Price and Enterprise Value Multiples and Their Uses

Having established the overarching relative valuation framework—encompassing both the method of comparables and the method of forecasted fundamentals—we now turn to the practical application of the most common valuation multiples. These ratios compare a company’s market value (either equity value or enterprise value) to underlying fundamental measures drawn from the income statement, balance sheet, or cash flow statement.

The critical principle governing multiple selection is claimant alignment: the numerator’s measure of market value must correspond to the same group of capital providers represented by the denominator’s fundamental measure. Equity-focused multiples (such as P/E, P/B, and dividend yield) use the market value of equity in the numerator, while enterprise value multiples (such as EV/EBITDA and EV/FCFF) use a measure available to all capital providers—both debt and equity holders.

Market Value as the Multiple Numerator

Enterprise Value (EV)

Enterprise value represents the total value of the firm to all capital providers. It is calculated as:

\begin{align*} \text{Enterprise Value} &= \text{Market Value of Debt} + \text{Market Value of Equity} + \text{Market Value of Preferred Shares} – \text{Cash and Short-Term Investments} \end{align*}

In practice, the book value of debt and preferred shares often serves as a reasonable proxy for market value when market prices are not readily available. Cash and short-term investments are subtracted because they represent non-operating assets that do not contribute to the firm’s core operating value.

Illustrative Example: Calculating Enterprise Value for Verona Industries

An analyst is estimating the enterprise value for Verona Industries, a publicly traded Italian manufacturing company, five months after its fiscal year-end. The company reports financial results semiannually. At fiscal year-end, Verona had 2.5 billion shares outstanding, closing at €30 per share. The most recent financial statements reported €25 billion in debt and €8 billion of cash.

Task 1: Calculate Verona’s EV at fiscal year-end.
\( EV = \text{Debt} + \text{Market Cap} – \text{Cash} \)
\( EV = 25 + (2.5 \times 30) – 8 = 25 + 75 – 8 = \text{€}92 \text{ billion} \)

Task 2: Incorporating subsequent events.
Five months later, the analyst incorporates the following news:

• Verona announced a €10 billion debt offering for share repurchases. The stock price did not change materially at the announcement.
• Verona’s share price rose from €30 to €33 over the five months.

Solution: The analyst’s mid-year EV estimate should reflect:

• Debt increased by €10 billion to €35 billion.
• The debt issuance funded share repurchases, reducing equity from €75 billion to €65 billion.
• Equity value subsequently increased by 10% [= (33 ÷ 30) − 1].

\( \text{Revised EV} = 35 + (65 \times 1.10) – 8 = 35 + 71.5 – 8 = \text{€}98.5 \text{ billion} \)

Task 3: Alternative scenario—debt used for operating assets.
If the debt proceeds were instead used to purchase operating assets, the equity would not decline. The equity term becomes 75 × 1.10 = 82.5.
\( \text{Revised EV} = 35 + 82.5 – 8 = \text{€}109.5 \text{ billion} \)

Standardized Measures in the Multiple Denominator

Income Statement Measures

Earnings-based multiples are among the most frequently used in valuation because profitability is a primary driver of firm value. The income statement hierarchy—from revenue down to net income—provides several denominator options, each with distinct advantages and limitations.

Earnings-Based Multiples

The price-to-earnings (P/E) ratio is defined as:

\begin{align*} P/E &= \frac{P_t}{EPS} \end{align*}

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).

The inverse of the P/E ratio, the earnings yield, is given by:

\begin{align*} \text{Earnings Yield} &= \frac{EPS_{t+1}}{P_t} \end{align*}

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:

\begin{align*} P_t &= \frac{EPS_{t+1}}{r_e} \end{align*}

For a firm with growth opportunities, the price includes an additional component—the present value of growth opportunities (PVGO):

\begin{align*} P_t &= \frac{EPS_{t+1}}{r_e} + PVGO \end{align*}

Rearranging and dividing by \( P_t \), we establish the relationship between forward earnings yield, cost of equity, and growth opportunities:

\begin{align*} \frac{EPS_{t+1}}{P_t} &= r_e \left(1 – \frac{PVGO_t}{P_t} \right) \end{align*}

Solving for the proportion of price attributable to growth opportunities:

\begin{align*} \frac{PVGO_t}{P_t} &= 1 – \frac{EPS_{t+1}/P_t}{r_e} \end{align*}

A negative PVGO suggests that reinvesting in the company would destroy value, implying that earnings should instead be distributed to shareholders.

