BMME303
Accounting, Analysis and Governance in Complex Deals
| Price | Value |
|---|---|
| Observable/Unique | Can be Ambiguous |
| No Model | Model/Theory Needed |
We will ignore this distinction and use the terms interchangeably
Under (restrictive) assumptions, multiple valuation methods collapse to the same result.
Let’s explore when discount valuation approaches and and ratio/multiple approaches can be seen as two sides of the same coin.
Assume that all earnings are paid out as dividends:
\[ \boxed{P_0 = \frac{D_1}{r - g}} = \frac{E_1}{r} \Rightarrow P_0 = \frac{E_1}{r} \]
with \(D=E\) and \(g=0\), where
DDM is one of the most fundamental approaches to valuation. It states that the value of a stock today equals the present value of all future dividends. (Session 1 BM04AFM!)
Rearrange \(P_0 = \frac{E_1}{r}\) from DDM w/o growth to derive at a forward looking P/E ratio:
\[ \frac{P_0}{E_1} = \frac{E_1/r}{E_1} \Rightarrow \boxed{\text{P/E} = \frac{1}{r}} \]
\(\Rightarrow\) The forward-looking P/E ratio is the ratio of the current share price to next year’s earnings
P/E ratio determines a common Multiples Approach to valuation: \[P_0 = E_1 \times \text{(Average of comparable firms' PE ratios)}\]
\(\Rightarrow\) Multiples are fundamentally connected to discount models!
Multiples Approach
\[P_0 = E_1 \times \text{(Average of comparable firms' PE ratios)}\]
DDM w/o Growth
\[P_0 = E_1 \times \frac{1}{r}\]
\(\Rightarrow\) Both approaches yield the same valuation when the average P/E of comparable firms appropriately reflects required return (and growth) of the focal firm.
Derive at another direct approach to equity valuation:
\[ \text{M/B} = \frac{P_0}{B_0} = \frac{ROE_1 \times B_0 / r}{B_0} \Rightarrow \boxed{\text{M/B} = \frac{ROE}{r}} \]
\(\Rightarrow\) M/B incorporate profitability beyond just the required return (P/E)
\[ \boxed{\text{M/B} = ROE \times\text{P/E}} \]
| w/o Growth | w Growth | Note | |
|---|---|---|---|
| P/E | \(\frac{1}{r}\) | \(\frac{1 - b}{r - ROE \times b}\) | P/E increases only if growth is value-creating (ROE > r) |
| M/B | \(\frac{ROE}{r}\) | \(\frac{ROE \times (1 - b)}{r - ROE \times b}\) | M/B is sensitive to both payout and profitability |
\(\Rightarrow\) Growth introduces important tradeoffs between payout, reinvestment rate, and return on equity
The growth rate \(g\) is defined as the product of the retention ratio \(b = \frac{E - D}{E}\) and the return on equity (ROE). This means that the growth rate is directly influenced by how much of the earnings are retained for reinvestment in the firm and how effectively those retained earnings generate returns.
| Equity-side | Enterprise-side | |
|---|---|---|
| Cost of Equity | WACC (Weighted Average Cost of Capital) | |
| ROE | ROIC (Return on Invested Capital) | |
| P/E | EV/EBIT or EV/EBIT(D)A | |
| M/B | EV / IC (Invested Capital) |
Equity value = Value of shareholders’ stake in the business
Enterprise value = Value of the whole business, sum of the market values of the various claims on the business
Value can be derived from the market value of a comparable company
\[ \begin{equation*} \text{Multiple} = \frac{\text{What you pay (price)}}{\text{What you get (book)}} \end{equation*} \]
\(\Rightarrow\) Willingness to pay each EUR of earnings, cash flow, or sales, …
\[MV_T=(MV_{C}/VI_{C})×VI_{T}\]
Where:
P/E ratio equivalence from earlier: P = PEs of Peers x E
Valuing Repsol YPF Using Comparable Integrated Oil Companies
| Comparable Company | Trailing P/E | Forward P/E | Price/Sales | Price/Book | Average |
|---|---|---|---|---|---|
| Exxon Mobil Corp. (XOM) | 11.25 | 8.73 | 1.17 | 3.71 | |
| British Petroleum (BP) | 9.18 | 7.68 | 0.69 | 2.17 | |
| Chevron Corp. (CVX) | 10.79 | 8.05 | 0.91 | 2.54 | |
| Royal Dutch Shell (RDS-B) | 7.36 | 8.35 | 0.61 | 1.86 | |
| ConocoPhillips (COP) | 11.92 | 6.89 | 0.77 | 1.59 | |
| Total SA (TOT) | 8.75 | 8.73 | 0.80 | 2.53 | |
| Eni SpA (E) | 3.17 | 7.91 | 0.36 | 0.81 | |
| PetroChina Co. (PTR) | 11.96 | 10.75 | 1.75 | 2.10 | |
| Average Multiple | 9.30 | 8.39 | 0.88 | 2.16 | |
| \(\times\) | |||||
| Repsol YPF (Projections) | $4.38 | $3.27 | $92.66 | $26.49 | |
| = Estimated Market Value | $40.72 | $27.42 | $81.77 | $57.32 | $51.81 |
Can you calculate a (Trailing) P/E ratio for a company? Try eBay!
