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The Rentz Corporation is attempting to determine the optimal level of current assets for the coming year. Management expects sales to increase to approximately \(\$ 2\) million as a result of an asset expansion presently being undertaken. Fixed assets total \(\$ 1\) million, and the firm wishes to maintain a 60 percent debt ratio. Rentz's interest cost is currently 8 percent on both short-term and longer-term debt (which the firm uses in its permanent structure). Three alternatives regarding the projected current asset level are available to the firm: (1) a tight policy requiring current assets of only 45 percent of projected sales, (2) a moderate policy of 50 percent of sales in current assets, and (3) a relaxed policy requiring current assets of 60 percent of sales. The firm expects to generate earnings before interest and taxes at a rate of 12 percent on total sales. a. What is the expected return on equity under each current asset level? (Assume a 40 percent effective federal-plus-state tax rate. b. In this problem, we have assumed that the level of expected sales is independent of current asset policy. Is this a valid assumption? c. How would the overall riskiness of the firm vary under each policy?

Step by step solution

01

Determine Current Asset Levels

Calculate the current asset levels for the three different policies based on the projected sales of \( \\(2 \text{ million} \). For the tight policy (45% of sales):\[\text{Tight Policy Current Assets} = 0.45 \times \\)2,000,000 = \\(900,000\]For the moderate policy (50% of sales):\[\text{Moderate Policy Current Assets} = 0.50 \times \\)2,000,000 = \\(1,000,000\]For the relaxed policy (60% of sales):\[\text{Relaxed Policy Current Assets} = 0.60 \times \\)2,000,000 = \$1,200,000\]

02

Calculate Total Assets

Add the fixed assets to each current asset level to calculate total assets for each policy.Since fixed assets are \( \\(1 \text{ million} \), add these to the current assets.Tight Policy:\[\text{Total Assets} = \\)900,000 + \\(1,000,000 = \\)1,900,000\]Moderate Policy:\[\text{Total Assets} = \\(1,000,000 + \\)1,000,000 = \\(2,000,000\]Relaxed Policy:\[\text{Total Assets} = \\)1,200,000 + \\(1,000,000 = \\)2,200,000\]

03

Calculate Debt and Equity Levels

Using the 60% debt ratio, calculate the levels of debt and equity under each policy.Tight Policy:\[\text{Debt} = 0.60 \times \\(1,900,000 = \\)1,140,000\]\[\text{Equity} = \\(1,900,000 - \\)1,140,000 = \\(760,000\]Moderate Policy:\[\text{Debt} = 0.60 \times \\)2,000,000 = \\(1,200,000\]\[\text{Equity} = \\)2,000,000 - \\(1,200,000 = \\)800,000\]Relaxed Policy:\[\text{Debt} = 0.60 \times \\(2,200,000 = \\)1,320,000\]\[\text{Equity} = \\(2,200,000 - \\)1,320,000 = \$880,000\]

04

Calculate Earnings Before Interest and Taxes (EBIT)

Calculate EBIT based on the expected 12% return on total sales.Sales are \( \\(2 \text{ million} \), so EBIT is:\[\text{EBIT} = 0.12 \times \\)2,000,000 = \$240,000\]

05

Calculate Interest Expense

Calculate the annual interest expense based on the debt level and the interest rate of 8% for each policy.Tight Policy:\[\text{Interest Expense} = 0.08 \times \\(1,140,000 = \\)91,200\]Moderate Policy:\[\text{Interest Expense} = 0.08 \times \\(1,200,000 = \\)96,000\]Relaxed Policy:\[\text{Interest Expense} = 0.08 \times \\(1,320,000 = \\)105,600\]

06

Calculate Earnings Before Tax (EBT)

Subtract the interest expense from EBIT to get EBT for each policy.Tight Policy:\[\text{EBT} = \\(240,000 - \\)91,200 = \\(148,800\]Moderate Policy:\[\text{EBT} = \\)240,000 - \\(96,000 = \\)144,000\]Relaxed Policy:\[\text{EBT} = \\(240,000 - \\)105,600 = \$134,400\]

07

Calculate Net Income After Tax

Apply the 40% tax rate to calculate net income for each policy.Tight Policy:\[\text{Net Income} = \\(148,800 \times (1 - 0.40) = \\)89,280\]Moderate Policy:\[\text{Net Income} = \\(144,000 \times (1 - 0.40) = \\)86,400\]Relaxed Policy:\[\text{Net Income} = \\(134,400 \times (1 - 0.40) = \\)80,640\]

08

Calculate Return on Equity (ROE)

Calculate ROE by dividing net income by equity for each policy.Tight Policy:\[\text{ROE} = \frac{\\(89,280}{\\)760,000} \approx 0.1174 \text{ or } 11.74\%\]Moderate Policy:\[\text{ROE} = \frac{\\(86,400}{\\)800,000} = 0.108 \text{ or } 10.8\%\]Relaxed Policy:\[\text{ROE} = \frac{\\(80,640}{\\)880,000} \approx 0.0917 \text{ or } 9.17\%\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Current Asset Policy

A current asset policy refers to how a company manages its short-term assets like cash, inventory, and accounts receivable. It's essential for maintaining liquidity and smooth business operations. In the Rentz Corporation exercise, three different policies are evaluated: tight, moderate, and relaxed.
The tight policy suggests maintaining lower levels of current assets at 45% of sales. This approach can increase efficiency and reduce holding costs but might risk inadequate liquidity for unexpected expenses or changes in sales volume. The moderate policy, which allocates 50% of sales to current assets, provides a balance by affording better liquidity while still maintaining cost efficiency. Finally, the relaxed policy allocates 60% of sales to current assets, offering high liquidity and safety against fluctuations.
Choosing the right current asset policy depends on a company’s risk tolerance and financial strategy. The tighter the policy, the higher the risk but also potentially the greater the returns, assuming the company can efficiently manage with lower liquidity.

Return on Equity (ROE)

ROE is a key metric for investors, as it measures how effectively a company is using its equity to generate profit. It is calculated as net income divided by shareholders' equity. In the Rentz Corporation scenario, ROE is impacted by the choice of current asset policy.
The calculation of ROE under each policy scenario provides insights into financial performance:

• Tight Policy: With ROE at about 11.74%, the tight policy efficiently uses equity, yielding the highest return.
• Moderate Policy: ROE drops to 10.8% with this balanced approach, still commendable but lower than the tight policy.
• Relaxed Policy: The most conservative approach results in a ROE of 9.17%, reflecting lower risk but also lower returns.

Choosing a policy affects cash usage and financial outcomes. A higher ROE means better use of shareholders' investments, but it must be aligned with acceptable risk levels and strategic goals.

Debt Ratio

The debt ratio is critical in understanding a company's financial leverage and risk. It is calculated by dividing total debt by total assets, provided as a percentage. Rentz Corporation uses a 60% debt ratio, indicating a considerable portion of its assets is financed through debt.
In practice, a high debt ratio might signify aggressive growth strategies using borrowed funds. However, it also implies higher interest obligations and financial risk, especially if sales or profits drop unexpectedly. Conversely, a lower debt ratio suggests less risk and lesser financial leverage but might also mean missing out on expansion opportunities.
A consistent 60% debt ratio across all asset policies implies Rentz is committed to growing with borrowed capital. This choice balances potential benefits against financial stability risks. Companies need to evaluate their debt levels in light of their overall financial strategy, market conditions, and risk appetite to maintain sufficient financial health.