Illustrative Example: PVGO Analysis for Four Firms

An analyst compiles the following data for four companies:

\begin{array}{l|l|l|l}
\text{Firm} & \text{Price} & \text{Cost of Equity } (r_e) & \text{Forward EPS Estimate} \\
\hline
\text{Aurora Corp} & \text{€50.00} & 10\% & \text{€3.00} \\
\hline
\text{Brighton Ltd} & \text{€120.00} & 9\% & \text{€8.75} \\
\hline
\text{Clover Inc} & \text{€35.00} & 12\% & \text{€0.84} \\
\hline
\text{Dalton Plc} & \text{€80.00} & 8\% & \text{€7.20} \\
\end{array}

1. Task 1: Calculate Aurora’s earnings yield and PVGO proportion.
   
   \( \text{Earnings Yield} = \frac{3.00}{50.00} = 6\% \)
   
   \( \frac{PVGO}{P} = 1 – \frac{3.00/50.00}{0.10} = 1 – \frac{0.06}{0.10} = 1 – 0.60 = 40\% \)
   
   Aurora’s stock price consists of 40% PVGO (€20 per share) and 60% (€30 per share), representing the present value of its forward earnings stream.
2. Task 2: Identify the firm with the lowest PVGO-to-price ratio.
   
   $$ \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: Dalton Plc has the lowest (negative) PVGO/P at −12.5%, indicating that the market expects the company’s reinvestment activities to diminish shareholder value.

Justified P/E from Fundamentals

Starting from the constant-growth dividend discount model:

\begin{align*} P_t &= \frac{Div_{t+1}}{r_e – g} \end{align*}

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:

\begin{align*} \frac{P_t}{EPS_t} &= \frac{\text{Payout Ratio} \times (1+g)}{r_e – g} \end{align*}

This formula reveals that P/E multiples are:

• Positively related to the payout ratio and growth rate
• Negatively related to the cost of equity

Illustrative Example: P/E Sensitivity Analysis

An 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.

1. Task 1: Calculate justified trailing P/E with \( g = 3\% \), \( r_e = 8\% \).
   
   \( \frac{P_t}{EPS_t} = \frac{0.80 \times (1 + 0.03)}{0.08 – 0.03} = \frac{0.824}{0.05} = 16.48 \)
2. Task 2: Effect of increasing the cost of equity to 12%.
   
   \( \frac{P_t}{EPS_t} = \frac{0.80 \times (1 + 0.03)}{0.12 – 0.03} = \frac{0.824}{0.09} = 9.16 \)
   
   Higher required returns reduce the justified multiple.
3. Task 3: Effect of increasing growth rate to 5%.
   
   \( \frac{P_t}{EPS_t} = \frac{0.80 \times (1 + 0.05)}{0.08 – 0.05} = \frac{0.84}{0.03} = 28.00 \)
   
   Higher growth expectations increase the justified multiple.

$$\begin{array}{l|l|l|l|l|l|l}
r_e \setminus g & 0\% & 1\% & 2\% & 3\% & 4\% & 5\% \\
\hline
8\% & 10.00 & 11.54 & 13.60 & 16.48 & 20.80 & 28.00 \\
\hline
9\% & 8.89 & 10.10 & 11.66 & 13.73 & 16.64 & 21.00 \\
\hline
10\% & 8.00 & 8.98 & 10.20 & 11.77 & 13.87 & 16.80 \\
\hline
11\% & 7.27 & 8.08 & 9.07 & 10.30 & 11.89 & 14.00 \\
\hline
12\% & 6.67 & 7.35 & 8.16 & 9.16 & 10.40 & 12.00 \\
\end{array}$$

Drawbacks of P/E Multiples

1. Zero or negative earnings render the multiple meaningless or misleading.
2. Non-recurring items (asset sales, restructuring charges, impairment losses) distort EPS.
3. Accounting differences across firms affect comparability.
4. Cyclicality makes trailing earnings unrepresentative of long-term earning power.

