📖 活动/效率比率

Financial Statement Analysis

I. Lesson Focus

This lesson focuses on activity (efficiency) ratios, with primary emphasis on the cash conversion cycle (CCC). Candidates must be able to calculate inventory, receivables, and payables turnover ratios and their associated days, construct the CCC formula, interpret its economic meaning, and understand its impact on working capital, liquidity, borrowing needs, and ultimately return on equity (ROE) through the DuPont framework.

II. The Problem

A manufacturing firm reports 85 days of inventory on hand, 42 days sales outstanding, and only 28 days payables outstanding, resulting in a cash conversion cycle of 99 days. The company must borrow heavily from banks to finance operations, incurring high interest expense that erodes net profit margins. Management wants to know how improving activity ratios can shorten the CCC and what quantifiable benefits a lower CCC delivers to the firm and its shareholders. This lesson solves that exact problem.

III. Core Concepts of Activity Ratios

Activity ratios, also called efficiency ratios, measure how effectively a company converts its assets into sales or turns liabilities into cash. The key ratios are inventory turnover, receivables turnover, payables turnover, total asset turnover, and the cash conversion cycle (CCC).

These ratios answer three fundamental operating questions: - How long does inventory sit in the warehouse before it is sold? - How long after delivery do customers take to pay? - How long does the company take to pay its suppliers?

IV. Key Turnover Ratios: Formulas and Interpretation

1. Inventory Turnover
   $$ \text{Inventory Turnover} = \frac{\text{Cost of Goods Sold}}{\text{Average Inventory}} $$ Days of Inventory on Hand (DOH):
   $$ \text{DOH} = \frac{365}{\text{Inventory Turnover}} \quad \text{or} \quad \frac{365 \times \text{Average Inventory}}{\text{COGS}} $$

2. Receivables Turnover
   $$ \text{Receivables Turnover} = \frac{\text{Revenue}}{\text{Average Receivables}} $$ Days Sales Outstanding (DSO):
   $$ \text{DSO} = \frac{365}{\text{Receivables Turnover}} \quad \text{or} \quad \frac{365 \times \text{Average Receivables}}{\text{Revenue}} $$

3. Payables Turnover
   $$ \text{Payables Turnover} = \frac{\text{Purchases (or approx. COGS)}}{\text{Average Payables}} $$ Days Payables Outstanding (DPO):
   $$ \text{DPO} = \frac{365}{\text{Payables Turnover}} \quad \text{or} \quad \frac{365 \times \text{Average Payables}}{\text{COGS}} $$

V. The Cash Conversion Cycle (CCC)

The CCC is the most comprehensive activity metric. It measures the number of days between paying cash for raw materials and receiving cash from customers. The formula is: $$ \text{CCC} = \text{DOH} + \text{DSO} - \text{DPO} $$ - A shorter CCC indicates superior working-capital management and less capital tied up in operations. - A negative CCC means the firm collects cash from customers before it pays suppliers (common at Amazon, Apple, and Walmart).

Economic impact of CCC: - Reducing CCC releases working capital → lower borrowing or more cash available for investment → reduced interest expense or higher investment income → higher free cash flow to the firm (FCFF) and higher firm value.

VI. Industry Characteristics and Trend Analysis

• Retail: Typically low DOH (fast turnover) and relatively high DPO (strong bargaining power with suppliers).
• Heavy industry: High DOH due to long production cycles, resulting in longer CCC.
• Trend analysis: A steadily rising CCC over several years signals inventory buildup, overly loose credit policy, or suppliers demanding faster payment. This requires immediate managerial attention.

Worked Cases

Case 1: Basic CCC Calculation

XYZ Company 2023 data (in thousands): - COGS = 1,200 - Average inventory = 200 - Revenue = 1,500 - Average receivables = 180 - Average payables = 150 - Purchases ≈ COGS = 1,200

Calculations: - DOH = (365 × 200) / 1,200 ≈ 60.83 days - DSO = (365 × 180) / 1,500 = 43.80 days - DPO = (365 × 150) / 1,200 = 45.63 days - CCC = 60.83 + 43.80 – 45.63 ≈ 59 days

Interpretation: The firm needs approximately 59 days to recover cash—14 days longer than the industry average of 45 days—indicating room for working-capital efficiency improvement.

