Equity part 2 Flashcards
Residual incomea nd priavte company valuation
What is residual income (RI)?
RI is net income minus a charge for equity capital, representing economic profit after accounting for the cost of equity.
Why does traditional accounting income overstate profitability for equity investors?
Because it includes the cost of debt (interest) but excludes the cost of equity capital.
How is residual income calculated?
Residual Income = Net Income − Equity Charge (Equity × Cost of Equity)
What does a negative residual income indicate?
The firm is economically unprofitable after accounting for the equity holders’ required return.
If a firm has $800M equity, 12.3% cost of equity, and $80.52M net income, what is residual income?
Equity charge = $800M × 0.123 = $98.4M; RI = $80.52M − $98.4M = −$17.88M
What is Economic Value Added (EVA)?
EVA = NOPAT − (WACC × total capital). Measures value added for shareholders by management.
How is NOPAT calculated?
NOPAT = EBIT × (1 − tax rate)
What is the difference between EVA and RI?
RI uses net income and cost of equity. EVA uses NOPAT and WACC, accounting for both debt and equity.
What adjustments are recommended before calculating EVA?
Capitalize R&D, treat leases as capital leases, remove deferred taxes, and add LIFO reserve.
If NOPAT = $2,100, WACC = 14.2%, capital = $18,000, what is EVA?
EVA = 2100 − (0.142 × 18000) = 2100 − 2556 = −$456
What is Market Value Added (MVA)?
MVA = Market value of firm − Book value of invested capital. It measures value created since inception.
How is the market value of a firm calculated?
Market Value = Market value of equity + Market value of long-term debt
If equity value = $25 × 800 shares and debt = $4,000, total capital = $21,000, what is MVA?
MV = $20,000 + $4,000 = $24,000; MVA = $24,000 − $21,000 = $3,000
What are common uses of residual income models?
Used for equity valuation, performance measurement, executive compensation, and goodwill impairment testing.
What is the residual income formula using ROE and book value?
RI = (ROE − r) × Bt−1
How do you calculate the intrinsic value of a stock using the RI model?
V0 = B0 + sum of discounted future residual incomes: RI1/(1+r)^1 + RI2/(1+r)^2 + …
What are the components of intrinsic value in the residual income model?
- Current book value (B0), 2. Present value of expected future residual income
Why is the RI model less sensitive to terminal value estimates?
Because current book value is known and contributes substantially to intrinsic value.
What are the advantages of the RI model over DDM or FCFE?
Less reliance on uncertain terminal values; includes book value which anchors the valuation.
If B0 = €18, r = 11%, EPS2025 = 2.05, what is RI for 2025?
RI = 2.05 − (0.11 × 18) = €0.07
What is the single-stage RI model formula?
V0 = B0 + [(ROE − r) × B0] / (r − g)
What are the fundamental drivers of residual income?
ROE, required return (r), book value (B0), and growth rate (g)
What happens to intrinsic value if ROE = r?
Intrinsic value equals book value; justified P/B = 1
What does a higher ROE than r imply in RI valuation?
Positive residual income and intrinsic value > book value
What is Tobin’s Q ratio?
Tobin’s Q = (Market value of debt + equity) / Replacement cost of assets
How is the RI model linked to the justified P/B ratio?
P/B = 1 + PV of expected residual income / B0; if ROE > r, P/B > 1
When is the justified P/B ratio greater than one?
When the firm’s ROE is greater than the required return on equity (r)
What is the economic meaning of justified P/B > 1 in RI models?
The firm is generating economic profit and is worth more than its book value
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What is the formula for the single-stage residual income valuation model?
V0 = B0 + [(ROE − r) × B0] / (r − g)
What does the single-stage RI model assume?
Constant ROE and earnings/dividend growth rate, implying RI persists indefinitely.
How is growth rate (g) calculated in the single-stage model?
g = retention ratio × ROE
What is the interpretation of the second term in the single-stage RI model?
It represents the present value of expected future economic profits (residual income).
If B0 = $23, ROE = 14%, r = 12%, payout ratio = 60%, what is g?
g = (1 − 0.6) × 0.14 = 0.056 = 5.6%
Using the same values, what is intrinsic value via the single-stage RI model?