Addressing Cyclicality: Normalized P/E

For cyclical companies, analysts often calculate normalized EPS using one of two methods:

Method 1: Historical Average EPS
$$ \text{Normalized EPS} = \frac{\text{Sum of EPS over the full cycle}}{\text{Number of years}} $$

Method 2: Average ROE Method
$$ \text{Normalized EPS} = \text{Average ROE over the cycle} \times \text{Current Book Value per Share} $$

Illustrative Example: Normalized P/E for Cyclical Company

Zensia SA, a European chemical company, shows the following data over a seven-year cycle:

$$ \begin{array}{l|l|l|l}
\text{Year} & \text{EPS} & \text{BVPS} & \text{ROE} \\
\hline
-7 & \text{€}0.62 & \text{€}3.00 & 20.7\% \\
\hline
-6 & \text{€}0.53 & \text{€}3.43 & 15.5\% \\
\hline
-5 & \text{€}0.24 & \text{€}3.57 & 6.7\% \\
\hline
-4 & \text{€}0.63 & \text{€}4.10 & 15.4\% \\
\hline
-3 & \text{€}1.49 & \text{€}5.49 & 27.1\% \\
\hline
-2 & \text{€}1.02 & \text{€}6.41 & 15.9\% \\
\hline
-1 & \text{€}0.89 & \text{€}7.20 & 12.4\% \\
\end{array} $$

Current stock price: €18.21. Trailing P/E = 18.21 / 0.89 = 20.46.

Task 1: Calculate normalized P/E using historical average EPS.
$$ \text{Average EPS} = \frac{0.62+0.53+0.24+0.63+1.49+1.02+0.89}{7} = \frac{5.42}{7} = \text{€}0.7743 \\ \text{Normalized P/E} = \frac{18.21}{0.7743} = 23.52 $$

Task 2: Calculate normalized P/E using average ROE.
$$ \text{Average ROE} = \frac{20.7+15.5+6.7+15.4+27.1+15.9+12.4}{7} = \frac{113.7}{7} = 16.24\% \\
\text{Normalized EPS} = 7.20 \times 0.1624 = \text{€}1.1693 \\
\text{Normalized P/E} = \frac{18.21}{1.1693} = 15.57$$

Revenue-Based Multiples: Price-to-Sales (P/S)

The price-to-sales ratio measures the market price per share divided by annual net sales per share:

$$ \begin{align*} P/S &= \frac{P_t}{\text{Sales per Share}} \end{align*} $$

Revenue-based multiples offer several advantages:

• Always positive (even when earnings are negative)
• More stable than earnings-based multiples
• Less susceptible to accounting manipulation

From the constant-growth DDM, recognizing that dividends divided by sales equals the product of net profit margin and payout ratio:

\begin{align*} \frac{P_t}{Sales_t} &= \frac{\text{Net Profit Margin} \times \text{Payout Ratio} \times (1+g)}{r_e – g} \end{align*}

This formula reveals that P/S is positively related to net profit margin, payout ratio, and growth, and negatively related to cost of equity.

Illustrative Example: P/S and Fundamentals

A company has:

• Payout ratio = 80%
• Expected growth = 3%
• Cost of equity = 8%
• Net profit margin = 15%

Task 1: Calculate justified P/S.

\(\frac{P_t}{\text{Sales}_t} = \frac{0.15 \times 0.80 \times 1.03}{0.08 – 0.03} = \frac{0.1236}{0.05} = 2.472\)

Task 2: Derive a justified P/E from P/S.

