Residual Income Model (RIM)¶

Valuation based on book value plus the present value of expected "excess" returns above the cost of equity.

Overview¶

RIM is particularly well-suited for financial institutions and asset-heavy businesses where book value is meaningful. It focuses on returns above what shareholders require, making it complementary to DCF.

Core Concept¶

Key Insight: A company is worth its book value plus (or minus) the present value of all future returns above (or below) the cost of equity.

Value = Book Value + PV(Future Residual Income)

Where:

Residual Income = (ROE - Cost of Equity) × Book Value

How It Works¶

1. Starting Point: Book Value¶

Book Value per Share = Total Equity / Shares Outstanding

Quality Check: - Adjust for intangibles (goodwill) - Check for off-balance sheet items - Verify accounting quality

2. Calculate Residual Income¶

For Each Future Period:

RI_t = (ROE_t - r_e) × BV_{t-1}

Where: - ROE_t = Return on Equity in period t - r_e = Cost of Equity (required return) - BV_{t-1} = Book Value at start of period

3. Project Book Value Growth¶

BV_t = BV_{t-1} × (1 + g)

Where g = Sustainable growth rate = ROE × (1 - Payout Ratio)

4. Terminal Value¶

Perpetuity Method:

Terminal RI = RI_final / (r_e - g_terminal)

Fade-to-Normal Method:

Assume ROE gradually converges to cost of equity

5. Sum to Fair Value¶

Fair Value = BV_0 + Σ(RI_t / (1 + r_e)^t) + (Terminal_RI / (1 + r_e)^n)

When RIM Works Best¶

Ideal Candidates¶

Financial Institutions: - Banks - Insurance companies - Asset managers - REITs (with adjustments)

Characteristics: - Meaningful book value - Stable ROE - Transparent balance sheets - Regulated industries

Why It's Better Than DCF for Banks¶

Cash Flow Ambiguity: Bank "cash flows" are hard to define
Book Value Relevance: Regulatory capital is key metric
ROE Focus: Banks managed on ROE targets
Balance Sheet Business: Assets/liabilities are the product

Model Advantages¶

1. Less Terminal Value Dependence¶

Unlike DCF where terminal value is 60-80%, RIM starts with current book value (tangible anchor)

2. Accounting-Based¶

Uses reported financials directly, easier to verify

3. Mean Reversion¶

Natural assumption that excess returns fade over time (competitive forces)

4. Handles Negatives¶

Works even with negative earnings (as long as positive equity)

Implementation¶

Parameters¶

Cost of Equity (CAPM):

r_e = Risk_Free_Rate + Beta × Market_Risk_Premium

Typical Values: - Banks: 10-12% - Utilities: 8-10% - Industrial: 10-14%

ROE Assumptions: - Use historical average - Adjust for one-time items - Consider industry trends

Forecast Horizon: - Explicit forecasts: 5-10 years - Fade period: 5 years to terminal - Terminal ROE: Converge to cost of equity

Code Example¶

from invest.valuation.rim_model import RIMModel

# Initialize
rim = RIMModel()

# Calculate
result = rim.calculate_fair_value(stock_data)

if result['suitable']:
    print(f"Book Value: ${result['details']['book_value']:.2f}")
    print(f"Residual Income PV: ${result['details']['ri_pv']:.2f}")
    print(f"Fair Value: ${result['fair_value']:.2f}")

Key Assumptions¶

1. Clean Surplus Relation¶

BV_t = BV_{t-1} + Earnings_t - Dividends_t

Must hold for RIM to be theoretically sound. Violated by: - Stock buybacks (adjust for repurchases) - Currency translation adjustments - Pension accounting

2. ROE Mean Reversion¶

Empirical Evidence: - High ROE (>20%) typically fades 50% in 5 years - Low ROE (<10%) typically improves but slowly - Industry median is attractor

Competitive Forces: - High returns attract competition - Low returns force restructuring or exit

