Earnings-Based Multiples<\/strong><\/p>\n\n\n\nThe price-to-earnings (P\/E) ratio is defined as:<\/p>\n\n\n\n
\\begin{align*} P\/E &= \\frac{P_t}{EPS} \\end{align*}<\/p>\n\n\n\n
Where \\( P_t \\) is the current share price, and \\( EPS \\) represents earnings per share. The EPS term may be trailing (based on the last four quarters) or forward (based on consensus analyst estimates for the next 12 months).<\/p>\n\n\n\n
The inverse of the P\/E ratio, the earnings yield, is given by:<\/p>\n\n\n\n
\\begin{align*} \\text{Earnings Yield} &= \\frac{EPS_{t+1}}{P_t} \\end{align*}<\/p>\n\n\n\n
This measure serves as a useful gauge of the market’s assessment of a company’s growth opportunities. Recall from the constant-growth model that a firm with no growth opportunities should be valued as:<\/p>\n\n\n\n
\\begin{align*} P_t &= \\frac{EPS_{t+1}}{r_e} \\end{align*}<\/p>\n\n\n\n
For a firm with growth opportunities, the price includes an additional component\u2014the present value of growth opportunities (PVGO):<\/p>\n\n\n\n
\\begin{align*} P_t &= \\frac{EPS_{t+1}}{r_e} + PVGO \\end{align*}<\/p>\n\n\n\n
Rearranging and dividing by \\( P_t \\), we establish the relationship between forward earnings yield, cost of equity, and growth opportunities:<\/p>\n\n\n\n
\\begin{align*} \\frac{EPS_{t+1}}{P_t} &= r_e \\left(1 – \\frac{PVGO_t}{P_t} \\right) \\end{align*}<\/p>\n\n\n\n
Solving for the proportion of price attributable to growth opportunities:<\/p>\n\n\n\n
\\begin{align*} \\frac{PVGO_t}{P_t} &= 1 – \\frac{EPS_{t+1}\/P_t}{r_e} \\end{align*}<\/p>\n\n\n\n
A negative PVGO suggests that reinvesting in the company would destroy value, implying that earnings should instead be distributed to shareholders.<\/p>\n\n\n\n
Illustrative Example: PVGO Analysis for Four Firms<\/strong><\/p>\n\n\n\nAn analyst compiles the following data for four companies:<\/p>\n\n\n\n
\\begin{array}{l|l|l|l}
\n\\text{Firm} & \\text{Price} & \\text{Cost of Equity } (r_e) & \\text{Forward EPS Estimate} \\\\
\n\\hline
\n\\text{Aurora Corp} & \\text{\u20ac50.00} & 10\\% & \\text{\u20ac3.00} \\\\
\n\\hline
\n\\text{Brighton Ltd} & \\text{\u20ac120.00} & 9\\% & \\text{\u20ac8.75} \\\\
\n\\hline
\n\\text{Clover Inc} & \\text{\u20ac35.00} & 12\\% & \\text{\u20ac0.84} \\\\
\n\\hline
\n\\text{Dalton Plc} & \\text{\u20ac80.00} & 8\\% & \\text{\u20ac7.20} \\\\
\n\\end{array}<\/p>\n\n\n\n
\n- Task 1: Calculate Aurora’s earnings yield and PVGO proportion.<\/strong>
\\( \\text{Earnings Yield} = \\frac{3.00}{50.00} = 6\\% \\)
\\( \\frac{PVGO}{P} = 1 – \\frac{3.00\/50.00}{0.10} = 1 – \\frac{0.06}{0.10} = 1 – 0.60 = 40\\% \\)
Aurora’s stock price consists of 40% PVGO (\u20ac20 per share) and 60% (\u20ac30 per share), representing the present value of its forward earnings stream.<\/li>\n\n\n\n- Task 2: Identify the firm with the lowest PVGO-to-price ratio.<\/strong>
$$ \\begin{array}{l|l|l}
\\text{Firm} & \\text{Calculation} & \\text{PVGO\/P} \\\\
\\hline
\\text{Brighton} & 1 – \\frac{8.75\/120}{0.09} = 1 – \\frac{0.0729}{0.09} = 1 – 0.81 & 19.0\\% \\\\
\\hline
\\text{Clover} & 1 – \\frac{0.84\/35}{0.12} = 1 – \\frac{0.024}{0.12} = 1 – 0.20 & 80.0\\% \\\\
\\hline
\\text{Dalton} & 1 – \\frac{7.20\/80}{0.08} = 1 – \\frac{0.09}{0.08} = 1 – 1.125 & -12.5\\% \\\\
\\end{array} $$
Answer:<\/strong> Dalton Plc has the lowest (negative) PVGO\/P at \u221212.5%, indicating that the market expects the company’s reinvestment activities to diminish shareholder value.<\/li>\n<\/ol>\n\n\n\nJustified P\/E from Fundamentals<\/strong><\/p>\n\n\n\nStarting from the constant-growth dividend discount model:<\/p>\n\n\n\n
\\begin{align*} P_t &= \\frac{Div_{t+1}}{r_e – g} \\end{align*}<\/p>\n\n\n\n
Dividing both sides by earnings per share and recognizing that \\( \\text{Payout Ratio} = Div_{t+1} \/ EPS_{t+1} \\), we derive the justified trailing P\/E:<\/p>\n\n\n\n
\\begin{align*} \\frac{P_t}{EPS_t} &= \\frac{\\text{Payout Ratio} \\times (1+g)}{r_e – g} \\end{align*}<\/p>\n\n\n\n
This formula reveals that P\/E multiples are:<\/p>\n\n\n\n