V0 = 23 + [(0.14 − 0.12) × 23] / (0.12 − 0.056) = 23 + 7.19 = $30.19
How can the Gordon growth model give the same result as the RI model?
Because both use the same inputs under the same assumptions; they are mathematically equivalent.
What is the formula to find implied growth rate (g) from the RI model?
g = r − [B0 × (ROE − r) / (V0 − B0)]
What does the implied growth rate formula tell us?
It reveals the market’s expectations for residual income growth given current P/B and other fundamentals.
If P/B = 2.50, B0 = €8, ROE = 13%, r = 11%, what is implied market price?
P0 = 8 × 2.50 = €20.00
What is the implied growth rate from the given data?
g = 0.11 − [8 × (0.13 − 0.11) / (20 − 8)] = 0.0967 = 9.67%
Adjustments before calculation NOPAT and invested capital
- Capitalize and amortize R&D
- Add them back to earnings to calculate NOPAT
Add back charges on strategic investments that will generate returns in the future
Eliminate deferred taxes and consider only cash taxes as expenses - Add LIFO reserve to invested capital and add back changes in LIFO reserve to NOPAT
What is continuing residual income?
Residual income expected beyond the short-term forecast horizon.
What is the persistence factor (ω)?
A value between 0 and 1 that captures how long residual income persists over time.
What is the formula for PV of continuing RI when ω is used?
PV = RIT / (1 + r − ω)
When ω = 1, what is the assumption?
Residual income persists at its current level forever.
When ω = 0, what is the assumption?
Residual income drops immediately to zero.
When 0 < ω < 1, what is the assumption?
Residual income declines gradually to zero as ROE falls to cost of equity.
What drives higher persistence factors?
Low dividend payouts, sustainable competitive advantage, stable industry returns.
What drives lower persistence factors?
High ROE, high accruals, nonrecurring items, competition eroding profitability.
What are the 3 components of intrinsic value in a multistage RI model?
V0 = B0 + PV of interim high-growth RI + PV of continuing RI
How is value affected by persistence assumptions?
More conservative assumptions (lower ω) reduce intrinsic value.
If Java Metals has RI from Year 1 to 5 and RI drops to zero after, what is the intrinsic value?
V0 = 5 + PV of residual income from years 1–5 = $6.25
If Java’s RI of $0.44 continues forever, what is its value in Year 4?
$0.44 / 0.10 = $4.40
What is Java’s total intrinsic value with perpetual RI?
V0 = 5 + PV(RI 1–4 + $4.40 at Year 4) = $8.98
If persistence factor ω = 0.4, how is terminal value calculated?
TV in Year 4 = 0.44 / (1.10 − 0.4) = $0.63
What is Java’s intrinsic value with ω = 0.4?
V0 = $6.40
If P/B at year 5 is expected to be 1.2 and B = 10.05, what is PT?
PT = 10.05 × 1.2 = $12.06
How do you calculate continuing RI value from PT and BT?
PV = (PT − BT + RI_T) / (1 + r)
What is Java’s value assuming P/B = 1.2 in Year 5?
V0 = $7.50
How do you determine if a stock is overvalued using RI?
If model value < market price → overvalued; > market price → undervalued; equal → fairly valued.
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How does the residual income model differ from DDM and FCFE models?
RI model starts with book value and adds PV of residual income; DDM/FCFE discount expected future cash flows.
When do all valuation models theoretically give the same intrinsic value?
When all assumptions and inputs are identical across the models.
Why might RI, DDM, and FCFE models give different results in practice?
Forecasting errors and differences in assumptions lead to different valuation outcomes.
What are key strengths of residual income models?
Less reliance on terminal value, uses available accounting data, suitable for non-dividend and negative-FCFE firms.
When are RI models most appropriate?
Firm does not pay dividends, negative expected FCFE, or uncertain terminal value forecast.
What are key weaknesses of residual income models?
Susceptible to accounting manipulation, requires many adjustments, assumes clean surplus relation.