Since \(\text{P/S} = \text{P/E} \times \text{Net Profit Margin}\):

\(\text{Justified P/E} = \frac{2.472}{0.15} = 16.48\)

Task 3: Effect of higher net profit margin.

If net profit margin increases to 20% with all else equal:

\(\frac{P_t}{\text{Sales}_t} = \frac{0.20 \times 0.80 \times 1.03}{0.08 – 0.03} = \frac{0.1648}{0.05} = 3.296\)

Percentage increase = \((3.296 \div 2.472) – 1 = 33.33\%\)

Task 4: Trade-off between payout ratio and growth.

If the payout ratio decreases from 80% to 70% and growth increases from 3% to 3.5%:

\(\frac{P_t}{\text{Sales}_t} = \frac{0.15 \times 0.70 \times 1.035}{0.08 – 0.035} = \frac{0.1087}{0.045} = 2.415\)

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.

Operating Income Multiples: EV/EBITDA and Related Measures

Since 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.

The enterprise value can be expressed using the constant-growth FCFF model:

\begin{align*} EV_t &= \frac{FCFF_{t+1}}{WACC – g} \end{align*}

Where FCFF is defined as:

\begin{align*} FCFF &= EBITDA(1-t) + \text{Depreciation}(t) – CapEx – \Delta \text{Working Capital} \end{align*}

Dividing both sides by EBITDA yields the justified EV/EBITDA multiple:

\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*}

This decomposition shows that the \(\text{EV/EBITDA}\) multiple is:

• Positively related to: after-tax income proportion, depreciation (due to tax shield)
• Negatively related to: capital expenditures, working capital investment, cost of capital, tax rate (through the first term), and reinvestment needs

Illustrative Example: Drayton’s EV/EBITDA Multiple

An analyst analyzes Drayton Company, which has an observed \(\text{EV/EBITDA}\) multiple of 3.52. Fundamental data:

• \(\text{WACC} = 7.1\%\)
• \(\text{Long-run FCFF growth} = 2.0\%\)
• \(\text{EBITDA} = \text{€}300\text{ million}\)
• \(\text{Depreciation} = \text{€}150\text{ million}\)
• \(\text{CapEx} = \text{€}190\text{ million}\)
• \(\text{Working capital} = \text{€}0\)
• \(\text{Tax rate} = 30\%\)

Task 1: Calculate justified EV/EBITDA.

\(\frac{\text{EV}}{\text{EBITDA}} = \frac{1 – 0.30}{0.071 – 0.02} + \frac{(150 \times 0.30) / 300}{0.071 – 0.02} – \frac{190 / 300}{0.071 – 0.02}\)

\(= \frac{0.70}{0.051} + \frac{0.15}{0.051} – \frac{0.6333}{0.051}\)

\(= 13.725 + 2.941 – 12.418 = 4.25\)

Task 2: Updated assumptions.

• \(\text{Tax rate} = 25\%\)
• \(\text{Long-run growth} = 2.5\%\)
• \(\text{CapEx} = \text{€}230\text{ million}\)
• \(\text{Depreciation} = \text{€}180\text{ million}\)

\(\frac{\text{EV}}{\text{EBITDA}} = \frac{1 – 0.25}{0.071 – 0.025} + \frac{(180 \times 0.25) / 300}{0.071 – 0.025} – \frac{230 / 300}{0.071 – 0.025}\)

\(= \frac{0.75}{0.046} + \frac{0.15}{0.046} – \frac{0.7667}{0.046}\)

\(= 16.304 + 3.261 – 16.667 = 2.90\)

Task 3: Identify the primary driver of the decline.

The 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.

