missing income from operations for the North division (a). Use the formula:\[\text{Income from Operations} = \text{Invested Assets} \times \text{Rate of Return on Investment}\]Let (b) denote Invested Assets for North. Given that Rate of Return is 20%, the equation becomes:\[(a) = \text{(b)} \times 0.20\]We also know from the profit margin that:\[\frac{\text{Income from Operations}}{\text{Sales}} = \text{Profit Margin}\]Substituting in known values for North:\[\frac{a}{365,000} = 0.16 \Rightarrow a = 365,000 \times 0.16 = 58,400\]By substituting back, we get:\[\text{(b)} \times 0.20 = 58,400 \Rightarrow \text{(b)} = \frac{58,400}{0.20} = 292,000\]Thus, the Income from Operations for North is \(58,400\) and Invested Assets are \(292,000\).

Step 2: Finding Investment Turnover

Calculate the investment turnover for the North division (c) using the formula:\[\text{Investment Turnover} = \frac{\text{Sales}}{\text{Invested Assets}} = \frac{365,000}{292,000} = 1.25\]Thus, (c) is 1.25.

Step 3: Find Sales for the East Division

For the East division (d), we need to use the given Profit Margin (12.5%):\[\frac{\text{Income from Operations}}{\text{Sales}} = 0.125 \Rightarrow \frac{60,000}{d} = 0.125 \Rightarrow d = \frac{60,000}{0.125} = 480,000\]So (d) is \(480,000\).

Step 4: Find Invested Assets for the East Division

For East's Invested Assets (e), use Investment Turnover (0.64):\[0.64 = \frac{480,000}{e} \Rightarrow e = \frac{480,000}{0.64} = 750,000\]So (e) is \(750,000\).

Step 5: Calculate Rate of Return for the East Division

To determine East's Rate of Return (f), use the formula:\[\text{Rate of Return} = \frac{60,000}{750,000} = 0.08 \,\text{or} \, 8y\]Hence (f) is \(8\%\).

Step 6: Finding South Division's Income and Metrics

For South's Income from Operations (g) with a 12% ROI:\[0.12 = \frac{g}{407,500} \Rightarrow g = 0.12 \times 407,500 = 48,900\]Apply the Profit Margin formula for South (h):\[0.12 = \frac{48,900}{326,000} \Rightarrow (h) = 0.15 \,\text{or} \, 15\%\]Investment Turnover for South (i):\[(i) = \frac{326,000}{407,500} \approx 0.80\]Thus, (g) is \(48,900\), (h) is \(15\%\), and (i) is \(0.80\).

Step 7: Rate of Return for the West Division

Calculate the West division's Rate of Return on Investment (j):\[(j) = \frac{119,000}{680,000} = 0.175 \,\text{or} \, 17.5\%\]Thus, (j) is \(17.5\%\).

Step 8: Profit Margin and Turnover for the West Division

Determine the Profit Margin for West (k):\[k = \frac{119,000}{850,000} \approx 0.14 \,\text{or} \, 14\%\]Investment Turnover for West (l):\[l = \frac{850,000}{680,000} \approx 1.25\]So, (k) is \(14\%\) and (l) is \(1.25\).

Step 9: Calculate Residual Income for All Divisions

Using the formula for residual income (RI):\[\text{RI} = \text{Income from Operations} - (\text{Invested Assets} \times \text{Minimum Rate of Return})\]Calculate RI for each division:- North: \(58,400 - (292,000 \times 0.10) = 29,200\)- East: \(60,000 - (750,000 \times 0.10) = -15,000\)- South: \(48,900 - (407,500 \times 0.10) = 8,150\)- West: \(119,000 - (680,000 \times 0.10) = 51,000\)

Step 10: Determine Most Profitable Division

The division with the highest rate of return on investment is North with \(20\%\), and in terms of residual income, West with \(51,000\) is the most profitable.

Key Concepts

Return on Investment

Return on Investment (ROI) is a key metric used to evaluate the profitability of an investment. ROI essentially measures how much income or profit is generated as a percentage of the invested assets. To calculate ROI, you would use the formula: \[ \text{ROI} = \frac{\text{Income from Operations}}{\text{Invested Assets}} \times 100 \% \] ROI is a common indicator of performance because it helps stakeholders understand how effectively their capital is being utilized to generate income. For instance, a ROI of 20% means that for every dollar invested, the company earns 20 cents as profit.

Why ROI Matters

Understanding ROI helps investors and management make informed decisions about where to allocate resources. It also facilitates comparisons across different divisions or potential projects. A higher ROI suggests more efficient operations and a higher return for investors, indicating sound management and investment strategies.

Profit Margin Calculation

Profit Margin is another crucial measure of a company's efficiency and profitability. It indicates what percentage of sales revenue turns into profit. The formula for determining profit margin is: \[ \text{Profit Margin} = \frac{\text{Income from Operations}}{\text{Sales}} \times 100 \% \] A higher profit margin indicates that a division is keeping a larger percentage of its sales as profit, signaling good cost management and pricing strategies. For example, if a division has a profit margin of 16%, it means that 16 cents of every dollar earned in sales is retained as profit after all expenses.

Importance of Profit Margin

Profit margin is an essential tool for comparing profitability between companies or divisions, regardless of size. It identifies how effectively a company is turning sales into actual profit, allowing managers to recognize strengths or areas needing improvement in cost control or sales effectiveness.

Residual Income Analysis

Residual Income (RI) is a financial metric that assesses a division's performance by considering the excess income generated over the minimum required return on its invested capital. It's calculated as follows: \[ \text{RI} = \text{Income from Operations} - (\text{Invested Assets} \times \text{Minimum Rate of Return}) \] A positive RI indicates that a division is generating more income than the minimum threshold, contributing positively to overall company value. Conversely, a negative RI suggests that improvements are needed to meet desired investment returns.

Why Use Residual Income?

Residual income provides insights that traditional ROI cannot. It aligns divisional objectives with those of the entire organization, ensuring that income exceeds opportunity costs. This makes RI a valuable metric for determining true economic profit and directing focus on maximizing shareholder value while maintaining efficient capital use.