\n- Positively related<\/strong> to the payout ratio and growth rate<\/li>\n\n\n\n
- Negatively related<\/strong> to the cost of equity<\/li>\n<\/ul>\n\n\n\n
Illustrative Example: P\/E Sensitivity Analysis<\/strong><\/p>\n\n\n\nAn analyst demonstrates the relationship between P\/E multiples and fundamentals by assuming a fixed payout ratio of 80% and varying the cost of equity and growth rate.<\/p>\n\n\n\n
\n- Task 1: Calculate justified trailing P\/E with \\( g = 3\\% \\), \\( r_e = 8\\% \\).<\/strong>
\\( \\frac{P_t}{EPS_t} = \\frac{0.80 \\times (1 + 0.03)}{0.08 – 0.03} = \\frac{0.824}{0.05} = 16.48 \\)<\/li>\n\n\n\n- Task 2: Effect of increasing the cost of equity to 12%.<\/strong>
\\( \\frac{P_t}{EPS_t} = \\frac{0.80 \\times (1 + 0.03)}{0.12 – 0.03} = \\frac{0.824}{0.09} = 9.16 \\)
Higher required returns reduce the justified multiple.<\/li>\n\n\n\n- Task 3: Effect of increasing growth rate to 5%.<\/strong>
\\( \\frac{P_t}{EPS_t} = \\frac{0.80 \\times (1 + 0.05)}{0.08 – 0.05} = \\frac{0.84}{0.03} = 28.00 \\)
Higher growth expectations increase the justified multiple.<\/li>\n<\/ol>\n\n\n\n$$\\begin{array}{l|l|l|l|l|l|l}
\nr_e \\setminus g & 0\\% & 1\\% & 2\\% & 3\\% & 4\\% & 5\\% \\\\
\n\\hline
\n8\\% & 10.00 & 11.54 & 13.60 & 16.48 & 20.80 & 28.00 \\\\
\n\\hline
\n9\\% & 8.89 & 10.10 & 11.66 & 13.73 & 16.64 & 21.00 \\\\
\n\\hline
\n10\\% & 8.00 & 8.98 & 10.20 & 11.77 & 13.87 & 16.80 \\\\
\n\\hline
\n11\\% & 7.27 & 8.08 & 9.07 & 10.30 & 11.89 & 14.00 \\\\
\n\\hline
\n12\\% & 6.67 & 7.35 & 8.16 & 9.16 & 10.40 & 12.00 \\\\
\n\\end{array}$$<\/p>\n\n\n\n
Drawbacks of P\/E Multiples<\/strong><\/p>\n\n\n\n\n- Zero or negative earnings<\/strong> render the multiple meaningless or misleading.<\/li>\n\n\n\n
- Non-recurring items<\/strong> (asset sales, restructuring charges, impairment losses) distort EPS.<\/li>\n\n\n\n
- Accounting differences<\/strong> across firms affect comparability.<\/li>\n\n\n\n
- Cyclicality<\/strong> makes trailing earnings unrepresentative of long-term earning power.<\/li>\n<\/ol>\n\n\n\n
Addressing Cyclicality: Normalized P\/E<\/strong><\/p>\n\n\n\nFor cyclical companies, analysts often calculate normalized EPS<\/strong> using one of two methods:<\/p>\n\n\n\nMethod 1: Historical Average EPS<\/strong>
\n$$ \\text{Normalized EPS} = \\frac{\\text{Sum of EPS over the full cycle}}{\\text{Number of years}} $$<\/p>\n\n\n\nMethod 2: Average ROE Method<\/strong>
\n$$ \\text{Normalized EPS} = \\text{Average ROE over the cycle} \\times \\text{Current Book Value per Share} $$<\/p>\n\n\n\nIllustrative Example: Normalized P\/E for Cyclical Company<\/strong><\/p>\n\n\n\nZensia SA<\/strong>, a European chemical company, shows the following data over a seven-year cycle:<\/p>\n\n\n\n$$ \\begin{array}{l|l|l|l}
\n\\text{Year} & \\text{EPS} & \\text{BVPS} & \\text{ROE} \\\\
\n\\hline
\n-7 & \\text{\u20ac}0.62 & \\text{\u20ac}3.00 & 20.7\\% \\\\
\n\\hline
\n-6 & \\text{\u20ac}0.53 & \\text{\u20ac}3.43 & 15.5\\% \\\\
\n\\hline
\n-5 & \\text{\u20ac}0.24 & \\text{\u20ac}3.57 & 6.7\\% \\\\
\n\\hline
\n-4 & \\text{\u20ac}0.63 & \\text{\u20ac}4.10 & 15.4\\% \\\\
\n\\hline
\n-3 & \\text{\u20ac}1.49 & \\text{\u20ac}5.49 & 27.1\\% \\\\
\n\\hline
\n-2 & \\text{\u20ac}1.02 & \\text{\u20ac}6.41 & 15.9\\% \\\\
\n\\hline
\n-1 & \\text{\u20ac}0.89 & \\text{\u20ac}7.20 & 12.4\\% \\\\
\n\\end{array} $$<\/p>\n\n\n\n
Current stock price: \u20ac18.21. Trailing P\/E = 18.21 \/ 0.89 = 20.46.<\/p>\n\n\n\n
Task 1: Calculate normalized P\/E using historical average EPS.<\/strong>
\n$$ \\text{Average EPS} = \\frac{0.62+0.53+0.24+0.63+1.49+1.02+0.89}{7} = \\frac{5.42}{7} = \\text{\u20ac}0.7743 \\\\ \\text{Normalized P\/E} = \\frac{18.21}{0.7743} = 23.52 $$<\/p>\n\n\n\nTask 2: Calculate normalized P\/E using average ROE.<\/strong>
\n$$ \\text{Average ROE} = \\frac{20.7+15.5+6.7+15.4+27.1+15.9+12.4}{7} = \\frac{113.7}{7} = 16.24\\% \\\\
\n\\text{Normalized EPS} = 7.20 \\times 0.1624 = \\text{\u20ac}1.1693 \\\\
\n\\text{Normalized P\/E} = \\frac{18.21}{1.1693} = 15.57$$<\/p>\n\n\n\nRevenue-Based Multiples: Price-to-Sales (P\/S)<\/strong><\/p>\n\n\n\nThe price-to-sales ratio measures the market price per share divided by annual net sales per share:<\/p>\n\n\n\n