Valuing Repsol YPF Using Comparable Integrated Oil Companies
\[MV_T=(MV_{IND}/VI_{IND})×VI_{T}\]
\[EV/EBITDA = (MV_{FCFE} + MV_{PF} + (MV_D - \text{Cash}))/EBITDA\]
Where:
\(\rightarrow\) construct a multiple for the whole enterprise (equity and debt) rather than just equity
Repsol and Eni are geographically diversified integrated oil and gas companies. The market value of Repsol’s common equity is $40.36 billion, and Eni’s is $54.30 billion. Neither firm has preferred stock outstanding. Repsol’s ($14.6 billion) and Eni’s ($8.8 billion) outstanding debt consists primarily of interest-only notes ($0.7 billion and $0.3 billion, respectively) with a balloon payment at maturity. The average maturity date for Repsol’s debt is 12 years; for Eni’s debt it is 10 years. Market rates of interest for firms like Eni and Repsol at that time for debt maturing within 10 to 12 years were 7% and 7.5%, respectively.
Calculate EV/EBITDA ratios for Repsol and Eni.
\[EV/EBITDA = (MV_{FCFE} + MV_{PF} + (MV_D - \text{Cash}))/EBITDA\]
Ingredients
Use the following formula to calculate the market/present value of the annuity payment
\[\text{MV Annuity} = \text{Payment} \times {\frac {1-(1+i)^{-n}}{i}}\]
then add the present value of the balloon payment at maturity
\[\text{MV Balloon} = \frac{\text{Balloon Payment}}{(1+i)^n}\]
to derive at the market value of debt:
\[ \text{MV}_D = \$0.7 \times \left[ \frac{1 - 1 / (1.075)^{12}}{0.075} \right] + \frac{\$14.6}{1.075^{12}} = \$0.7 \times 7.74 + \$6.13 = \$11.55 \text{bn} \]
\[ \text{MV}_D = \$0.3 \times \left[ \frac{1 - 1 / (1.070)^{10}}{0.07} \right] + \frac{\$8.8}{1.07^{10}}= \$0.3 \times 7.02 + \$4.47 = \$6.58 \text{bn} \]
Book value of debt is often used as a proxy for market value, but this can be misleading for long-term or off-market debt.
\[EV/EBITDA = (MV_{FCFE} + 0 + (MV_D - \text{Cash}))/EBITDA\]
| Balance Sheet | Repsol | ENI |
|---|---|---|
| Cash | 3.8 | 6.2 |
| … | ||
| Income Statement | Repsol | ENI |
| Depreciation | 4.10 | 8.10 |
| EBIT | 8.0 | 27.6 |
| Interest expense | 0.7 | 0.3 |
| … |
\(\frac{(\$40.36 + 0 + \$11.55 - \$3.8)}{(\$8.0 + \$4.1)} = 3.98\)
\(\frac{(\$54.30 + 0 + \$6.58 - \$6.2)}{(\$27.60 + \$8.1)} = 1.53\)
Assume that 2 firms are direct competitors and have P/E ratios of 10 and 20, respectively.
Which is the cheaper firm?
\(\rightarrow\) Not possible to answer without knowing growth rates of earnings (and what return can be earned from reinvested earnings)!
\(\rightarrow\) The PEG ratio adjusts for differences in growth rates among comparable firms
\(\rightarrow\) The PEG ratio (A) adjusts for differences in growth rates among comparable firms:
\[ A = \frac{MV_C/VI_C}{VI_{CGR}} \]
Where:
\(\Rightarrow\) A is the PEG ratio for comparable firms
When applying this adjustment, the Market Value Multiple Valuation \[MV_T=(MV_{C}/VI_{C})×VI_{T}\]
becomes
\[\boxed{MV_T = A \times VI_{TGR} \times VI_T}\]
where
\(A\) = PEG ratio for comparable firms, which is the market price to value indicator relative to growth rate for comparable firms
\(VI_T\) = Value indicator for target
\(VI_{TGR}\) = Projected growth rate in value indicator of target firm
An analyst is asked to determine whether Basic Energy Service (BES) or Composite Production Services (CPS) is more attractive as an acquisition target. Both firms provide engineering, construction, and specialty services to the oil, gas, refinery, and petrochemical industries. BES and CPS have projected annual earnings per share growth rates of 15% and 9%, respectively. BES’s and CPS’s current earnings per share are $2.05 and $3.15, respectively. The current share prices for BES are $31.48 and for CPX are $26.00. The industry average [assume that industry peers are comparable firms here] price-to-earnings ratio and growth rate are 12.4% and 11%, respectively.
