CFA L1 / FRA / M11. Analysis Techniques
Module 11 · FRA

Financial Analysis Techniques

EN: Complete ratio toolkit — activity, liquidity, solvency, profitability, valuation, and the DuPont decomposition.
VN: Bộ ratio đầy đủ và phân rã DuPont.

In this module
  1. Activity ratios
  2. Liquidity ratios
  3. Solvency ratios
  4. Profitability ratios
  5. DuPont decomposition
  6. Valuation ratios

1. Activity Ratios Core

About: Measure how efficiently a firm uses assets. Receivables/inventory/payables turnover and their day-counts (DSO/DOH/DPO). CCC = DSO + DOH − DPO; lower is better liquidity.Tóm tắt: Đo hiệu quả sử dụng tài sản. Vòng quay AR/HTK/AP và DSO/DOH/DPO. CCC = DSO + DOH − DPO.
\[ \text{Receivables turnover} = \frac{\text{Revenue}}{\text{Avg. AR}}, \quad DSO = \frac{365}{\text{turnover}} \] \[ \text{Inventory turnover} = \frac{COGS}{\text{Avg. Inv}}, \quad DOH = \frac{365}{\text{turnover}} \] \[ \text{Payables turnover} = \frac{\text{Purchases}}{\text{Avg. AP}}, \quad DPO = \frac{365}{\text{turnover}} \] \[ \text{Total asset turnover} = \frac{\text{Revenue}}{\text{Avg. Total Assets}} \] \[ \text{Cash conversion cycle} = DSO + DOH - DPO \]
Practice problem

Revenue $1,200, avg AR $150, COGS $720, avg inventory $90, avg AP $80, purchases $750. Compute DSO, DOH, DPO, CCC.

Show solution
AR turnover = 8 → DSO = 365/8 ≈ 45.6
Inv turnover = 8 → DOH ≈ 45.6
AP turnover = 9.375 → DPO ≈ 38.9
CCC = 45.6 + 45.6 − 38.9
CCC ≈ 52.3 days

2. Liquidity Ratios Core

About: Short-term solvency. Current (CA/CL — broad), Quick (excludes inventory — stricter), Cash ratio (just cash + ST inv — most strict). Defensive interval = days expense covered.Tóm tắt: Khả năng thanh toán ngắn hạn. Current/Quick/Cash. Defensive interval = số ngày chi tiêu.
\[ \text{Current ratio} = \frac{\text{Current assets}}{\text{Current liabilities}} \] \[ \text{Quick (acid-test)} = \frac{\text{Cash} + \text{ST inv} + \text{AR}}{\text{Current liab}} \] \[ \text{Cash ratio} = \frac{\text{Cash} + \text{ST inv}}{\text{Current liab}} \] \[ \text{Defensive interval} = \frac{\text{Cash} + \text{ST inv} + \text{AR}}{\text{Daily expenditures}} \]
Practice problem

CA $300, Inv $100, CL $200. Compute current and quick ratios.

Show solution
Current = 300/200 = 1.5
Quick ≈ (300 − 100)/200
Current 1.5; Quick ≈ 1.0

3. Solvency Ratios Core

About: Long-term debt-paying capacity. D/E, D/A, financial leverage (TA/E). Coverage ratios: TIE, fixed-charge. Higher = riskier (more debt) but possibly higher returns.Tóm tắt: Khả năng trả nợ dài hạn. D/E, D/A, đòn bẩy tài chính, TIE, fixed-charge.
\[ \text{Debt-to-equity} = \frac{\text{Total debt}}{\text{Total equity}} \] \[ \text{Debt-to-assets} = \frac{\text{Total debt}}{\text{Total assets}} \] \[ \text{Financial leverage} = \frac{\text{Avg. TA}}{\text{Avg. Equity}} \] \[ \text{Interest coverage (TIE)} = \frac{EBIT}{\text{Interest expense}} \] \[ \text{Fixed charge coverage} = \frac{EBIT + \text{Lease}}{\text{Interest} + \text{Lease}} \]
Practice problem

Debt $400, Equity $200, EBIT $90, Interest $30. Compute D/E, financial leverage (TA/E), TIE.