$$ \\begin{align*} P\/S &= \\frac{P_t}{\\text{Sales per Share}} \\end{align*} $$<\/p>\n\n\n\n
Revenue-based multiples offer several advantages:<\/p>\n\n\n\n
\n- Always positive<\/strong> (even when earnings are negative)<\/li>\n\n\n\n
- More stable<\/strong> than earnings-based multiples<\/li>\n\n\n\n
- Less susceptible<\/strong> to accounting manipulation<\/li>\n<\/ul>\n\n\n\n
From the constant-growth DDM, recognizing that dividends divided by sales equals the product of net profit margin and payout ratio:<\/p>\n\n\n\n
\\begin{align*} \\frac{P_t}{Sales_t} &= \\frac{\\text{Net Profit Margin} \\times \\text{Payout Ratio} \\times (1+g)}{r_e – g} \\end{align*}<\/p>\n\n\n\n
This formula reveals that P\/S is positively related to net profit margin, payout ratio, and growth, and negatively related to cost of equity.<\/p>\n\n\n\n
Illustrative Example: P\/S and Fundamentals<\/strong><\/p>\n\n\n\nA company has:<\/p>\n\n\n\n
\n- Payout ratio = 80%<\/li>\n\n\n\n
- Expected growth = 3%<\/li>\n\n\n\n
- Cost of equity = 8%<\/li>\n\n\n\n
- Net profit margin = 15%<\/li>\n<\/ul>\n\n\n\n
Task 1: Calculate justified P\/S.<\/strong><\/p>\n\n\n\n\\(\\frac{P_t}{\\text{Sales}_t} = \\frac{0.15 \\times 0.80 \\times 1.03}{0.08 – 0.03} = \\frac{0.1236}{0.05} = 2.472\\)<\/p>\n\n\n\n
Task 2: Derive a justified P\/E from P\/S.<\/strong><\/p>\n\n\n\nSince \\(\\text{P\/S} = \\text{P\/E} \\times \\text{Net Profit Margin}\\):<\/p>\n\n\n\n
\\(\\text{Justified P\/E} = \\frac{2.472}{0.15} = 16.48\\)<\/p>\n\n\n\n
Task 3: Effect of higher net profit margin.<\/strong><\/p>\n\n\n\nIf net profit margin increases to 20% with all else equal:<\/p>\n\n\n\n
\\(\\frac{P_t}{\\text{Sales}_t} = \\frac{0.20 \\times 0.80 \\times 1.03}{0.08 – 0.03} = \\frac{0.1648}{0.05} = 3.296\\)<\/p>\n\n\n\n
Percentage increase = \\((3.296 \\div 2.472) – 1 = 33.33\\%\\)<\/p>\n\n\n\n
Task 4: Trade-off between payout ratio and growth.<\/strong><\/p>\n\n\n\nIf the payout ratio decreases from 80% to 70% and growth increases from 3% to 3.5%:<\/p>\n\n\n\n
\\(\\frac{P_t}{\\text{Sales}_t} = \\frac{0.15 \\times 0.70 \\times 1.035}{0.08 – 0.035} = \\frac{0.1087}{0.045} = 2.415\\)<\/p>\n\n\n\n
The justified P\/S declines slightly from 2.472 to 2.415, demonstrating that the reduction in current dividends outweighs the benefit of higher expected growth.<\/p>\n\n\n\n
Operating Income Multiples: EV\/EBITDA and Related Measures<\/strong><\/p>\n\n\n\nSince operating income is available to both debt and equity holders, these measures are appropriately paired with enterprise value in the numerator. This approach facilitates comparisons across firms with different capital structures.<\/p>\n\n\n\n
The enterprise value can be expressed using the constant-growth FCFF model:<\/p>\n\n\n\n
\\begin{align*} EV_t &= \\frac{FCFF_{t+1}}{WACC – g} \\end{align*}<\/p>\n\n\n\n
Where FCFF is defined as:<\/p>\n\n\n\n
\\begin{align*} FCFF &= EBITDA(1-t) + \\text{Depreciation}(t) – CapEx – \\Delta \\text{Working Capital} \\end{align*}<\/p>\n\n\n\n
Dividing both sides by EBITDA yields the justified EV\/EBITDA multiple:<\/p>\n\n\n\n
\\begin{align*} \\frac{EV}{EBITDA} &= \\frac{1-t}{WACC – g} + \\frac{\\text{Depreciation} \\times t \/ EBITDA}{WACC – g} – \\frac{CapEx \/ EBITDA}{WACC – g} – \\frac{\\Delta \\text{Working Capital} \/ EBITDA}{WACC – g} \\end{align*}<\/p>\n\n\n\n
This decomposition shows that the \\(\\text{EV\/EBITDA}\\) multiple is:<\/p>\n\n\n\n
\n- Positively related<\/strong> to: after-tax income proportion, depreciation (due to tax shield)<\/li>\n\n\n\n
- Negatively related<\/strong> to: capital expenditures, working capital investment, cost of capital, tax rate (through the first term), and reinvestment needs<\/li>\n<\/ul>\n\n\n\n
Illustrative Example: Drayton’s EV\/EBITDA Multiple<\/strong><\/p>\n\n\n\nAn analyst analyzes Drayton Company<\/strong>, which has an observed \\(\\text{EV\/EBITDA}\\) multiple of 3.52. Fundamental data:<\/p>\n\n\n\n\n- \\(\\text{WACC} = 7.1\\%\\)<\/li>\n\n\n\n
