Residual Income Valuation and Applications

### Which statement best describes the concept of residual income? - [ ] It is a measure of total assets minus total liabilities. - [x] It is net income minus an equity charge representing the cost of equity. - [ ] It is the difference between operating income and inventory costs. - [ ] It represents the realized capital gains minus transaction costs. > **Explanation:** Residual income specifically accounts for the cost of equity by subtracting the equity charge from net income, ensuring that the returns on equity exceed the required rate of return. ### When is the Residual Income Model most useful compared to the Dividend Discount Model? - [ ] When a firm has perfectly stable dividend growth. - [ ] When a firm’s dividend policy grows at the same rate as earnings. - [x] When a firm’s dividends are irregular or minimal, but its accounting earnings are more predictable. - [ ] When a firm pays out all its earnings as dividends every year. > **Explanation:** The RI model becomes especially beneficial when dividends are either nonexistent or unpredictable, but you can still forecast net income and book value reliably. ### In a single-stage residual income model with constant growth, the total equity value is generally equal to: - [ ] Book value of equity minus present value of future residual incomes. - [ ] Free cash flow plus residual income. - [x] Current book value of equity plus the present value of future residual incomes. - [ ] Current book value of equity times the retention rate. > **Explanation:** The RIM formula typically combines the existing book value of equity with the discounted residual income stream. ### Which of the following best represents the equity charge in a residual income model? - [ ] Required return on equity times dividends paid. - [x] Required return on equity times the book value of equity. - [ ] Required return on equity times the market capitalization. - [ ] Required return on equity times cash flow from operations. > **Explanation:** The equity charge reflects the cost of using shareholder capital and is computed by multiplying the book value of equity by the required rate of return on equity. ### Which factor is most likely to cause a difference in reported net income and book value between US GAAP and IFRS for the same firm? - [ ] Different rules for classifying current vs. long-term debt. - [ ] Varied timing for recognizing cash inflows. - [x] Capitalization of certain development costs under IFRS versus expensing under US GAAP. - [ ] Restrictions on declaring dividends in certain jurisdictions. > **Explanation:** IFRS allows specific development costs to be capitalized, whereas US GAAP typically requires expensing. This difference can significantly alter both net income and the book value of equity. ### A company’s single-stage residual income valuation suggests a justified P/B ratio of 2.0. If the firm’s actual market P/B ratio is 1.2, which conclusion is best supported by the model? - [x] The company is undervalued according to the RI model. - [ ] The company is overvalued according to the RI model. - [ ] The company’s net income is too high for the residual income approach. - [ ] The company’s cost of equity is lower than the market average. > **Explanation:** A justified P/B that is higher than the market-based P/B implies that the firm might be undervalued from the perspective of the RIM. ### Why might the multi-stage residual income model be critical for valuing a high-growth tech startup? - [ ] Because the cost of equity is typically negative for startups. - [x] Because the growth of residual income is unlikely to be constant over the firm’s life cycle. - [ ] Because net income is always zero in the early years, making the single-stage model irrelevant. - [ ] Because the cost of equity automatically adjusts to zero at the stable growth phase. > **Explanation:** High-growth startups often experience multiple phases—initial high growth, a transition period, and then a more stable phase. A multi-stage model captures these changes more accurately. ### Which of the following steps is least likely to be part of a multi-stage residual income valuation? - [ ] Forecasting phased growth rates for different periods. - [ ] Calculating residual income in each phase and discounting to present value. - [ ] Estimating a terminal value at the beginning of stable growth. - [x] Treating the growth rate and the cost of equity as identical across all valuation periods. > **Explanation:** A hallmark of the multi-stage method is that growth rates and possibly cost of equity or margins can vary across different phases. Treating them identically defeats the purpose. ### The fundamental formula for the Residual Income Model can be expressed as: - [ ] V₀ = D₀ + (FCF / (r - g)). - [x] V₀ = B₀ + Σ(RIₜ / (1 + rₑ)ᵗ). - [ ] V₀ = E₀ × (1 + g) / (r - g). - [ ] V₀ = (ROE - rₑ) × B₀ / (1 + g). > **Explanation:** The standard RIM formula states that the firm’s current value is equal to the current book value of equity plus the present value of all future residual income streams. ### For a given period, if a company’s net income is exactly equal to its equity charge, the residual income for that period is: - [x] Zero - [ ] Positive - [ ] Negative - [ ] Indeterminate > **Explanation:** Residual income = Net income − Equity charge. If they match, the firm is effectively breaking even on the cost of equity, leading to zero residual income.