What is the clean surplus relation?
Bt = Bt−1 + Et − Dt; ending book value = beginning book value + earnings − dividends.
When are RI models not appropriate?
When clean surplus is violated significantly or ROE/book value estimates are highly uncertain.
What are clean surplus violations?
Adjustments that bypass income statement like CTA, pension changes, revaluation surplus, etc.
What happens if clean surplus relation is violated?
Net income is incorrect; ROE estimates become unreliable.
How should operating leases be treated for RI models?
Capitalize them by increasing assets/liabilities with PV of lease payments.
What adjustments should be made for LIFO inventory accounting?
Add LIFO reserve to inventory and equity.
How should pension assets/liabilities be adjusted?
Adjust to reflect the funded status (plan assets – PBO).
When should deferred tax liabilities be reclassified to equity?
When they are not expected to reverse.
How should R&D expenses affect RI valuation?
Productive R&D increases ROE; unproductive R&D decreases ROE.
How should nonrecurring items be treated in RI models?
They should be excluded from residual income forecasts.
What aggressive accounting practices must be adjusted for in RI models?
Revenue acceleration, expense deferral, overstated assets.
What challenges exist with RI models in international settings?
Accounting standards differences, unreliable earnings, clean surplus violations.
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What are company-specific factors that distinguish private firms?
Stage of life cycle, size, quality of management, management/shareholder overlap, financial disclosure quality, and tax focus.
What are stock-specific factors that distinguish private firms?
Liquidity, restrictions on marketability, and concentration of control.
How does management/shareholder overlap affect private firms?
It reduces principal-agent conflict and allows for a long-term focus.
Why do private firms often have higher required returns?
Due to greater risk, limited financial disclosures, and lack of liquidity.
What are the main uses of private firm valuation?
Transactions, compliance, and litigation.
What are examples of transaction-related valuations?
Venture capital financing, IPOs, M&A, bankruptcy, managerial compensation, and debt financing.
What are examples of compliance-related valuations?
Financial reporting (e.g., goodwill impairment), stock compensation, and tax compliance.
What are examples of litigation-related valuations?
Shareholder suits, damage claims, lost profits, and divorce settlements.
What is the definition of normalized earnings for private firms?
Earnings if the firm were acquired, adjusted for nonrecurring, discretionary, or tax-motivated items.
What are common adjustments when calculating normalized earnings?
Excess compensation, nonoperating assets, related party transactions, personal expenses, and lease rate adjustments.
How should real estate be treated in private firm valuation?
Separate it as a nonoperating asset and adjust rent/depreciation to market rates.
What scenarios should be considered for future private firm operations?
Sale, IPO, continued private operations, or bankruptcy.
Why is FCFF often preferred for private firm valuation?
It is less sensitive to leverage changes and uses WACC, which is more stable than cost of equity.
If owner compensation is $2.5M and market rate is $1M, how is SG&A adjusted?
SG&A is reduced by $1.5M to normalize compensation.
If lease expense is $100K and market rate is $130K, how is SG&A adjusted?
SG&A is increased by $30K to reflect market lease rate.
If office building is noncore with $150K SG&A and $25K depreciation, what is adjustment?
Reduce SG&A by $150K and depreciation by $25K.
What is the formula for FCFF?
FCFF = Operating Income after tax + Depreciation − CapEx − Change in Working Capital.
Why is FCFF preferred when capital structure will change?
Because WACC is less sensitive to leverage changes than cost of equity used in FCFE.
What is FCFF if: Op. income after tax = $2.5368M, Dep = $416K, CapEx = $464K, ΔWC = $80K?
FCFF = 2.5368M + 416K − 464K − 80K = $2.4088M
What factors require adjustment when estimating discount rate for private firms?
Size premiums, availability/cost of debt, acquirer vs. target, projection risk, life cycle stage.
Why is WACC typically higher for private firms?
They have less access to debt, more operating risk, and smaller size.
Why shouldn’t acquirers use their own discount rate to value targets?
Because it underestimates the target’s risk and overvalues the firm.
Why is projection risk higher in private companies?
Due to less reliable information and possibly inexperienced management.
