Level 3 — ProductionFinancial Ratios

Financial Ratios

⏱ 45 minutes60 marksprintable — key stays hidden on paper

Level 3 — Production (from-scratch derivations, code-from-memory, explain-out-loud) Time limit: 45 minutes Total marks: 60

Answer all questions. Show every step of derivation. Where code is requested, write it from memory; syntax need not be perfect but logic must be correct.

Question 1 — Derive and connect valuation ratios (12 marks)

A company reports the following for the most recent year:

Net income = $480$ million
Shares outstanding = $120$ million
Share price = $64$
Total dividends paid = $144$ million
Book value of equity = $1{,}600$ million

(a) From first principles, derive EPS, and then express the P/E ratio in terms of price and EPS. Compute both. (3)

(b) Derive the dividend payout ratio and dividend yield from their definitions. Compute both. (3)

(c) Show algebraically that dividend yield $=$ (payout ratio) $/$ (P/E ratio). Verify numerically with your results. (3)

(d) Compute the P/B ratio. Explain out loud (2–3 sentences) why a high P/B combined with a high P/E might indicate the market expects strong future ROE. (3)

Question 2 — DuPont decomposition from scratch (12 marks)

(a) Starting from $\text{ROE} = \dfrac{\text{Net Income}}{\text{Equity}}$ , derive the 3-factor DuPont decomposition, naming each factor. (4)

(b) A firm has: Net income $= 300$ , Revenue $= 5{,}000$ , Total assets $= 4{,}000$ , Equity $= 1{,}500$ . Compute net margin, asset turnover, equity multiplier, and confirm they multiply to ROE. (5)

(c) Extend to the 5-factor DuPont model, naming the two additional factors that split net margin. Explain out loud what each captures. (3)

Question 3 — EV/EBITDA and margins (10 marks)

Given: Market cap $= 2{,}000$ , Total debt $= 600$ , Cash $= 200$ , EBITDA $= 400$ , Revenue $= 3{,}200$ , Gross profit $= 1{,}280$ , Operating income $= 352$ .

(a) Derive Enterprise Value from memory and compute EV/EBITDA. (3)

(b) Compute gross, operating, and net-equivalent (use operating as proxy) margins. (3)

(c) Explain out loud why EV/EBITDA is often preferred over P/E when comparing two companies with very different debt levels. (4)

Question 4 — Liquidity, leverage & coverage (10 marks)

Balance sheet extract: Current assets $= 900$ (of which inventory $= 300$ ), Current liabilities $= 500$ , Total debt $= 1{,}200$ , Equity $= 800$ , EBIT $= 360$ , Interest expense $= 90$ .

(a) Compute current ratio and quick ratio. State one reason quick ratio can be more informative. (3)

(b) Compute debt-to-equity and interest coverage. (3)

(c) A lender's covenant requires interest coverage $\geq 3.0$ . By how much can EBIT fall (in absolute terms) before the covenant is breached? Show the algebra. (4)

Question 5 — Turnover & FCF yield (10 marks)

Data: COGS $= 2{,}400$ , Average inventory $= 300$ , Credit sales $= 3{,}650$ , Average receivables $= 200$ . Also: Operating cash flow $= 520$ , CapEx $= 170$ , Market cap $= 2{,}800$ .

(a) Compute inventory turnover, days inventory outstanding (365-day year), and receivables turnover. (4)

(b) Derive Free Cash Flow and FCF yield from definitions and compute both. (3)

(c) Explain out loud how a rising receivables turnover with flat inventory turnover could still signal a cash-flow problem — or not. (3)

Question 6 — PEG synthesis (6 marks)

A stock trades at a P/E of $30$ with expected earnings growth of $20\%$ per year.

(a) Compute the PEG ratio and interpret it. (2)

(b) Write a short pseudocode / Python function (from memory) peg(price, eps, growth_pct) that returns the PEG ratio, guarding against zero growth. (4)

Answer keyMark scheme & solutions

Question 1 (12)

(a) EPS $= \dfrac{\text{Net Income}}{\text{Shares}} = \dfrac{480}{120} = 4$ (1) P/E $= \dfrac{\text{Price}}{\text{EPS}} = \dfrac{64}{4} = 16$ (2 for definition + value)

(b) Payout $= \dfrac{\text{Dividends}}{\text{Net Income}} = \dfrac{144}{480} = 0.30 = 30\%$ (1.5) DPS $= 144/120 = 1.2$ ; Yield $= \dfrac{\text{DPS}}{\text{Price}} = \dfrac{1.2}{64} = 0.01875 = 1.875\%$ (1.5)

(c) Yield $= \dfrac{\text{DPS}}{P} = \dfrac{\text{Payout}\times \text{EPS}}{P} = \dfrac{\text{Payout}}{P/\text{EPS}} = \dfrac{\text{Payout}}{\text{P/E}}$ (2) Check: $0.30 / 16 = 0.01875$ ✓ (1)

