📖 营运资本综合练习

Corporate Finance

I. Lesson Focus

This lesson integrates and applies all core working capital concepts through comprehensive calculations, scenario analysis, and common CFA traps. It reviews the cash conversion cycle, efficiency ratios, working capital strategies, and their impact on liquidity, profitability, and free cash flow. The focus is on developing the ability to diagnose problems from a set of financial data and recommend corrective actions.

II. The Problem

A manufacturing firm experiences rapid sales growth in 2023 but suddenly faces a cash shortage. Accounts payable have risen sharply, inventory days have increased from 45 to 68 days, and the cost of short-term bank borrowing has risen. Management is unsure whether this is a normal consequence of business expansion or a sign of deteriorating working capital management. How can an analyst systematically evaluate working capital efficiency? How can key ratios and the cash conversion cycle be used to isolate the true problems and recommend specific improvements? This mirrors the integrated vignette-style questions frequently tested on the CFA Level I exam.

III. Core Working Capital Concepts Review

Working capital = Current assets − Current liabilities.
Net operating working capital (NOWC) typically excludes cash and short-term debt and focuses on operating items: (Accounts receivable + Inventory + Other operating current assets) − (Accounts payable + Accruals + Other operating current liabilities).

In corporate finance, the primary goal of working capital management is to support operations with the minimum capital tied up while avoiding liquidity crises. Effective management directly improves free cash flow to the firm (FCFF) and return on equity (ROE).

IV. Key Working Capital Efficiency Ratios

1. Cash Conversion Cycle (CCC)
   $$ CCC = DIO + DSO - DPO $$
   where:
2. DIO (Days Inventory Outstanding) = 365 / Inventory turnover = Average inventory / (COGS / 365)
3. DSO (Days Sales Outstanding) = 365 / Receivables turnover = Average receivables / (Revenue / 365)

4. DPO (Days Payables Outstanding) = 365 / Payables turnover = Average payables / (COGS / 365)

5. Working Capital Turnover = Revenue / Average working capital

6. Current ratio = Current assets / Current liabilities
   Quick ratio (Acid-test) = (Cash + Marketable securities + Receivables) / Current liabilities

7. Receivables turnover, Inventory turnover, and Payables turnover.

V. Working Capital Management Strategies

• Aggressive: Low levels of current assets financed heavily by short-term debt; shorter CCC; higher risk and potentially higher returns.
• Moderate: Matches the maturity of assets and liabilities.
• Conservative: Holds higher cash and current assets, relies more on long-term financing; longer CCC; better liquidity but lower profitability.

Firms should select a strategy based on industry norms, seasonality, sales growth, and the relative cost of short-term versus long-term financing.

VI. Optimizing Individual Working Capital Accounts

• Receivables: Credit policy (credit period, cash discounts, credit standards) and collection policy.
• Inventory: Economic order quantity (EOQ), reorder point, just-in-time (JIT) systems.
• Payables: Trade credit utilization balanced against early-payment discounts and impact on credit rating.
• Cash: Transaction, precautionary, and speculative motives; preparation of cash budgets.

Worked Cases

Case 1: Cash Conversion Cycle Calculation and Interpretation

ABC Company 2023 data (in millions of CNY):
Revenue = 182.5, COGS = 127.75
Average receivables = 15, average inventory = 22, average payables = 18

Calculations:
DIO = 365 × 22 / 127.75 ≈ 62.8 days
DSO = 365 × 15 / 182.5 ≈ 30.0 days
DPO = 365 × 18 / 127.75 ≈ 51.4 days
CCC = 62.8 + 30.0 − 51.4 = 41.4 days

Interpretation: A CCC of 41.4 days means the firm takes 41.4 days on average between paying suppliers and collecting from customers. If the industry average CCC is 28 days, the firm is tying up excess capital of approximately (41.4 − 28) × (182.5 / 365) ≈ 6.7 million CNY.

Case 2: Impact of Policy Change on CCC and Cash Flow

XYZ Company plans to relax its credit policy. Sales are expected to rise 15%, DSO increases from 25 to 35 days, DIO remains 48 days, and DPO remains 42 days. Original revenue = 300 million CNY, variable cost ratio = 70%.

