CFA Exam Question of the Day

Rationale:
The implied market value per share for Alpha Corp post-split-off is calculated as follows: 1. **Calculate Beta Solutions' Equity Value (MV_equity_Beta):** * Beta's EV = LTM EBITDA × Multiple = $500 million × 8.0 = $4,000 million. * Beta's Equity Value = EV – Debt = $4,000 million – $1,500 million = $2,500 million. 2. **Calculate the value of Beta Solutions' equity distributed:** * Distributed Equity = 80% × $2,500 million = $2,000 million. 3. **Determine the market value of Alpha Corp shares tendered:** * The exchange offer provides a 10% premium to Alpha shareholders. This means for every $1.00 of Alpha shares tendered, shareholders receive $1.10 worth of Beta shares. Therefore, the market value of Alpha shares tendered (X) is such that X × 1.10 = $2,000 million. * Value of Alpha shares tendered (X) = $2,000 million / 1.10 = $1,818.18 million. 4. **Calculate the number of Alpha Corp shares retired:** * Shares retired = Value of Alpha shares tendered / Alpha's current share price = $1,818.18 million / $100 = 18.1818 million shares. 5. **Calculate Alpha Corp's new total market capitalization:** * Alpha's original market cap = $100/share × 100 million shares = $10,000 million. * The market value of the remaining Alpha Corp is its original market cap minus the value of the distributed portion of Beta Solutions' equity. Alpha effectively divests $2,000 million of value. * New Alpha Market Cap = Original Alpha Market Cap – Value of Beta equity distributed = $10,000 million – $2,000 million = $8,000 million. 6. **Calculate Alpha Corp's new shares outstanding:** * New Shares Outstanding = Original Shares – Shares Retired = 100 million – 18.1818 million = 81.8182 million shares. 7. **Calculate Alpha Corp's new share price:** * New Share Price = New Market Cap / New Shares Outstanding = $8,000 million / 81.8182 million shares = $97.7777, which rounds to $97.78. Regarding the incorrect options: * The option reflecting $100.00 likely results from either incorrectly assuming the value of Alpha shares tendered is equal to the value of Beta shares distributed (i.e., ignoring the premium in the shares retired calculation, leading to 20M shares retired and $8,000M / 80M = $100), or by incorrectly adjusting the market cap. * The option reflecting $91.67 likely results from incorrectly subtracting the *entire* Beta Solutions' equity value ($2,500 million) from Alpha's market cap instead of just the distributed portion ($2,000 million), leading to a new market cap of $10,000M - $2,500M = $7,500M. When divided by the correct new shares outstanding of 81.8182M, this yields $7,500M / 81.8182M = $91.67. * The option reflecting $102.56 likely results from an inversion of the premium calculation when determining shares retired. If the value of Alpha shares tendered was incorrectly calculated as $2,000 million * 1.10 = $2,200 million, this would lead to 22 million shares retired. Then, $8,000 million / (100 million - 22 million) = $8,000 million / 78 million = $102.56.

Rationale:
The intrinsic value per share using the Residual Income Model is calculated as: V0 = B0 + Sum[RI_t / (1+r)^t] + PV(TV_RI_T). First, calculate the book value per share (B_t) and residual income (RI_t) for the explicit forecast period: B0 = $50.00, r = 0.11 Year 1: RI1 = E1 - (r * B0) = $6.00 - (0.11 * $50.00) = $6.00 - $5.50 = $0.50 B1 = B0 + E1 - D1 = $50.00 + $6.00 - $2.50 = $53.50 Year 2: RI2 = E2 - (r * B1) = $6.80 - (0.11 * $53.50) = $6.80 - $5.885 = $0.915 B2 = B1 + E2 - D2 = $53.50 + $6.80 - $3.00 = $57.30 Year 3: RI3 = E3 - (r * B2) = $7.50 - (0.11 * $57.30) = $7.50 - $6.303 = $1.197 B3 = B2 + E3 - D3 = $57.30 + $7.50 - $3.50 = $61.30 Next, determine the terminal value of residual income (TV_RI3). The statement 'earnings to grow at a constant rate of 2.0% indefinitely, with the payout ratio remaining constant' implies a sustainable growth rate (g) of 2.0%. The payout ratio in Year 3 is D3/E3 = $3.50/$7.50 = 0.4667. This means the implied return on equity (ROE) in the stable growth phase would be g / (1 - payout ratio) = 0.02 / (1 - 0.4667) = 0.02 / 0.5333 = 0.0375 or 3.75%. Since this implied long-term ROE (3.75%) is significantly below the required rate of return (11.0%), it is not economically plausible for the company to generate positive residual income growing at 2.0% indefinitely. In such a scenario, the most reasonable assumption is that residual income will eventually fade to zero. Therefore, TV_RI3 = 0. Now, calculate the present value of the explicit residual incomes: PV(RI1) = $0.50 / (1.11)^1 = $0.450450 PV(RI2) = $0.915 / (1.11)^2 = $0.741064 PV(RI3) = $1.197 / (1.11)^3 = $0.871147 Finally, sum the components to find the intrinsic value: V0 = B0 + PV(RI1) + PV(RI2) + PV(RI3) + PV(TV_RI3) V0 = $50.00 + $0.450450 + $0.741064 + $0.871147 + $0 = $52.062661 Rounded to two decimal places, the intrinsic value is $52.06. The option $61.93 results from incorrectly assuming residual income grows at 2.0% indefinitely (i.e., TV_RI3 = RI4 / (r - g), where RI4 = RI3 * (1+g)). This common error overlooks the implication of the low long-term ROE relative to the cost of equity. The option $61.74 results from using RI3 instead of RI4 in the numerator for the terminal value calculation (i.e., TV_RI3 = RI3 / (r - g)), while still incorrectly assuming positive growing residual income. The option $56.95 results from a fundamental error in calculating residual income (using B_t instead of B_{t-1} for RI_t = E_t - r * B_{t-1}), combined with the incorrect assumption of residual income growing at 2.0% indefinitely.