- \\(\\text{Long-run FCFF growth} = 2.0\\%\\)<\/li>\n\n\n\n
- \\(\\text{EBITDA} = \\text{\u20ac}300\\text{ million}\\)<\/li>\n\n\n\n
- \\(\\text{Depreciation} = \\text{\u20ac}150\\text{ million}\\)<\/li>\n\n\n\n
- \\(\\text{CapEx} = \\text{\u20ac}190\\text{ million}\\)<\/li>\n\n\n\n
- \\(\\text{Working capital} = \\text{\u20ac}0\\)<\/li>\n\n\n\n
- \\(\\text{Tax rate} = 30\\%\\)<\/li>\n<\/ul>\n\n\n\n
Task 1: Calculate justified EV\/EBITDA.<\/strong><\/p>\n\n\n\n\\(\\frac{\\text{EV}}{\\text{EBITDA}} = \\frac{1 – 0.30}{0.071 – 0.02} + \\frac{(150 \\times 0.30) \/ 300}{0.071 – 0.02} – \\frac{190 \/ 300}{0.071 – 0.02}\\)<\/p>\n\n\n\n
\\(= \\frac{0.70}{0.051} + \\frac{0.15}{0.051} – \\frac{0.6333}{0.051}\\)<\/p>\n\n\n\n
\\(= 13.725 + 2.941 – 12.418 = 4.25\\)<\/p>\n\n\n\n
Task 2: Updated assumptions.<\/strong><\/p>\n\n\n\n\n- \\(\\text{Tax rate} = 25\\%\\)<\/li>\n\n\n\n
- \\(\\text{Long-run growth} = 2.5\\%\\)<\/li>\n\n\n\n
- \\(\\text{CapEx} = \\text{\u20ac}230\\text{ million}\\)<\/li>\n\n\n\n
- \\(\\text{Depreciation} = \\text{\u20ac}180\\text{ million}\\)<\/li>\n<\/ul>\n\n\n\n
\\(\\frac{\\text{EV}}{\\text{EBITDA}} = \\frac{1 – 0.25}{0.071 – 0.025} + \\frac{(180 \\times 0.25) \/ 300}{0.071 – 0.025} – \\frac{230 \/ 300}{0.071 – 0.025}\\)<\/p>\n\n\n\n
\\(= \\frac{0.75}{0.046} + \\frac{0.15}{0.046} – \\frac{0.7667}{0.046}\\)<\/p>\n\n\n\n
\\(= 16.304 + 3.261 – 16.667 = 2.90\\)<\/p>\n\n\n\n
Task 3: Identify the primary driver of the decline.<\/strong><\/p>\n\n\n\nThe decline from 4.25 to 2.90 was primarily driven by the increase in capital expenditures, which carries a negative coefficient in the \\(\\text{EV\/EBITDA}\\) formula. The lower tax rate and higher growth had positive effects, but the higher \\(\\text{CapEx}\\) requirement dominated.<\/p>\n\n\n\n
Balance Sheet Measures<\/strong><\/p>\n\n\n\nBalance sheet multiples relate market value to the book value of assets or equity. The most common is the price-to-book (P\/B)<\/strong> ratio:<\/p>\n\n\n\n\\begin{align*} P\/B &= \\frac{P_t}{BVE_t} \\end{align*}<\/p>\n\n\n\n
The justified \\(\\text{P\/B}\\) from fundamentals (derived earlier) is:<\/p>\n\n\n\n
\\(\\frac{P_t}{\\text{BVE}_t} = \\frac{\\text{ROE} – g}{r_e – g}\\)<\/p>\n\n\n\n
For firms with differing leverage or negative equity, broader measures are appropriate:<\/p>\n\n\n\n
$$ \\begin{align*} \\text{Value to Book} &= \\frac{\\text{Market Value of Equity} + \\text{Market Value of Debt}}{\\text{Book Value of Equity} + \\text{Book Value of Debt}} \\\\
\n\\text{EV to Book} &= \\frac{\\text{Market Value of Equity} + \\text{Market Value of Debt} – \\text{Cash}}{\\text{Book Value of Equity} + \\text{Book Value of Debt} – \\text{Cash}} \\end{align*} $$<\/p>\n\n\n\n
The justified EV\/Book multiple can be expressed as:<\/p>\n\n\n\n
$$ \\frac{EV}{\\text{Book Value of Capital}} = \\frac{\\text{Return on Capital} \\times (1 – \\text{Reinvestment Rate})}{WACC – g} $$<\/p>\n\n\n\n
Cash Flow Statement Measures<\/strong><\/p>\n\n\n\nCash flow\u2013based multiples offer advantages over earnings-based measures:<\/p>\n\n\n\n
\n- Cash flows are direct inputs to DCF models<\/li>\n\n\n\n
- Less susceptible to manipulation and accounting differences<\/li>\n\n\n\n
- More directly linked to value drivers<\/li>\n<\/ul>\n\n\n\n
Dividend Yield<\/strong><\/p>\n\n\n\nThe dividend yield<\/strong> represents dividends per share divided by share price:<\/p>\n\n\n\n$$\\begin{align*} \\text{Dividend Yield} &= \\frac{Div_t}{P_t} \\end{align*} $$<\/p>\n\n\n\n
From the constant-growth DDM:<\/p>\n\n\n\n
$$ \\begin{align*} \\frac{Div_t}{P_t} &= \\frac{r_e – g}{1 + g} \\end{align*} $$<\/p>\n\n\n\n
This reveals that dividend yields are:<\/p>\n\n\n\n
\n- Positively<\/strong> related to the cost of equity<\/li>\n\n\n\n
- Negatively related<\/strong> to growth expectations<\/li>\n<\/ul>\n\n\n\n
Illustrative Example: Dividend Yield Fundamentals<\/strong><\/p>\n\n\n\nA company has:<\/p>\n\n\n\n
\n- \\(\\text{Payout ratio} = 80\\%\\)<\/li>\n\n\n\n
- \\(\\text{Cost of equity} = 8\\%\\)<\/li>\n\n\n\n