(d) P/B $= \dfrac{\text{Price}\times\text{Shares}}{\text{Book equity}} = \dfrac{64\times120}{1600} = \dfrac{7680}{1600} = 4.8$ (2) Explanation: since $\text{P/B} \approx \text{P/E}\times\text{ROE}$ , a high P/B with high P/E is consistent only if the market prices in high future ROE; investors pay a premium above book because they expect equity to earn well above the cost of capital. (1)

Question 2 (12)

(a) $\text{ROE} = \dfrac{NI}{E} = \dfrac{NI}{Rev}\times\dfrac{Rev}{Assets}\times\dfrac{Assets}{E}$ (3) = Net margin × Asset turnover × Equity multiplier (1)

(b) Net margin $= 300/5000 = 0.06$ ; Asset turnover $= 5000/4000 = 1.25$ ; Equity multiplier $= 4000/1500 = 2.6\overline{6}$ (3) Product $= 0.06\times1.25\times2.6667 = 0.20 = 20\%$ (1) Direct ROE $= 300/1500 = 0.20$ ✓ (1)

(c) 5-factor splits net margin into: Tax burden $(NI/EBT)$ and Interest burden $(EBT/EBIT)$ , plus Operating margin $(EBIT/Rev)$ . Tax burden captures effect of taxation; interest burden captures drag of financing costs. (3)

Question 3 (10)

(a) EV $=$ Market cap $+$ Debt $-$ Cash $= 2000+600-200 = 2400$ (2) EV/EBITDA $= 2400/400 = 6.0$ (1)

(b) Gross margin $= 1280/3200 = 40\%$ ; Operating margin $= 352/3200 = 11\%$ . (2 + 1)

(c) EV/EBITDA is capital-structure neutral: EV includes debt and EBITDA is pre-interest, so two firms with different leverage are comparable. P/E depends on net income which is after interest, so leverage distorts it. (4)

Question 4 (10)

(a) Current ratio $= 900/500 = 1.8$ (1) Quick ratio $= (900-300)/500 = 600/500 = 1.2$ (1) Quick excludes inventory which may be slow/hard to convert to cash. (1)

(b) D/E $= 1200/800 = 1.5$ (1.5) Interest coverage $= EBIT/Interest = 360/90 = 4.0$ (1.5)

(c) Breach when $\dfrac{EBIT}{90} = 3.0 \Rightarrow EBIT = 270$ . (2) Current EBIT $= 360$ , so it can fall by $360-270 = 90$ . (2)

Question 5 (10)

(a) Inventory turnover $= COGS/\text{avg inv} = 2400/300 = 8$ (1.5) DIO $= 365/8 = 45.625$ days (1.5) Receivables turnover $= 3650/200 = 18.25$ (1)

(b) FCF $=$ OCF $-$ CapEx $= 520-170 = 350$ (1.5) FCF yield $= 350/2800 = 0.125 = 12.5\%$ (1.5)

(c) Rising receivables turnover = collecting faster (good for cash). But if flat inventory turnover means stock is building relative to sales, cash is tied up in inventory; net effect on cash depends on which dominates. Faster collection alone is positive. (3)

Question 6 (6)

(a) PEG $= \dfrac{\text{P/E}}{\text{growth \%}} = \dfrac{30}{20} = 1.5$ . Above 1 suggests possibly overvalued relative to growth. (2)

(b) (4)

def peg(price, eps, growth_pct):
    if eps == 0 or growth_pct == 0:
        return None          # undefined
    pe = price / eps
    return pe / growth_pct

Marks: correct P/E (1), correct division by growth (1), zero-guard (1), function structure (1).

[
{"claim":"Q1 EPS=4 and P/E=16","code":"eps=480/120; pe=64/eps; result=(eps==4 and pe==16)"},
{"claim":"Q1c yield equals payout/PE = 0.01875","code":"payout=144/480; pe=16; yld=(144/120)/64; result=abs(yld-payout/pe)<1e-9 and abs(yld-0.01875)<1e-9"},
{"claim":"Q2 DuPont product equals ROE 0.20","code":"nm=300/5000; at=5000/4000; em=4000/1500; result=abs(nm*at*em-300/1500)<1e-9"},
{"claim":"Q3 EV/EBITDA = 6.0","code":"ev=2000+600-200; result=abs(ev/400-6.0)<1e-9"},
{"claim":"Q4c EBIT can fall by 90 before coverage<3","code":"breach=3.0*90; result=abs((360-breach)-90)<1e-9"},
{"claim":"Q5 FCF yield = 12.5%","code":"fcf=520-170; result=abs(fcf/2800-0.125)<1e-9"},
{"claim":"Q6 PEG = 1.5","code":"result=abs((30/20)-1.5)<1e-9"}
]