Balance Sheet Measures

Balance sheet multiples relate market value to the book value of assets or equity. The most common is the price-to-book (P/B) ratio:

\begin{align*} P/B &= \frac{P_t}{BVE_t} \end{align*}

The justified \(\text{P/B}\) from fundamentals (derived earlier) is:

\(\frac{P_t}{\text{BVE}_t} = \frac{\text{ROE} – g}{r_e – g}\)

For firms with differing leverage or negative equity, broader measures are appropriate:

$$ \begin{align*} \text{Value to Book} &= \frac{\text{Market Value of Equity} + \text{Market Value of Debt}}{\text{Book Value of Equity} + \text{Book Value of Debt}} \\
\text{EV to Book} &= \frac{\text{Market Value of Equity} + \text{Market Value of Debt} – \text{Cash}}{\text{Book Value of Equity} + \text{Book Value of Debt} – \text{Cash}} \end{align*} $$

The justified EV/Book multiple can be expressed as:

$$ \frac{EV}{\text{Book Value of Capital}} = \frac{\text{Return on Capital} \times (1 – \text{Reinvestment Rate})}{WACC – g} $$

Cash Flow Statement Measures

Cash flow–based multiples offer advantages over earnings-based measures:

• Cash flows are direct inputs to DCF models
• Less susceptible to manipulation and accounting differences
• More directly linked to value drivers

Dividend Yield

The dividend yield represents dividends per share divided by share price:

$$\begin{align*} \text{Dividend Yield} &= \frac{Div_t}{P_t} \end{align*} $$

From the constant-growth DDM:

$$ \begin{align*} \frac{Div_t}{P_t} &= \frac{r_e – g}{1 + g} \end{align*} $$

This reveals that dividend yields are:

• Positively related to the cost of equity
• Negatively related to growth expectations

Illustrative Example: Dividend Yield Fundamentals

A company has:

• \(\text{Payout ratio} = 80\%\)
• \(\text{Cost of equity} = 8\%\)
• \(\text{Growth} = 3\%\)
• \(\text{Justified trailing P/E} = 16.48\)

Task 1: Calculate justified trailing dividend yield.

Using the relationship: \(\text{Dividend Yield} = \text{Payout Ratio} \times (1 / \text{P/E})\)

\(\text{Dividend Yield} = 0.80 \times \frac{1}{16.48} = 4.85\%\)

Using the DDM-derived formula:

\(\frac{\text{Div}_t}{P_t} = \frac{0.08 – 0.03}{1.03} = 4.85\%\)

Task 2: Effect of lower payout ratio with higher ROE.

If \(\text{ROE} = 15\%\) and the payout ratio decreases to 70%:

\(g = (1 – 0.70) \times 0.15 = 4.5\%\)

\(\frac{\text{Div}_t}{P_t} = \frac{0.08 – 0.045}{1.045} = 3.35\%\)

Free Cash Flow Multiples

The price-to-FCFE multiple is derived from the constant-growth FCFE model:

$$ \begin{align*} \frac{P_t}{FCFE_{t+1}} &= \frac{1}{r_e – g} \end{align*} $$

Similarly, the EV-to-FCFF multiple is:

\begin{align*} \frac{EV_t}{FCFF_{t+1}} &= \frac{1}{WACC – g} \end{align*}

Both multiples are:

• Positively related to growth expectations
• Negatively related to required returns

Industry-Specific Measures

In capital-intensive industries, analysts often use measures tied directly to operational assets or output:

• \(\text{EV/Production}\) (e.g., \(\text{EV}\) per barrel of oil equivalent per day)
• \(\text{EV/Developed Reserves}\) (e.g., \(\text{EV}\) per barrel of proven reserves)
• \(\text{EV/Passenger Capacity}\) (for airlines)
• \(\text{EV/Subscriber}\) (for telecommunications)
• \(\text{EV/Store}\) (for retailers)

These measures offer advantages:

• Direct linkage to industry-specific value drivers
• Reduced accounting distortions
• Comparability across firms with different accounting policies

However, they lack comparability across industries and are difficult to connect to fundamental valuation models.