How is private company beta estimated from a public firm?
Unlever beta using public firm D/E and relever using private firm’s D/E.
What is the expanded CAPM?
CAPM + small stock premium + company-specific risk premium.
What is the build-up method?
Risk-free rate + equity premium + size premium + industry risk premium + company-specific premium.
When is the build-up method used?
When no comparable public companies exist for beta estimation.
What is required return using CAPM with Rf=3.6%, beta=1.3, ERP=6%?
3.6% + 1.3 × 6% = 11.4%
What is required return using expanded CAPM (add 3% and 2%)?
11.4% + 3% + 2% = 16.4%
What is return using build-up method: Rf=3.6%, ERP=6%, industry=1%, small=3%, company=2%?
3.6% + 6% + 1% + 3% + 2% = 15.6%
What is DLOC (Discount for Lack of Control)?
Discount applied due to inability to influence firm decisions as a minority owner.
How is DLOC calculated from control premium?
DLOC = 1 − [1 / (1 + control premium)]
What is DLOM (Discount for Lack of Marketability)?
Discount for inability to sell shares easily due to no active market.
What factors increase DLOM?
Ownership concentration, contractual restrictions, no planned IPO.
What is the total discount when DLOC=20%, DLOM=13%?
1 − [(1−0.20)(1−0.13)] = 30.4%
What are synergy adjustments for Buyer A and B if exec pay cut = $300K and SG&A savings = $400K?
Buyer B EBITDA = $5.1M; Buyer A EBITDA = $5.5M with added synergy savings.
How do DLOM and DLOC affect value of minority interest?
They reduce it significantly, especially when sale is unlikely.
How is value of minority interest calculated?
Equity × % ownership × (1 − DLOC) × (1 − DLOM)
What are the three main approaches to private firm valuation?
Income approach, market approach, and asset-based approach.
When is the asset-based approach most appropriate?
For early-stage or distressed companies with high uncertainty in future cash flows.
What approach uses present value of future income?
Income approach.
What is the key consideration in selecting a valuation approach?
Life cycle stage, firm size, and nature of assets (operating vs. nonoperating).
What are three income-based methods?
Free Cash Flow (FCF) method, Capitalized Cash Flow (CCM) method, and Excess Earnings Method (EEM).
What is the formula for firm value using CCM?
Value = FCFF1 / (WACC − g)
What is the capitalization rate in the CCM?
WACC − growth rate
What is the formula to estimate equity value from firm value?
Equity value = Firm value − Market value of debt
What is the formula for reinvestment rate (b) in CCM?
b = g / WACC
When is the CCM most appropriate?
For small firms with stable growth and uncertain projections.
What is the excess earnings method (EEM)?
Firm value = WC + FA + PV of intangible asset earnings (excess earnings growing perpetuity)
What are the three market-based valuation methods?
Guideline public company method (GPCM), guideline transactions method (GTM), and prior transaction method.
How is enterprise value estimated using GPCM?
Apply adjusted EV/EBITDA multiple from public comps to subject firm’s EBITDA.
What adjustments are required in GPCM?
Control premiums, industry conditions, consideration type, reasonableness, size/leverage.
What is the control premium?
Difference between pro rata value of controlling and non-controlling interests.
How is EV/EBITDA calculated using industry weights?
EV/EBITDA = ∑ (industry weight × industry multiple)
Why might GTM be preferred over GPCM?
GTM already reflects control premiums in acquisition prices.
What should be considered in GTM comparables?
Transaction type (strategic/financial), contingent consideration, type of payment.
How do you value a firm with FCFF = $12.1M, g = 4%, WACC = 15%?
Firm value = $12.1M / (0.15 − 0.04) = $110M
If firm value is $110M and debt is $4M, what is equity value?
Equity = $110M − $4M = $106M
How do you value intangibles with EE = $12K, g = 5%, r = 14%?
PV = $12K × 1.05 / (0.14 − 0.05) = $140K
Using GTM: EBITDA = $18.2M, adjusted multiple = 5.0, what’s EV?
EV = 5.0 × $18.2M = $91M