- \\(\\text{Growth} = 3\\%\\)<\/li>\n\n\n\n
- \\(\\text{Justified trailing P\/E} = 16.48\\)<\/li>\n<\/ul>\n\n\n\n
Task 1: Calculate justified trailing dividend yield.<\/strong><\/p>\n\n\n\nUsing the relationship: \\(\\text{Dividend Yield} = \\text{Payout Ratio} \\times (1 \/ \\text{P\/E})\\)<\/p>\n\n\n\n
\\(\\text{Dividend Yield} = 0.80 \\times \\frac{1}{16.48} = 4.85\\%\\)<\/p>\n\n\n\n
Using the DDM-derived formula:<\/p>\n\n\n\n
\\(\\frac{\\text{Div}_t}{P_t} = \\frac{0.08 – 0.03}{1.03} = 4.85\\%\\)<\/p>\n\n\n\n
Task 2: Effect of lower payout ratio with higher ROE.<\/strong><\/p>\n\n\n\nIf \\(\\text{ROE} = 15\\%\\) and the payout ratio decreases to 70%:<\/p>\n\n\n\n
\\(g = (1 – 0.70) \\times 0.15 = 4.5\\%\\)<\/p>\n\n\n\n
\\(\\frac{\\text{Div}_t}{P_t} = \\frac{0.08 – 0.045}{1.045} = 3.35\\%\\)<\/p>\n\n\n\n
Free Cash Flow Multiples<\/strong><\/p>\n\n\n\nThe price-to-FCFE multiple is derived from the constant-growth FCFE model:<\/p>\n\n\n\n
$$ \\begin{align*} \\frac{P_t}{FCFE_{t+1}} &= \\frac{1}{r_e – g} \\end{align*} $$<\/p>\n\n\n\n
Similarly, the EV-to-FCFF multiple is:<\/p>\n\n\n\n
\\begin{align*} \\frac{EV_t}{FCFF_{t+1}} &= \\frac{1}{WACC – g} \\end{align*}<\/p>\n\n\n\n
Both multiples are:<\/p>\n\n\n\n
\n- Positively related<\/strong> to growth expectations<\/li>\n\n\n\n
- Negatively related<\/strong> to required returns<\/li>\n<\/ul>\n\n\n\n
Industry-Specific Measures<\/strong><\/p>\n\n\n\nIn capital-intensive industries, analysts often use measures tied directly to operational assets or output:<\/p>\n\n\n\n
\n- \\(\\text{EV\/Production}\\)<\/strong> (e.g., \\(\\text{EV}\\) per barrel of oil equivalent per day)<\/li>\n\n\n\n
- \\(\\text{EV\/Developed Reserves}\\)<\/strong> (e.g., \\(\\text{EV}\\) per barrel of proven reserves)<\/li>\n\n\n\n
- \\(\\text{EV\/Passenger Capacity}\\)<\/strong> (for airlines)<\/li>\n\n\n\n
- \\(\\text{EV\/Subscriber}\\)<\/strong> (for telecommunications)<\/li>\n\n\n\n
- \\(\\text{EV\/Store}\\)<\/strong> (for retailers)<\/li>\n<\/ul>\n\n\n\n
These measures offer advantages:<\/p>\n\n\n\n
\n- Direct linkage to industry-specific value drivers<\/li>\n\n\n\n
- Reduced accounting distortions<\/li>\n\n\n\n
- Comparability across firms with different accounting policies<\/li>\n<\/ul>\n\n\n\n
However, they lack comparability across industries and are difficult to connect to fundamental valuation models.<\/p>\n\n\n\n
Summary of Key Multiples and Their Drivers<\/strong><\/p>\n\n\n\n$$ \\begin{array}{l|l|l}
\n\\text{Multiple} & \\text{Fundamental Drivers} & \\text{Primary Applications} \\\\
\n\\hline
\n\\text{P\/E} & \\text{Payout ratio, growth rate, cost of equity} & \\text{Positive EPS firms} \\\\
\n\\hline
\n\\text{P\/S} & \\text{Net profit margin, payout ratio, growth} & \\text{Early-stage, cyclical, or loss-making firms} \\\\
\n\\hline
\n\\text{P\/B} & \\text{ROE, growth rate, cost of equity} & \\text{Firms with similar leverage and asset profiles} \\\\
\n\\hline
\n\\text{EV\/EBITDA} & \\text{Tax rate, depreciation, CapEx, WACC, growth} & \\text{Capital-intensive firms} \\\\
\n\\hline
\n\\text{EV\/FCFF} & \\text{WACC, growth rate} & \\text{Firms with stable cash flows} \\\\
\n\\hline
\n\\text{P\/FCFE} & \\text{Cost of equity, growth rate} & \\text{Firms with stable FCFE} \\\\
\n\\hline
\n\\text{Dividend Yield} & \\text{Cost of equity, growth rate} & \\text{Mature, dividend-paying firms} \\\\
\n\\hline
\n\\text{EV\/Production} & \\text{Operational efficiency, commodity prices} & \\text{Natural resource companies} \\\\
\n\\end{array} $$<\/p>\n\n\n\n
Comprehensive Example 1: Comparative P\/E and PVGO Analysis<\/strong><\/p>\n\n\n\nScenario:<\/strong> An analyst is evaluating four technology firms in the same industry segment. The following data is available:<\/p>\n\n\n\n$$
\n\\begin{array}{l|l|l|l|l|l}
\n\\textbf{Company} & \\textbf{Price} & \\textbf{Forward EPS} & \\textbf{Cost of Equity} & \\textbf{Payout Ratio} & \\textbf{Expected Growth} \\\\
\n\\hline
\n\\text{TechAlpha} & \\$85.00 & \\$4.25 & 9.5\\% & 65\\% & 5.0\\% \\\\
\n\\hline
\n\\text{TechBeta} & \\$120.00 & \\$5.00 & 10.0\\% & 70\\% & 4.0\\% \\\\