Summary of Key Multiples and Their Drivers

$$ \begin{array}{l|l|l}
\text{Multiple} & \text{Fundamental Drivers} & \text{Primary Applications} \\
\hline
\text{P/E} & \text{Payout ratio, growth rate, cost of equity} & \text{Positive EPS firms} \\
\hline
\text{P/S} & \text{Net profit margin, payout ratio, growth} & \text{Early-stage, cyclical, or loss-making firms} \\
\hline
\text{P/B} & \text{ROE, growth rate, cost of equity} & \text{Firms with similar leverage and asset profiles} \\
\hline
\text{EV/EBITDA} & \text{Tax rate, depreciation, CapEx, WACC, growth} & \text{Capital-intensive firms} \\
\hline
\text{EV/FCFF} & \text{WACC, growth rate} & \text{Firms with stable cash flows} \\
\hline
\text{P/FCFE} & \text{Cost of equity, growth rate} & \text{Firms with stable FCFE} \\
\hline
\text{Dividend Yield} & \text{Cost of equity, growth rate} & \text{Mature, dividend-paying firms} \\
\hline
\text{EV/Production} & \text{Operational efficiency, commodity prices} & \text{Natural resource companies} \\
\end{array} $$

Comprehensive Example 1: Comparative P/E and PVGO Analysis

Scenario: An analyst is evaluating four technology firms in the same industry segment. The following data is available:

$$
\begin{array}{l|l|l|l|l|l}
\textbf{Company} & \textbf{Price} & \textbf{Forward EPS} & \textbf{Cost of Equity} & \textbf{Payout Ratio} & \textbf{Expected Growth} \\
\hline
\text{TechAlpha} & \$85.00 & \$4.25 & 9.5\% & 65\% & 5.0\% \\
\hline
\text{TechBeta} & \$120.00 & \$5.00 & 10.0\% & 70\% & 4.0\% \\
\hline
\text{TechGamma} & \$45.00 & \$2.50 & 8.5\% & 60\% & 6.0\% \\
\hline
\text{TechDelta} & \$200.00 & \$8.00 & 11.0\% & 55\% & 3.5\% \\
\end{array} $$

Task A: Calculate each firm’s forward P/E, earnings yield, PVGO proportion, and justified trailing P/E.

TechAlpha:

\(\text{Forward P/E} = \frac{85.00}{4.25} = 20.00\text{x}\)

\(\text{Earnings Yield} = \frac{4.25}{85.00} = 5.00\%\)

\(\text{PVGO/P} = 1 – \left(\frac{0.05}{0.095}\right) = 1 – 0.5263 = 47.37\%\)

\(\text{Justified P/E} = \frac{0.65 \times (1.05)}{0.095 – 0.05} = \frac{0.6825}{0.045} = 15.17\text{x}\)

TechBeta:

\(\text{Forward P/E} = \frac{120.00}{5.00} = 24.00\text{x}\)

\(\text{Earnings Yield} = \frac{5.00}{120.00} = 4.17\%\)

\(\text{PVGO/P} = 1 – \left(\frac{0.0417}{0.10}\right) = 1 – 0.4167 = 58.33\%\)

\(\text{Justified P/E} = \frac{0.70 \times (1.04)}{0.10 – 0.04} = \frac{0.728}{0.06} = 12.13\text{x}\)

TechGamma:

\(\text{Forward P/E} = \frac{45.00}{2.50} = 18.00\text{x}\)

\(\text{Earnings Yield} = \frac{2.50}{45.00} = 5.56\%\)

\(\text{PVGO/P} = 1 – \left(\frac{0.0556}{0.085}\right) = 1 – 0.6536 = 34.64\%\)

\(\text{Justified P/E} = \frac{0.60 \times (1.06)}{0.085 – 0.06} = \frac{0.636}{0.025} = 25.44\text{x}\)

TechDelta:

\(\text{Forward P/E} = \frac{200.00}{8.00} = 25.00\text{x}\)

\(\text{Earnings Yield} = \frac{8.00}{200.00} = 4.00\%\)

\(\frac{\text{PVGO}}{P} = 1 – \left(\frac{0.04}{0.11}\right) = 1 – 0.3636 = 63.64\%\)

