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

\[ \text{Receivables turnover} = \frac{\text{Revenue}}{\text{Avg. AR}}, \quad DSO = \frac{365}{\text{turnover}} \] \[ \text{Inventory turnover} = \frac{COGS}{\text{Avg. Inv}}, \quad DOH = \frac{365}{\text{turnover}} \] \[ \text{Payables turnover} = \frac{\text{Purchases}}{\text{Avg. AP}}, \quad DPO = \frac{365}{\text{turnover}} \] \[ \text{Total asset turnover} = \frac{\text{Revenue}}{\text{Avg. Total Assets}} \] \[ \text{Cash conversion cycle} = DSO + DOH - DPO \]
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

\[ \text{Current ratio} = \frac{\text{Current assets}}{\text{Current liabilities}} \] \[ \text{Quick (acid-test)} = \frac{\text{Cash} + \text{ST inv} + \text{AR}}{\text{Current liab}} \] \[ \text{Cash ratio} = \frac{\text{Cash} + \text{ST inv}}{\text{Current liab}} \] \[ \text{Defensive interval} = \frac{\text{Cash} + \text{ST inv} + \text{AR}}{\text{Daily expenditures}} \]
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

\[ \text{Debt-to-equity} = \frac{\text{Total debt}}{\text{Total equity}} \] \[ \text{Debt-to-assets} = \frac{\text{Total debt}}{\text{Total assets}} \] \[ \text{Financial leverage} = \frac{\text{Avg. TA}}{\text{Avg. Equity}} \] \[ \text{Interest coverage (TIE)} = \frac{EBIT}{\text{Interest expense}} \] \[ \text{Fixed charge coverage} = \frac{EBIT + \text{Lease}}{\text{Interest} + \text{Lease}} \]
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

\[ \text{Gross margin} = \frac{\text{Gross profit}}{\text{Revenue}} \] \[ \text{Operating margin} = \frac{\text{Operating income}}{\text{Revenue}} \] \[ \text{Net margin} = \frac{NI}{\text{Revenue}} \] \[ \text{ROA} = \frac{NI}{\text{Avg. TA}}, \qquad \text{ROE} = \frac{NI}{\text{Avg. Equity}} \] \[ \text{Operating ROA} = \frac{EBIT}{\text{Avg. TA}} \]
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

\[ \text{ROE} = \underbrace{\frac{NI}{\text{Rev}}}_{\text{Net margin}} \times \underbrace{\frac{\text{Rev}}{\text{TA}}}_{\text{Asset turnover}} \times \underbrace{\frac{\text{TA}}{\text{Equity}}}_{\text{Leverage}} \] \[ \text{5-step ROE} = \frac{NI}{EBT} \times \frac{EBT}{EBIT} \times \frac{EBIT}{\text{Rev}} \times \frac{\text{Rev}}{\text{TA}} \times \frac{\text{TA}}{\text{Eq}} \]

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

\[ \text{P/E} = \frac{\text{Price}}{EPS}, \qquad \text{P/B} = \frac{\text{Price}}{\text{Book value per share}} \] \[ \text{P/S} = \frac{\text{Price}}{\text{Sales per share}}, \qquad \text{P/CF} = \frac{\text{Price}}{\text{CFO per share}} \] \[ \text{Dividend yield} = \frac{D_0}{P_0}, \qquad \text{Payout ratio} = \frac{\text{Dividends}}{NI} \] \[ \text{Retention} = 1 - \text{Payout}, \qquad g = \text{ROE} \times \text{Retention} \]
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