\n\\hline
\n\\text{TechGamma} & \\$45.00 & \\$2.50 & 8.5\\% & 60\\% & 6.0\\% \\\\
\n\\hline
\n\\text{TechDelta} & \\$200.00 & \\$8.00 & 11.0\\% & 55\\% & 3.5\\% \\\\
\n\\end{array} $$<\/p>\n\n\n\n
Task A: Calculate each firm’s forward P\/E, earnings yield, PVGO proportion, and justified trailing P\/E.<\/strong><\/p>\n\n\n\nTechAlpha:<\/strong><\/p>\n\n\n\n\\(\\text{Forward P\/E} = \\frac{85.00}{4.25} = 20.00\\text{x}\\)<\/p>\n\n\n\n
\\(\\text{Earnings Yield} = \\frac{4.25}{85.00} = 5.00\\%\\)<\/p>\n\n\n\n
\\(\\text{PVGO\/P} = 1 – \\left(\\frac{0.05}{0.095}\\right) = 1 – 0.5263 = 47.37\\%\\)<\/p>\n\n\n\n
\\(\\text{Justified P\/E} = \\frac{0.65 \\times (1.05)}{0.095 – 0.05} = \\frac{0.6825}{0.045} = 15.17\\text{x}\\)<\/p>\n\n\n\n
TechBeta:<\/strong><\/p>\n\n\n\n\\(\\text{Forward P\/E} = \\frac{120.00}{5.00} = 24.00\\text{x}\\)<\/p>\n\n\n\n
\\(\\text{Earnings Yield} = \\frac{5.00}{120.00} = 4.17\\%\\)<\/p>\n\n\n\n
\\(\\text{PVGO\/P} = 1 – \\left(\\frac{0.0417}{0.10}\\right) = 1 – 0.4167 = 58.33\\%\\)<\/p>\n\n\n\n
\\(\\text{Justified P\/E} = \\frac{0.70 \\times (1.04)}{0.10 – 0.04} = \\frac{0.728}{0.06} = 12.13\\text{x}\\)<\/p>\n\n\n\n
TechGamma:<\/strong><\/p>\n\n\n\n\\(\\text{Forward P\/E} = \\frac{45.00}{2.50} = 18.00\\text{x}\\)<\/p>\n\n\n\n
\\(\\text{Earnings Yield} = \\frac{2.50}{45.00} = 5.56\\%\\)<\/p>\n\n\n\n
\\(\\text{PVGO\/P} = 1 – \\left(\\frac{0.0556}{0.085}\\right) = 1 – 0.6536 = 34.64\\%\\)<\/p>\n\n\n\n
\\(\\text{Justified P\/E} = \\frac{0.60 \\times (1.06)}{0.085 – 0.06} = \\frac{0.636}{0.025} = 25.44\\text{x}\\)<\/p>\n\n\n\n
TechDelta:<\/strong><\/p>\n\n\n\n\\(\\text{Forward P\/E} = \\frac{200.00}{8.00} = 25.00\\text{x}\\)<\/p>\n\n\n\n
\\(\\text{Earnings Yield} = \\frac{8.00}{200.00} = 4.00\\%\\)<\/p>\n\n\n\n
\\(\\frac{\\text{PVGO}}{P} = 1 – \\left(\\frac{0.04}{0.11}\\right) = 1 – 0.3636 = 63.64\\%\\)<\/p>\n\n\n\n
\\(\\text{Justified P\/E} = \\frac{0.55 \\times (1.035)}{0.11 – 0.035} = \\frac{0.56925}{0.075} = 7.59\\text{x}\\)<\/p>\n\n\n\n
Task B: Interpret the findings.<\/strong><\/p>\n\n\n\n$$
\n\\begin{array}{l|l|l|l|l}
\n\\text{Company} & \\text{Forward P\/E} & \\text{PVGO\/P} & \\text{Actual vs. Justified P\/E} & \\text{Conclusion} \\\\
\n\\hline
\n\\text{TechAlpha} & 20.00\\text{x} & 47.37\\% & 20.00 > 15.17 & \\text{Overvalued} \\\\
\n\\hline
\n\\text{TechBeta} & 24.00\\text{x} & 58.33\\% & 24.00 > 12.13 & \\text{Overvalued} \\\\
\n\\hline
\n\\text{TechGamma} & 18.00\\text{x} & 34.64\\% & 18.00 < 25.44 & \\text{Undervalued} \\\\ \\hline \\text{TechDelta} & 25.00\\text{x} & 63.64\\% & 25.00 > 7.59 & \\text{Significantly overvalued} \\\\
\n\\end{array}
\n$$<\/p>\n\n\n\n
TechGamma stands out as the most attractive investment opportunity\u2014it has the lowest P\/E despite having the highest justified multiple based on its fundamentals. Its high growth rate (6%) and moderate cost of equity (8.5%) drive its justified P\/E to 25.44x, well above its actual 18.00x.<\/p>\n\n\n\n
TechDelta, despite having the highest raw P\/E (25.00x), is fundamentally justified at only 7.59x\u2014its low payout ratio and growth rate combined with high cost of equity make it significantly overvalued. The PVGO analysis confirms that investors are paying a premium for growth (63.64% of price) that may not materialize given the firm’s fundamentals.<\/p>\n\n\n\n
Comprehensive Example 2: EV\/EBITDA and P\/S Cross-Industry Comparison<\/strong><\/p>\n\n\n\nScenario:<\/strong> An analyst is comparing two companies in the transportation sector: AeroVentures<\/strong> (an airline) and LogiTrack<\/strong> (a logistics firm). While both operate in transportation, they have very different capital structures and operational characteristics.<\/p>\n\n\n\n$$
\n\\begin{array}{l|l|l}
\n\\text{Metric} & \\text{AeroVentures} & \\text{LogiTrack} \\\\
\n\\hline
\n\\text{Market Cap} & \\text{\u20ac}18.5\\text{ billion} & \\text{\u20ac}12.2\\text{ billion} \\\\
\n\\hline
\n\\text{Total Debt} & \\text{\u20ac}8.2\\text{ billion} & \\text{\u20ac}4.1\\text{ billion} \\\\
\n\\hline