3. Book Value Quality¶

Red Flags: - Large goodwill (>30% of equity) - Frequent write-downs - Off-balance sheet vehicles - Mark-to-model assets

Sector Applications¶

Banks¶

Perfect fit: - Book value = regulatory capital - ROE = primary management metric - Stable business model

Adjustments: - Normalize for credit cycles - Adjust for loan loss reserves - Consider Basel III impacts

Insurance¶

Good fit: - Assets = liabilities + equity - Underwriting profit + investment returns

Adjustments: - Normalize catastrophe losses - Adjust reserves for conservatism - Consider float value

Asset-Heavy Industrials¶

Moderate fit: - Book value less relevant - ROIC often better than ROE

Use with caution: - Depreciation policy affects book value - Asset impairments common - Intangibles growing

Limitations¶

1. Growth Companies¶

Book value is tiny relative to intangible value (brand, patents, network effects)

2. Accounting Dependence¶

Vulnerable to accounting manipulation: - Aggressive revenue recognition - Understated reserves - Goodwill avoidance

3. Assumes Clean Surplus¶

Share buybacks, special dividends, FX adjustments violate assumption

4. Terminal Value Still Matters¶

If ROE >> r_e persists, terminal value dominates (same DCF problem)

Comparison to DCF¶

Aspect	RIM	DCF
Starting Point	Book Value	Cash Flows
Best For	Banks, asset-heavy	Operating companies
Terminal Value	Smaller component	Larger component
Accounting	Direct use	Adjustments needed
Growth Bias	Less sensitive	Very sensitive
Intangibles	Undervalues	Better capture

Academic Foundation¶

Core Theory¶

Edwards & Bell (1961): The Theory and Measurement of Business Income
Early residual income concepts
Ohlson (1995): "Earnings, Book Values, and Dividends in Equity Valuation"
Modern RIM framework
Proof of equivalence to dividend discount model
Feltham & Ohlson (1995): "Valuation and Clean Surplus Accounting"
Clean surplus relation formalization

Empirical Validation¶

Frankel & Lee (1998): RIM explains 70% of stock price variation
Dechow, Hutton & Sloan (1999): RIM outperforms DCF for banks
Penman & Sougiannis (1998): Combining earnings and book value improves forecasts

Advanced Extensions¶

1. ROE Decomposition (DuPont)¶

ROE = Net Margin × Asset Turnover × Equity Multiplier

Forecast each component separately for detailed analysis

2. Economic Value Added (EVA)¶

Related concept: Value = Capital + PV(EVA)

EVA = NOPAT - (Capital × WACC)

3. ROIC-Based Variant¶

Use ROIC instead of ROE for capital structure neutrality

When to Use¶

Primary Valuation Method¶

Banks and financial institutions
Mature, stable companies with clean accounting
Asset-heavy businesses with transparent books

Secondary Check¶

Validate DCF for companies with significant book value
Assess quality of returns (ROE vs cost of equity)

Avoid¶

Tech/software companies (minimal book value)
Companies with aggressive accounting
High-growth unprofitable companies

References¶

Dechow, P., Hutton, A., & Sloan, R. (1999). "An Empirical Assessment of the Residual Income Valuation Model". Journal of Accounting and Economics.
Edwards, E., & Bell, P. (1961). The Theory and Measurement of Business Income. University of California Press.
Feltham, G., & Ohlson, J. (1995). "Valuation and Clean Surplus Accounting for Operating and Financial Activities". Contemporary Accounting Research.
Frankel, R., & Lee, C. (1998). "Accounting Valuation, Market Expectation, and Cross-Sectional Stock Returns". Journal of Accounting and Economics.
Ohlson, J. (1995). "Earnings, Book Values, and Dividends in Equity Valuation". Contemporary Accounting Research.
Penman, S., & Sougiannis, T. (1998). "A Comparison of Dividend, Cash Flow, and Earnings Approaches to Equity Valuation". Contemporary Accounting Research.