Show solution
D/E = 400/200 = 2.0
TA = D + E = 600 → TA/E = 3.0
TIE = 90/30 = 3.0
D/E 2.0; Leverage 3.0; TIE 3.0

4. Profitability Ratios Core

About: Margins (gross/operating/net) — at each level of cost. ROA — returns per dollar of assets. ROE — returns per dollar of equity. Operating ROA isolates operations from financing/tax.Tóm tắt: Margin (gross/op/net), ROA, ROE. Operating ROA tách operations khỏi financing/tax.
\[ \text{Gross margin} = \frac{\text{Gross profit}}{\text{Revenue}} \] \[ \text{Operating margin} = \frac{\text{Operating income}}{\text{Revenue}} \] \[ \text{Net margin} = \frac{NI}{\text{Revenue}} \] \[ \text{ROA} = \frac{NI}{\text{Avg. TA}}, \qquad \text{ROE} = \frac{NI}{\text{Avg. Equity}} \] \[ \text{Operating ROA} = \frac{EBIT}{\text{Avg. TA}} \]
Practice problem

Revenue $1,000, COGS $700, NI $80, avg TA $800, avg E $400. Compute gross margin, net margin, ROA, ROE.

Show solution
GM = 300/1000 = 30%
NM = 80/1000 = 8%
ROA = 80/800 = 10%
ROE = 80/400 = 20%
GM 30%; NM 8%; ROA 10%; ROE 20%

5. DuPont Decomposition Core

About: Decomposes ROE into 3 levers (margin × turnover × leverage) or 5 levers (tax/interest burden + EBIT margin + turnover + leverage). Identifies WHERE returns come from.Tóm tắt: Phân rã ROE thành 3 hoặc 5 đòn bẩy. Xác định returns đến từ đâu.
\[ \text{ROE} = \underbrace{\frac{NI}{\text{Rev}}}_{\text{Net margin}} \times \underbrace{\frac{\text{Rev}}{\text{TA}}}_{\text{Asset turnover}} \times \underbrace{\frac{\text{TA}}{\text{Equity}}}_{\text{Leverage}} \] \[ \text{5-step ROE} = \frac{NI}{EBT} \times \frac{EBT}{EBIT} \times \frac{EBIT}{\text{Rev}} \times \frac{\text{Rev}}{\text{TA}} \times \frac{\text{TA}}{\text{Eq}} \]

5-step interpretation

  • Tax burden NI / EBT — lower tax = higher.
  • Interest burden EBT / EBIT — less interest = higher.
  • EBIT margin EBIT / Rev — operating efficiency.
  • Asset turnover Rev / TA — asset efficiency.
  • Leverage TA / Eq — equity multiplier.
Practice problem

Net margin 8%, asset turnover 1.5×, financial leverage 2×. Compute ROE.

Show solution
ROE = 0.08 × 1.5 × 2
= 24%

6. Valuation Ratios (per-share) Core

About: Price multiples (P/E, P/B, P/S, P/CF) for relative valuation. Dividend yield/payout for income. Sustainable growth g = ROE × retention.Tóm tắt: Hệ số giá (P/E, P/B, P/S, P/CF). Yield/payout. Tăng trưởng bền vững g = ROE × retention.
\[ \text{P/E} = \frac{\text{Price}}{EPS}, \qquad \text{P/B} = \frac{\text{Price}}{\text{Book value per share}} \] \[ \text{P/S} = \frac{\text{Price}}{\text{Sales per share}}, \qquad \text{P/CF} = \frac{\text{Price}}{\text{CFO per share}} \] \[ \text{Dividend yield} = \frac{D_0}{P_0}, \qquad \text{Payout ratio} = \frac{\text{Dividends}}{NI} \] \[ \text{Retention} = 1 - \text{Payout}, \qquad g = \text{ROE} \times \text{Retention} \]
Practice problem

Price $40, EPS $2, BV per share $20. Compute P/E and P/B.

Show solution
P/E = 40/2 = 20×
P/B = 40/20 = 2.0×
P/E 20; P/B 2.0