\n\\text{Cash and Equivalents} & \\text{\u20ac}3.8\\text{ billion} & \\text{\u20ac}2.9\\text{ billion} \\\\
\n\\hline
\n\\text{Revenue} & \\text{\u20ac}14.1\\text{ billion} & \\text{\u20ac}9.8\\text{ billion} \\\\
\n\\hline
\n\\text{EBITDA} & \\text{\u20ac}3.8\\text{ billion} & \\text{\u20ac}2.7\\text{ billion} \\\\
\n\\hline
\n\\text{Net Income} & \\text{\u20ac}1.1\\text{ billion} & \\text{\u20ac}1.5\\text{ billion} \\\\
\n\\hline
\n\\text{Net Profit Margin} & 7.8\\% & 15.3\\% \\\\
\n\\hline
\n\\text{WACC} & 8.5\\% & 7.2\\% \\\\
\n\\hline
\n\\text{Expected FCFF Growth} & 3.0\\% & 4.5\\% \\\\
\n\\hline
\n\\text{Tax Rate} & 25\\% & 25\\% \\\\
\n\\hline
\n\\text{Depreciation} & \\text{\u20ac}2.1\\text{ billion} & \\text{\u20ac}0.8\\text{ billion} \\\\
\n\\hline
\n\\text{CapEx} & \\text{\u20ac}2.4\\text{ billion} & \\text{\u20ac}0.9\\text{ billion} \\\\
\n\\hline
\n\\text{Working Capital Investment} & \\text{\u20ac}0.3\\text{ billion} & \\text{\u20ac}0.1\\text{ billion} \\\\
\n\\hline
\n\\text{Payout Ratio} & 40\\% & 60\\% \\\\
\n\\hline
\n\\text{ROE} & 12\\% & 18\\% \\\\
\n\\end{array} $$<\/p>\n\n\n\n
Task A: Calculate enterprise value and key multiples for both companies.<\/strong><\/p>\n\n\n\nAeroVentures:<\/strong><\/p>\n\n\n\n$$ \\text{EV} = 18.5 + 8.2 – 3.8 = \\text{\u20ac}22.9\\text{ billion} \\\\
\n\\text{P\/E} = \\frac{18.5}{1.1} = 16.82\\text{x} \\\\
\n\\text{EV\/EBITDA} = \\frac{22.9}{3.8} = 6.03\\text{x} \\\\
\n\\text{P\/S} = \\frac{18.5}{14.1} = 1.31\\text{x} $$<\/p>\n\n\n\n
LogiTrack:<\/strong><\/p>\n\n\n\n$$ \\text{EV} = 12.2 + 4.1 – 2.9 = \\text{\u20ac}13.4\\text{ billion}
\n\\text{P\/E} = \\frac{12.2}{1.5} = 8.13\\text{x}
\n\\text{EV\/EBITDA} = \\frac{13.4}{2.7} = 4.96\\text{x}
\n\\text{P\/S} = \\frac{12.2}{9.8} = 1.24\\text{x} $$<\/p>\n\n\n\n
Task B: Calculate justified multiples using the method of forecasted fundamentals.<\/strong><\/p>\n\n\n\nJustified P\/E:<\/strong><\/p>\n\n\n\nAeroVentures:<\/p>\n\n\n\n
\\(\\text{Justified P\/E} = \\frac{0.40 \\times (1.03)}{0.085 – 0.03} = \\frac{0.412}{0.055} = 7.49\\text{x}\\)<\/p>\n\n\n\n
LogiTrack:<\/p>\n\n\n\n
\\(\\text{Justified P\/E} = \\frac{0.60 \\times (1.045)}{0.072 – 0.045} = \\frac{0.627}{0.027} = 23.22\\text{x}\\)<\/p>\n\n\n\n
Justified P\/S:<\/strong><\/p>\n\n\n\nAeroVentures:<\/p>\n\n\n\n
\\(\\text{Justified P\/S} = \\frac{0.078 \\times 0.40 \\times 1.03}{0.085 – 0.03} = \\frac{0.0321}{0.055} = 0.58\\text{x}\\)<\/p>\n\n\n\n
LogiTrack:<\/p>\n\n\n\n
\\(\\text{Justified P\/S} = \\frac{0.153 \\times 0.60 \\times 1.045}{0.072 – 0.045} = \\frac{0.0959}{0.027} = 3.55\\text{x}\\)<\/p>\n\n\n\n
Justified EV\/EBITDA:<\/strong><\/p>\n\n\n\nAeroVentures:<\/p>\n\n\n\n
$$ \\begin{align*} \\frac{\\text{EV}}{\\text{EBITDA}} &= \\frac{1 – 0.25}{0.085 – 0.03} + \\frac{(2.1 \\times 0.25) \/ 3.8}{0.085 – 0.03} – \\frac{2.4 \/ 3.8}{0.085 – 0.03} – \\frac{0.3 \/ 3.8}{0.085 – 0.03} \\\\
\n&= \\frac{0.75}{0.055} + \\frac{0.1382}{0.055} – \\frac{0.6316}{0.055} – \\frac{0.0789}{0.055} \\\\
\n& = 13.636 + 2.513 – 11.484 – 1.435 = 3.23\\text{x} \\end{align*} $$<\/p>\n\n\n\n
LogiTrack:<\/p>\n\n\n\n
$$ \\begin{align*}\\frac{\\text{EV}}{\\text{EBITDA}}& = \\frac{1 – 0.25}{0.072 – 0.045} + \\frac{(0.8 \\times 0.25) \/ 2.7}{0.072 – 0.045} – \\frac{0.9 \/ 2.7}{0.072 – 0.045} – \\frac{0.1 \/ 2.7}{0.072 – 0.045} \\\\
\n&= \\frac{0.75}{0.027} + \\frac{0.0741}{0.027} – \\frac{0.3333}{0.027} – \\frac{0.0370}{0.027} \\\\
\n& = 27.778 + 2.744 – 12.346 – 1.370 = 16.81\\text{x} \\end{align*} $$<\/p>\n\n\n\n
Task C: Interpret the findings and draw relative valuation conclusions.<\/strong><\/p>\n\n\n\n$$ \\begin{array}{l|l|l|l|l}
\n\\text{Multiple} & \\text{AeroVentures Actual} & \\text{AeroVentures Justified} & \\text{LogiTrack Actual} & \\text{LogiTrack Justified} \\\\
\n\\hline
\n\\text{P\/E} & 16.82\\text{x} & 7.49\\text{x} & 8.13\\text{x} & 23.22\\text{x} \\\\
\n\\hline
\n\\text{P\/S} & 1.31\\text{x} & 0.58\\text{x} & 1.24\\text{x} & 3.55\\text{x} \\\\
\n\\hline
\n\\text{EV\/EBITDA} & 6.03\\text{x} & 3.23\\text{x} & 4.96\\text{x} & 16.81\\text{x} \\\\
\n\\end{array} $$<\/p>\n\n\n\n