\(\text{Justified P/E} = \frac{0.55 \times (1.035)}{0.11 – 0.035} = \frac{0.56925}{0.075} = 7.59\text{x}\)

Task B: Interpret the findings.

$$
\begin{array}{l|l|l|l|l}
\text{Company} & \text{Forward P/E} & \text{PVGO/P} & \text{Actual vs. Justified P/E} & \text{Conclusion} \\
\hline
\text{TechAlpha} & 20.00\text{x} & 47.37\% & 20.00 > 15.17 & \text{Overvalued} \\
\hline
\text{TechBeta} & 24.00\text{x} & 58.33\% & 24.00 > 12.13 & \text{Overvalued} \\
\hline
\text{TechGamma} & 18.00\text{x} & 34.64\% & 18.00 < 25.44 & \text{Undervalued} \\ \hline \text{TechDelta} & 25.00\text{x} & 63.64\% & 25.00 > 7.59 & \text{Significantly overvalued} \\
\end{array}
$$

TechGamma stands out as the most attractive investment opportunity—it 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.

TechDelta, despite having the highest raw P/E (25.00x), is fundamentally justified at only 7.59x—its 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.

Comprehensive Example 2: EV/EBITDA and P/S Cross-Industry Comparison

Scenario: An analyst is comparing two companies in the transportation sector: AeroVentures (an airline) and LogiTrack (a logistics firm). While both operate in transportation, they have very different capital structures and operational characteristics.

$$
\begin{array}{l|l|l}
\text{Metric} & \text{AeroVentures} & \text{LogiTrack} \\
\hline
\text{Market Cap} & \text{€}18.5\text{ billion} & \text{€}12.2\text{ billion} \\
\hline
\text{Total Debt} & \text{€}8.2\text{ billion} & \text{€}4.1\text{ billion} \\
\hline
\text{Cash and Equivalents} & \text{€}3.8\text{ billion} & \text{€}2.9\text{ billion} \\
\hline
\text{Revenue} & \text{€}14.1\text{ billion} & \text{€}9.8\text{ billion} \\
\hline
\text{EBITDA} & \text{€}3.8\text{ billion} & \text{€}2.7\text{ billion} \\
\hline
\text{Net Income} & \text{€}1.1\text{ billion} & \text{€}1.5\text{ billion} \\
\hline
\text{Net Profit Margin} & 7.8\% & 15.3\% \\
\hline
\text{WACC} & 8.5\% & 7.2\% \\
\hline
\text{Expected FCFF Growth} & 3.0\% & 4.5\% \\
\hline
\text{Tax Rate} & 25\% & 25\% \\
\hline
\text{Depreciation} & \text{€}2.1\text{ billion} & \text{€}0.8\text{ billion} \\
\hline
\text{CapEx} & \text{€}2.4\text{ billion} & \text{€}0.9\text{ billion} \\
\hline
\text{Working Capital Investment} & \text{€}0.3\text{ billion} & \text{€}0.1\text{ billion} \\
\hline
\text{Payout Ratio} & 40\% & 60\% \\
\hline
\text{ROE} & 12\% & 18\% \\
\end{array} $$

Task A: Calculate enterprise value and key multiples for both companies.

AeroVentures:

$$ \text{EV} = 18.5 + 8.2 – 3.8 = \text{€}22.9\text{ billion} \\
\text{P/E} = \frac{18.5}{1.1} = 16.82\text{x} \\
\text{EV/EBITDA} = \frac{22.9}{3.8} = 6.03\text{x} \\
\text{P/S} = \frac{18.5}{14.1} = 1.31\text{x} $$

LogiTrack:

$$ \text{EV} = 12.2 + 4.1 – 2.9 = \text{€}13.4\text{ billion}
\text{P/E} = \frac{12.2}{1.5} = 8.13\text{x}
\text{EV/EBITDA} = \frac{13.4}{2.7} = 4.96\text{x}
\text{P/S} = \frac{12.2}{9.8} = 1.24\text{x} $$

Task B: Calculate justified multiples using the method of forecasted fundamentals.

