debt-to-equity ratio is 0.5の場合は
MVCE/(MVD+MVCE)＝1.0/(0.5+1.0)になることに注意（ミスに注意）
Sum-of-the-parts analysis is most useful when valuing a company with segments in different industries that have different valuation characteristics.
Ibbotson–Chen earnings model
Equity risk premium={[(1+EINFL)(1+EGREPS)(1+EGPE)− 1.0]+EINC} −Expected risk-free return
EINFL = 4% per year (long-term forecast of inflation)
EGREPS = 5% per year (growth in real earnings)
EGPE = 1% per year (growth in market P/E)
EINC = 1% per year (dividend yield or the income portion)
Risk-free return = 7% per year (for 10-year maturities)
Total return = Dividend yield + Capital gains yield (i.e., constant growth rate).
P0/E1 = [1/r] + [PVGO/E1],
Market value added = Market value of capital − Total capital
FCFE = NI – Net capital expenditure – WCInv + New debt financing
The major concepts are as follows:
- EPS plus per-share depreciation, amortization, and depletion (CF)
Limitation: Ignores changes in working capital and noncash revenue; not a free cash flow concept.
- Cash flow from operations (CFO)
Limitation: Not a free cash flow concept, so not directly linked to theory.
- Free cash flow to equity (FCFE)
Limitation: Often more variable and more frequently negative than other cash flow concepts.
- Earnings before interest, taxes, depreciation, and amortization (EBITDA)
Limitation: Ignores changes in working capital and noncash revenue; not a free cash flow concept. Relative to its use in P/EBITDA, EBITDA is mismatched with the numerator because it is a pre-interest concept.
Market value added = Market value of company – Accounting book value of total capital
Market value of firm = Market value of debt + Market value of equity
EVA=NOPAT−WACC×Beginning book value of assets
Real required rate of return = Country return ± Industry adjustment ± Size adjustment ± Leverage adjustment
WCInv
=
Increase in accounts receivable + Increase in inventory – Increase in accounts payable – Increase in accrued liabilities
Net borrowing=Increase in notes payable+Increase in long-term debt
When the company being analyzed has significant noncash charges other than depreciation expense, this sales-based methodology will result in a less accurate estimate of FCFE than one obtained by forecasting all the individual components of FCFE.
EV = Market value of common equity + Market value of preferred stock + Market value of debt – Cash, cash equivalents, and short-term investments
Equity risk premium according to the macroeconomic model:
[(1 + EINFL)(1 + EGREPS)(1 + EGPE) – 1] + EINC – Expected risk-free rate
EINFL = expected inflation
EGREPS = expected growth in real earnings per share
EGPE = expected growth in P/E
EINC = expected income component
High P/Es on depressed earnings per share (EPS) at the bottom of the cycle and low P/Es on unusually high EPS at the top of the cycle reflect the countercyclical property of P/Es known as the Molodovsky effect.
EEM では、運転資金、固定資産、無形資産を異なる割引率で評価することができる。EEMが民間企業全体の価格決定に用いられることはまれである
Generally, the EEM is used to value intangible assets and very small businesses when other such market approach methods are not feasible, and the EEM is rarely used in pricing entire private businesses.
EEM = The return required for working capital is $2,000,000 × 5.0% = $100,000, and the return required for fixed assets is $5,500,000 × 8.0% = $440,000, or $540,000 in total.
The residual income for intangible assets =(the normalized earnings – required return for working capital and fixed assets)×long-term growth rate of residual income/(15.0% discount rate for intangibles less 5.0% long-term growth rate of residual income).
The excess earnings consist of any remaining income after returns to working capital and fixed assets are considered. Fair value estimates and rate of return requirements for working capital and fixed assets are provided. The return required for working capital is $2,000,000 × 5.0% = $100,000, and the return required for fixed assets is $5,500,000 × 8.0% = $440,000, or $540,000 in total.
The market value of invested capital is the total of the values of working capital, fixed assets, and intangible assets. This value is $2,000,000 + $5,500,000 + $4,830,000 = $12,330,000.
Required rate of ROE=r
Normalized EPS is the level of earnings per share that the company could currently achieve under mid-cyclical conditions.
FCFE=Net income−(1−DR)(FCInv−Depreciation) −(1−DR)(WCInv),
FCFE=Net income−(1−DR)(FCInv−Depreciation+WCInv)
=Net income−(1−DR)(Net investment in operating assets).
ノーマライズド・ファイナンシャル・ステートメント（Normalized Financial Statements）とは？企業の決算の実態を把握するために、企業の非経常的な費用や収益を調整することがあります。この調整後の財務諸表が正規化財務諸表と呼ばれるものです。
EV = Market value of debt + Market value of common equity + Market value of preferred equity – Cash and short-term investments.
Return on working capital = 0.08 × US$10,000,000 = US$800,000
Return on fixed assets = 0.12 × US$45,000,000 = US$5,400,000
Return on intangibles = US$35,000,000 – US$800,000 – US$5,400,000 = US$28,800,000
Value of intangibles using CCM = US$28,800,000/(0.20 − 0.06) = US$205.71 million.
The Fed model considers the equity market to be undervalued when the market’s current earnings yield is greater than the 10-year Treasury bond yield. The Yardeni model incorporates the consensus five-year earnings growth rate forecast for the market index, a variable missing in the Fed model.
The harmonic mean is sometimes used to reduce the impact of large outliers
FCFF is preferred over FCFE when a company is leveraged and expecting a change in capital structure. FCFF growth will reflect fundamentals more clearly because FCFE growth will reflect fluctuating amounts of net borrowing. Second, in a forward-looking context, the required return on equity might be expected to be more sensitive to changes in financial leverage than changes in the WACC.
Bond yield plus risk premium cost of equity = Yield to maturity on the company’s long-term debt + Risk premium.
The Fama–French model estimate for return on equity is calculated using the formula
ri=RF+βmktiRMRF+βsizeiSMB+βvalueiHML
ri = Required return on share i
RF = Current expected risk-free return on the short-term government bill
The return on capital employed (ROCE) is a pre-tax return measure that can be useful in the peer comparison of companies in countries with different tax structures. ROCEは、利息及び税金控除前利益（EBIT /営業利益）を使用資本で割って計算します。ROCEの使用資本とは、有利子負債と自己資本を足したものです。無利子の負債（流動負債）は除きます。
ROIC is an after-tax measure and will increase with earnings growth if additional capital is not contributed. Return on capital employed (ROCE) is the associated pre-tax measure.
The fraction of the company’s value that comes from its growth opportunities = PVGO/PRICE
g = PRAT =
P (Profit margin)
=
NI/Sales
R (Retention)
=
b = (EPS – DPS)/EPS
A (Asset turnover)
=
Sales/Average total assets
T (Leverage)
=
Average total assets/Average shareholders’ equity