Case 2: Impact of Policy Changes on CCC

A company plans the following initiatives: - Adopt JIT to reduce DOH from 75 to 50 days - Tighten credit policy to reduce DSO from 40 to 32 days - Suppliers respond by shortening DPO from 55 to 45 days

New CCC = 50 + 32 – 45 = 37 days
Original CCC = 75 + 40 – 55 = 60 days
Reduction of 23 days. With annual sales of RMB 300 million (daily sales ≈ RMB 821,918), the firm releases approximately 23 × 821,918 ≈ RMB 18.9 million in working capital, materially lowering financing needs.

Case 3: Integrated Scenario with DuPont Analysis

Company A reports ROE of 12%, net profit margin 8%, asset turnover 1.2×, and financial leverage 1.25×. Its CCC is 82 days versus an industry median of 51 days. The CFO targets a reduction to 55 days.

Assuming other factors constant, the improvement primarily raises asset turnover. Each 0.1× increase in asset turnover lifts ROE by roughly 1 percentage point. The projected new asset turnover of 1.45× would increase ROE to approximately 14.5%, creating substantial shareholder value.

Traps

Key Formulas

• Inventory Turnover = COGS / Avg. Inventory
• Receivables Turnover = Sales / Avg. Receivables
• Payables Turnover = COGS / Avg. Payables
• Operating Cycle = DOH + DSO
• CCC = DOH + DSO – DPO
• Total Asset Turnover = Sales / Avg. Total Assets (inversely related to CCC)
• Shorter CCC generally improves ROE via higher asset turnover in the DuPont decomposition

Practice Questions

Q1. A company has DOH = 68 days, DSO = 35 days, and DPO = 42 days. Its cash conversion cycle is closest to:
A. 61 days
B. 75 days
C. 103 days
D. 145 days

Q2. Which of the following changes is most likely to shorten the cash conversion cycle?
A. Extending customer credit terms
B. Increasing safety stock levels
C. Accelerating payments to suppliers
D. Implementing vendor-managed inventory (VMI) and lowering inventory levels

Q3. A firm reports COGS of RMB 8 million, average inventory of RMB 1.5 million, and a receivables turnover of 8 times. Using 365 days, its DSO is closest to:
A. 45.6 days
B. 68.4 days
C. 91.25 days
D. Cannot be calculated

Q4. In the DuPont analysis, activity ratios primarily affect which component?
A. Net profit margin
B. Asset turnover
C. Financial leverage
D. Tax rate

Q5. A negative cash conversion cycle most likely indicates that the company:
A. Has extremely poor working-capital management
B. Collects cash from customers before paying suppliers
C. Has very slow inventory turnover
D. Has an excessively long receivables collection period

Q6. Which statement about payables turnover is most accurate?
A. A higher turnover is always better
B. A lower turnover (longer DPO) allows the firm to use suppliers’ funds interest-free for longer
C. It should always be kept at the highest level in the industry
D. It is positively correlated with inventory turnover

Q7. A company plans to reduce its days of inventory on hand from 90 to 60 days while keeping all else constant. The effect on CCC will be:
A. CCC increases by 30 days
B. CCC decreases by 30 days
C. CCC remains unchanged
D. Cannot be determined

Q8. A retailer has sales of RMB 40 million, average receivables RMB 3.2 million, average inventory RMB 2.8 million, COGS RMB 28 million, and average payables RMB 2.1 million. Its cash conversion cycle is closest to:
A. 68.2 days
B. 79.5 days
C. 91.3 days
D. 103.7 days

Answers

Takeaways

• CCC = DOH + DSO – DPO is the single most important summary metric of working-capital efficiency
• Reducing CCC frees working capital, lowers financing costs, improves free cash flow, and increases ROE
• Always use average balances ((beginning + ending)/2) when calculating turnover ratios
• A negative CCC signals superior operations but must be monitored for supply-chain stability risk
• Activity ratios integrate tightly with profitability (DuPont) and liquidity analysis; exam questions frequently combine them
• Industry peer comparison and multi-year trends are usually more informative than absolute ratio levels