Calculate valuations using the PEG ratio (for comparable firms) and discuss which firm is a more attractive takeover target as of now.
| Firm | Implied Price | Current Price | Upside (%) |
|---|---|---|---|
| BES | $34.66 | $31.48 | +10.1% |
| CPS | $31.96 | $26.00 | +23.0% |
CPS appears to be a more attractive acquisition target than BES based on the PEG ratio, as it has a higher upside potential of 23% compared to BES’s 10.1% (although BES has both a higher growth rate and a higher implied share price).
BES might be a more attractive acquisition target if it generates increasing future financial returns (and if its projected earnings stream is viewed as less risky).
One can move from a PEG ratio for comparable firms to a PEG ratio for the target firm by using (i) the target firm’s market price to value indicator in the numerator (\(MV_T/VI_T\),e.g., P/E) and (ii) the target firm’s projected growth rate (\(VI_{TGR}\)) in the denominator:
\[ A_T = \frac{MV_T/VI_T}{VI_{TGR}} \]
What to do when earnings are missing?
\(\Rightarrow\) implied assumption that a single value driver is representative of the total value of the business (Dot-com bubble)
| Methodology | Use this methodology when: |
|---|---|
| Discounted cash flow | • The firm is publicly traded or private with identifiable cash flows • A start-up has some history of facilitating cash flow forecasts • An analyst has a long-time horizon • An analyst has confidence in forecasting the firm’s cash flows • Current or near-term earnings or cash flows are negative but are expected to turn positive in the future • A firm’s competitive advantage is expected to be sustainable • The magnitude and timing of cash flows vary significantly |
| Comparable companies | • There are many firms exhibiting similar growth, return, and risk characteristics • An analyst has a short-term time horizon • Prior, current, or near-term earnings or cash flows are positive • An analyst has confidence the markets are, on average, right • Sufficient information to predict cash flows is lacking • Firms are cyclical; for P/E ratios, use normalized earnings (i.e., earnings averaged throughout the business cycle) • Growth rate differences among firms are large; use the PEG ratio |
| Comparable transactions | • Recent transactions of similar firms exist • An analyst has a short-term time horizon • An analyst has confidence the markets are, on average, right • Sufficient information to predict cash flows is lacking |
| Same or comparable industry | • Firms within an industry or a comparable industry are substantially similar in terms of profitability, growth, and risk • An analyst has confidence the markets are, on average, right • Sufficient information to predict cash flows is lacking |
| Replacement-cost approach | • An analyst wants to know the current cost of replicating a firm’s assets • The firm’s assets are easily identifiable, tangible, and separable • The firm’s earnings or cash flows are negative |
| Tangible book value | • The firm’s assets are highly liquid • The firm is a financial services or product distribution business • The firm’s earnings and cash flows are negative |
| Breakup value | • The sum of the value of the businesses/product lines comprising a firm is believed to exceed its value as a going concern |
| Liquidation value | • An analyst wants to know asset values if they were liquidated today • Assets are separable, tangible, and marketable • Firms are bankrupt or subject to substantial financial distress • An orderly liquidation is possible |
| Real options (contingent claims) | • Additional value can be created if management has a viable option to expand, delay, or abandon an investment • Assets not currently generating cash flows have the potential to do so • Assets have characteristics most resembling financial options • The asset owner has some degree of exclusivity (e.g., a patent) |
What drives investment IBs’ choice of peers in comparable companies analysis?
Board’s Fiduciary Responsibilities (duties of care and loyalty) in transactions require professional/external evaluation of transaction fairness
FOs historically evolved following the Trans Union case
Can be strategic tools influenced by litigation risk and agency conflicts
Fee structures create potential conflicts of interest
Market-based methods are derived from fundamental discount principles
Multiples (comparables, transactions, asset-based) serve different contexts
Method selection depends on company characteristics and available information
Each method has strengths and limitations
Titlepage photo by Dennis Möller on Unsplash