Justified P/E:

AeroVentures:

\(\text{Justified P/E} = \frac{0.40 \times (1.03)}{0.085 – 0.03} = \frac{0.412}{0.055} = 7.49\text{x}\)

LogiTrack:

\(\text{Justified P/E} = \frac{0.60 \times (1.045)}{0.072 – 0.045} = \frac{0.627}{0.027} = 23.22\text{x}\)

Justified P/S:

AeroVentures:

\(\text{Justified P/S} = \frac{0.078 \times 0.40 \times 1.03}{0.085 – 0.03} = \frac{0.0321}{0.055} = 0.58\text{x}\)

LogiTrack:

\(\text{Justified P/S} = \frac{0.153 \times 0.60 \times 1.045}{0.072 – 0.045} = \frac{0.0959}{0.027} = 3.55\text{x}\)

Justified EV/EBITDA:

AeroVentures:

$$ \begin{align*} \frac{\text{EV}}{\text{EBITDA}} &= \frac{1 – 0.25}{0.085 – 0.03} + \frac{(2.1 \times 0.25) / 3.8}{0.085 – 0.03} – \frac{2.4 / 3.8}{0.085 – 0.03} – \frac{0.3 / 3.8}{0.085 – 0.03} \\
&= \frac{0.75}{0.055} + \frac{0.1382}{0.055} – \frac{0.6316}{0.055} – \frac{0.0789}{0.055} \\
& = 13.636 + 2.513 – 11.484 – 1.435 = 3.23\text{x} \end{align*} $$

LogiTrack:

$$ \begin{align*}\frac{\text{EV}}{\text{EBITDA}}& = \frac{1 – 0.25}{0.072 – 0.045} + \frac{(0.8 \times 0.25) / 2.7}{0.072 – 0.045} – \frac{0.9 / 2.7}{0.072 – 0.045} – \frac{0.1 / 2.7}{0.072 – 0.045} \\
&= \frac{0.75}{0.027} + \frac{0.0741}{0.027} – \frac{0.3333}{0.027} – \frac{0.0370}{0.027} \\
& = 27.778 + 2.744 – 12.346 – 1.370 = 16.81\text{x} \end{align*} $$

Task C: Interpret the findings and draw relative valuation conclusions.

$$ \begin{array}{l|l|l|l|l}
\text{Multiple} & \text{AeroVentures Actual} & \text{AeroVentures Justified} & \text{LogiTrack Actual} & \text{LogiTrack Justified} \\
\hline
\text{P/E} & 16.82\text{x} & 7.49\text{x} & 8.13\text{x} & 23.22\text{x} \\
\hline
\text{P/S} & 1.31\text{x} & 0.58\text{x} & 1.24\text{x} & 3.55\text{x} \\
\hline
\text{EV/EBITDA} & 6.03\text{x} & 3.23\text{x} & 4.96\text{x} & 16.81\text{x} \\
\end{array} $$

Interpretation:

The two companies tell dramatically different stories depending on which multiple is examined.

AeroVentures appears significantly overvalued on every justified multiple basis:

• 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.
• The \(\text{EV/EBITDA}\) analysis reveals the underlying problem: AeroVentures requires massive reinvestment (\(\text{CapEx}\) of \(\text{€}2.4\text{ billion}\) versus \(\text{EBITDA}\) of \(\text{€}3.8\text{ billion}\)), leaving little free cash flow after sustaining its fleet. The justified \(\text{EV/EBITDA}\) of only \(3.23\text{x}\) reflects this capital intensity.
• 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.

LogiTrack presents a more nuanced picture:

• 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 (\(4.5\%\)).
• 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 \(\text{€}0.9\text{ billion}\) versus \(\text{EBITDA}\) of \(\text{€}2.7\text{ billion}\)) and higher profitability generate substantial free cash flow, warranting a much higher multiple.
• 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.

Overall Conclusion:

Using 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—perhaps 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.