Interpretation:<\/strong><\/p>\n\n\n\nThe two companies tell dramatically different stories depending on which multiple is examined.<\/p>\n\n\n\n
AeroVentures<\/strong> appears significantly overvalued on every justified multiple basis:<\/p>\n\n\n\n\n- Its actual \\(\\text{P\/E}\\) of \\(16.82\\text{x}\\) far exceeds the justified \\(7.49\\text{x}\\), indicating that investors are paying a substantial premium for the airline’s earnings given its high capital intensity, modest growth (\\(3\\%\\)), and elevated cost of capital.<\/li>\n\n\n\n
- The \\(\\text{EV\/EBITDA}\\) analysis reveals the underlying problem: AeroVentures requires massive reinvestment (\\(\\text{CapEx}\\) of \\(\\text{\u20ac}2.4\\text{ billion}\\) versus \\(\\text{EBITDA}\\) of \\(\\text{\u20ac}3.8\\text{ billion}\\)), leaving little free cash flow after sustaining its fleet. The justified \\(\\text{EV\/EBITDA}\\) of only \\(3.23\\text{x}\\) reflects this capital intensity.<\/li>\n\n\n\n
- The \\(\\text{P\/S}\\) analysis confirms that despite reasonable revenue growth, the low net profit margin (\\(7.8\\%\\)) and modest payout ratio (\\(40\\%\\)) cannot justify the current sales multiple.<\/li>\n<\/ul>\n\n\n\n
LogiTrack<\/strong> presents a more nuanced picture:<\/p>\n\n\n\n\n- Its actual \\(\\text{P\/E}\\) of \\(8.13\\text{x}\\) is well below the justified \\(23.22\\text{x}\\), suggesting the stock is significantly undervalued on an earnings basis. The high justified multiple stems from its superior \\(\\text{ROE}\\) (\\(18\\%\\)), higher payout ratio (\\(60\\%\\)), lower cost of capital (\\(7.2\\%\\)), and stronger growth (\\(4.5\\%\\)).<\/li>\n\n\n\n
- The \\(\\text{EV\/EBITDA}\\) analysis shows a similar pattern: actual \\(4.96\\text{x}\\) versus justified \\(16.81\\text{x}\\). LogiTrack’s lower capital intensity (\\(\\text{CapEx}\\) of \\(\\text{\u20ac}0.9\\text{ billion}\\) versus \\(\\text{EBITDA}\\) of \\(\\text{\u20ac}2.7\\text{ billion}\\)) and higher profitability generate substantial free cash flow, warranting a much higher multiple.<\/li>\n\n\n\n
- However, the \\(\\text{P\/S}\\) analysis reveals a potential warning sign: the actual \\(\\text{P\/S}\\) of \\(1.24\\text{x}\\) is below the justified \\(3.55\\text{x}\\) on an earnings-based justification. This discrepancy may reflect the market’s concern about LogiTrack’s revenue growth sustainability or potential competitive pressures.<\/li>\n<\/ul>\n\n\n\n
Overall Conclusion:<\/strong><\/p>\n\n\n\nUsing the method of forecasted fundamentals across all three multiples, LogiTrack appears consistently undervalued relative to its fundamentals, while AeroVentures appears overvalued. However, a prudent analyst would investigate why the market is pricing LogiTrack so conservatively despite its superior fundamentals\u2014perhaps there are industry-specific risks, regulatory concerns, or competitive threats not captured in the financial statements. This demonstrates how relative valuation should be a starting point for analysis, not an endpoint, and how different multiples can provide complementary perspectives on a company’s valuation.<\/p>\n\n\n\n
<\/p>\n\n\n\n
\n
\n Start Free Trial \u2192\n <\/a>\n\n \n Strengthen your understanding of price and enterprise value multiples, their uses, and CFA Level I Equity valuation concepts with study notes, practice questions, and mock exams.\n <\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
Having established the overarching relative valuation framework\u2014encompassing both the method of comparables and the method of forecasted fundamentals\u2014we now turn to the practical application of the most common valuation multiples. These ratios compare a company’s market value (either equity value…<\/p>\n","protected":false},"author":15,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[8],"tags":[],"class_list":["post-63788","post","type-post","status-publish","format-standard","hentry","category-equity","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"\n
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