Rationale:
The most consistent action with the CFA Institute Code of Ethics and Standards of Professional Conduct, particularly Standard V(A) - Diligence and Reasonable Basis and Standard I(C) - Misrepresentation, is to ensure that all performance claims are based on a diligent and reasonable foundation. Any known data integrity issue, especially concerning a critical data stream during a volatile period, must be rectified and re-validated before the model is deployed. The original reported alpha of 120 bps over 156 weeks (18,720 bps-weeks total) includes an exceptional 250 bps alpha generated during the 12-week corrupted period (3,000 bps-weeks). This means the potentially compromised period contributes 3,000 / 18,720 = 16.03% of the total reported alpha. This is a material portion, making the overall reported alpha potentially misleading if not based on sound data. Delaying deployment to fix and re-validate the data ensures the integrity of the model's performance claims and protects clients. Adding a prominent disclaimer, while showing some transparency, does not absolve the firm of its responsibility to perform diligent research and avoid misrepresentation. A disclaimer cannot substitute for reliable data underpinning performance claims, especially when the issue could be material. Adjusting the reported overall alpha downwards by an arbitrary percentage of the corrupted period's contribution is an attempt to quantify a fix but does not address the root cause of the data integrity problem. This approach lacks diligence, as it's an estimation rather than a remediation and re-validation, and could still misrepresent the model's true capabilities. Deploying the model as is, by claiming the impact is statistically insignificant, violates Standard V(A) - Diligence and Reasonable Basis and Standard I(C) - Misrepresentation. Such an assumption, without proper validation and remediation of the corrupted data, prioritizes potential short-term business gain over ethical conduct and due diligence, especially given the 'critical' nature of the data stream and the 'volatile' period.

Rationale:
The additional sensitivity to Market Beta for a highly leveraged firm compared to a firm with low leverage is represented by the coefficient of the interaction term (`b5`). For a firm with low leverage (High_Leverage = 0), the sensitivity to Market Beta is `b1`. For a highly leveraged firm (High_Leverage = 1), the sensitivity to Market Beta is `b1 + b5`. Therefore, the *additional* sensitivity for a highly leveraged firm is `(b1 + b5) - b1 = b5`. Given `b5 = 0.40`, this implies an additional 0.40 percentage points, or 40 basis points, of expected return for every one-unit increase in Market Beta. To assess statistical significance at a 5% level, we compare the absolute value of the t-statistic to the critical value (approximately 2.0 for a two-tailed test). The t-statistic for `b5` is 3.1, which is greater than 2.0, indicating that the additional sensitivity is statistically significant. The option stating 80 basis points represents the sensitivity to Market Beta for a firm with low leverage (`b1`), not the additional sensitivity for a highly leveraged firm. While `b1` is statistically significant, it does not answer the specific question about the incremental effect. The option stating 120 basis points represents the *total* sensitivity to Market Beta for a highly leveraged firm (`b1 + b5 = 0.80 + 0.40 = 1.20`), not the additional sensitivity compared to a low leverage firm. The option stating 40 basis points but asserting it is not statistically significant correctly identifies the value of the additional sensitivity but incorrectly assesses its statistical significance. With a t-statistic of 3.1, which exceeds the critical value of approximately 2.0 at the 5% significance level, the additional sensitivity is indeed statistically significant.

Rationale:
The implied annualized convenience yield (c) can be derived from the approximate relationship between the futures price (F), spot price (S), annualized risk-free rate (r), and time to expiration (T) in years, assuming negligible storage costs: F = S * (1 + (r - c) * T). This can be rearranged to solve for c. 1. **Calculate the annualized implied rate from futures to spot:** The annualized rate implied by the one-month futures premium is `((F / S) - 1) / T`. `((75.75 / 75.00) - 1) / (1/12) = (1.01 - 1) / (1/12) = 0.01 * 12 = 0.12` or 12.00%. 2. **Identify the annualized risk-free rate:** The annualized risk-free rate (r) is 50 basis points, which is `0.0050` or 0.50%. 3. **Calculate the implied annualized convenience yield (c):** From the relationship `(r - c) = ((F / S) - 1) / T`, we can solve for `c`: `c = r - ((F / S) - 1) / T` `c = 0.0050 - 0.12 = -0.1150` or -11.50%. A negative convenience yield implies that the benefits of holding the physical commodity (e.g., ability to meet unexpected demand) are less than the costs of holding it (e.g., interest forgone on capital) relative to the benefit of holding a futures contract. This scenario, where the actual futures price is significantly higher than the spot price adjusted for the risk-free rate (F > S * (1 + r*T)), indicates a market in **contango**. In contango, futures prices are higher than current spot prices, and for a long futures position, rolling over contracts typically results in a negative roll yield. The option suggesting a positive 11.50% convenience yield and backwardation incorrectly applies the sign convention for convenience yield or misinterprets the relationship. A positive convenience yield would typically indicate backwardation, but the calculation here yields a negative value. The option suggesting a -6.00% convenience yield indicates a calculation error, likely from incorrectly annualizing or combining the risk-free rate and the futures premium (e.g., `((F/S - 1) - r) * 12 = (0.01 - 0.005) * 12 = 0.06`). The option suggesting a 0.50% convenience yield and backwardation incorrectly assumes the convenience yield is simply the risk-free rate and misinterprets the market state, failing to account for the significant premium of the futures price over the spot price.