New CCC = 48 + 35 − 42 = 41 days (original CCC = 31 days).
Additional working capital required ≈ (41 − 31) × (300 × 1.15 / 365) ≈ 10.96 million CNY.
Incremental contribution margin = 300 × 0.15 × (1 − 0.70) = 13.5 million CNY.
Conclusion: Although CCC lengthens, the extra profit exceeds the financing cost (assume 10% cost of funds → ≈1.1 million interest), so the policy is value-adding.

Case 3: Comprehensive Ratio Analysis and Strategy Recommendation

PQR Company: current ratio = 1.8, quick ratio = 0.9, CCC = 65 days, working capital turnover = 6.2×. Industry benchmarks: current ratio 2.1, CCC 38 days. Inventory turnover is only 4.8× (industry 7.2×) and payables turnover is too slow.

Recommendations:
1. Improve inventory management to reduce DIO from 76 to 50 days, potentially releasing ≈12 million CNY.
2. Extend payables modestly without damaging supplier relationships or credit score.
3. Introduce factoring to reduce DSO.
Expected outcome: CCC falls to 42 days, working capital turnover rises to 8.5×, and ROE could increase by approximately 1.8 percentage points.

Traps

Key Formulas

• $CCC = DIO + DSO - DPO$
• $DIO = 365 \times \text{Average Inventory} / \text{COGS}$
• $DSO = 365 \times \text{Average Receivables} / \text{Revenue}$
• $DPO = 365 \times \text{Average Payables} / \text{COGS}$
• Working Capital Turnover = Revenue / Average Working Capital
• Net Operating Working Capital = (AR + Inv + Other Op. CA) − (AP + Accruals + Other Op. CL)
• Cash impact of WC change = −ΔNOWC

Practice Questions

Q1. A company has average inventory of CNY 4.5 million and COGS of CNY 29.2 million. Its DIO is closest to:
A. 45 days　B. 56 days　C. 62 days　D. 78 days

Q2. If a firm’s CCC shortens from 38 to 25 days while revenue remains CNY 500 million and other factors constant, the most likely result is:
A. Free cash flow decreases　B. Net operating working capital decreases　C. Inventory turnover declines　D. Days payables outstanding increases sharply

Q3. Which of the following changes is most likely to lengthen the cash conversion cycle?
A. Shortening the credit period offered to customers　B. Increasing safety stock levels　C. Paying suppliers earlier to capture a 2/10 net 30 discount　D. Implementing a JIT inventory system

Q4. A firm reports a current ratio of 2.5 and a quick ratio of 0.8. The most likely problem is:
A. Excess cash holdings　B. High and potentially obsolete inventory levels　C. Insufficient accounts payable　D. Excessive long-term debt

Q5. A conservative working capital policy is typically characterized by:
A. A short CCC　B. Heavy use of short-term borrowing　C. Higher levels of cash and inventory　D. High working capital turnover

Q6. Firm A’s sales grew 22% in 2023, yet its CCC rose from 42 to 61 days. The most plausible explanation is:
A. Significant improvement in working capital management　B. Receivables and inventory grew faster than sales　C. Successful extension of payables terms　D. A large reduction in current liabilities

Q7. Which statement about the working capital turnover ratio is correct?
A. A higher ratio indicates poorer management　B. A higher ratio indicates more revenue generated per unit of working capital　C. It is always negatively correlated with CCC　D. It applies only to manufacturing firms

Q8. When calculating the cash-flow impact of a change in net operating working capital, the correct treatment is:
A. An increase in NOWC is a cash inflow　B. A decrease in NOWC is a cash inflow　C. Only changes in cash and short-term debt matter　D. Inventory changes are ignored

Answers

Takeaways

• The cash conversion cycle is the central metric for working capital efficiency; DIO and DPO must consistently use COGS.
• Improvements in CCC generally release cash, boost free cash flow, and increase firm value.
• Current and quick ratios must be interpreted together; a single ratio can be misleading.
• Working capital strategy selection requires balancing profitability, liquidity risk, and industry context.
• Use average balances rather than year-end figures when calculating days ratios; adjust for seasonality when material.
• Policy changes must be evaluated jointly with incremental profit, financing costs, and effect on CCC rather than cycle length alone.