CFA Exam Question of the Day

Rationale:
To determine the firm's new WACC, it is necessary to first calculate the unlevered beta using the current capital structure, then relever this beta for the target capital structure, and finally use the new cost of equity in the WACC formula. The current WACC and standard deviation of equity returns are irrelevant for this calculation. First, calculate the unlevered beta (βU) using the current levered beta (βL), current debt-to-equity ratio (D/E), and tax rate (t): βU = βL / [1 + (D/E) * (1 - t)] βU = 1.25 / [1 + 0.60 * (1 - 0.25)] βU = 1.25 / [1 + 0.60 * 0.75] βU = 1.25 / [1 + 0.45] βU = 1.25 / 1.45 ≈ 0.862069 Next, calculate the new levered beta (βL_new) using the unlevered beta and the target debt-to-equity ratio: βL_new = βU * [1 + (Target D/E) * (1 - t)] βL_new = 0.862069 * [1 + 0.80 * (1 - 0.25)] βL_new = 0.862069 * [1 + 0.80 * 0.75] βL_new = 0.862069 * [1 + 0.60] βL_new = 0.862069 * 1.60 ≈ 1.379310 Then, calculate the new cost of equity (Ke_new) using the Capital Asset Pricing Model (CAPM): Ke_new = Risk-free rate + βL_new * Market Risk Premium Ke_new = 0.03 + 1.379310 * 0.06 Ke_new = 0.03 + 0.0827586 Ke_new ≈ 0.112759 or 11.28% Finally, calculate the new WACC using the target capital structure weights. With a target D/E of 0.80, the weight of debt (wd) = D/(D+E) = 0.80/(0.80+1) = 0.80/1.80 ≈ 0.4444, and the weight of equity (we) = E/(D+E) = 1/(0.80+1) = 1/1.80 ≈ 0.5556. WACC = (wd * Pre-tax cost of debt * (1 - t)) + (we * Ke_new) WACC = (0.4444 * 0.07 * (1 - 0.25)) + (0.5556 * 0.112759) WACC = (0.4444 * 0.07 * 0.75) + (0.5556 * 0.112759) WACC = (0.4444 * 0.0525) + 0.062648 WACC = 0.023331 + 0.062648 WACC ≈ 0.085979 or 8.60% The option of 8.17% results from using the original levered beta (1.25) to calculate the cost of equity (10.50%) instead of adjusting it for the new capital structure, which incorrectly assumes the cost of equity does not change with increased leverage. The option of 9.38% results from omitting the tax shield benefit on the cost of debt (i.e., using Kd instead of Kd * (1-t)) in the WACC calculation, which is a fundamental error in WACC computation. The option of 13.67% results from an incorrect application of the unlevering beta formula (multiplying instead of dividing by the leverage factor), which significantly overstates the unlevered beta and subsequently the new cost of equity and WACC.

Rationale:
The CFA Institute Standards require members to deal fairly and objectively with all clients (Standard III(B) Fair Dealing) and to place client interests before their own (Standard VI(B) Priority of Transactions). The correct action involves executing trades for all eligible discretionary client accounts simultaneously (or as a block trade) and allocating shares according to a pre-determined, objective procedure to ensure fair treatment. Following this, non-discretionary clients should be informed of the recommendation. Only after all client orders have been completed can the portfolio manager consider placing a personal order. This sequence upholds the principle of client priority and fair dealing without disadvantaging any client type. Prioritizing the largest or most strategically important clients violates Standard III(B) Fair Dealing by giving preferential treatment. Placing a personal order before all client orders are complete, even if for a small amount, violates Standard VI(B) Priority of Transactions. Notifying all non-discretionary clients and awaiting their instructions before placing any orders, including for discretionary accounts, might seem fair but violates the duty of loyalty and prudence (Standard III(A) Loyalty, Prudence, and Care) owed to discretionary clients, especially in a time-sensitive scenario. Delaying action for discretionary clients could be detrimental to their interests if the opportunity is missed or diluted due to the delay. Fair dealing means dealing fairly, not necessarily identically, especially when different account types have different mandates and capabilities to act.

Rationale:
The accumulated value is found by first determining the effective annual rate (EAR) and then carefully calculating the future value of the deferred annuity. First, the stated annual interest rate of 4.00% compounded semi-annually must be converted to an effective annual rate (EAR) to match the annual contributions. EAR = (1 + Stated Annual Rate / m)^m - 1 EAR = (1 + 0.04 / 2)^2 - 1 = (1.02)^2 - 1 = 1.0404 - 1 = 0.0404 or 4.04%. Next, determine the future value of the deferred annuity. The first contribution occurs exactly three years from today (at time t=3), and there are 15 annual contributions. This means the contributions occur at t=3, t=4, ..., up to t=3 + 15 - 1 = t=17. The question asks for the accumulated value immediately after the final contribution, which is at t=17. One precise method for calculating the future value of such a deferred ordinary annuity is to: 1. Calculate the present value (PV) of the 15-year ordinary annuity at the point in time immediately preceding the first payment. Since the first payment is at t=3, this PV is effectively at t=2. PV at t=2 = PMT * [ (1 - (1 + EAR)^-n) / EAR ] PV at t=2 = $250,000 * [ (1 - (1.0404)^-15) / 0.0404 ] PV at t=2 = $250,000 * 11.087354 = $2,771,838.56 2. Discount this PV from t=2 back to today (t=0) to find the present value of the entire stream of payments at the start of the project. PV at t=0 = PV at t=2 / (1 + EAR)^2 PV at t=0 = $2,771,838.56 / (1.0404)^2 = $2,771,838.56 / 1.082432 = $2,560,750.37 3. Compound this PV at t=0 forward to the desired future date of t=17 (the time of the final contribution). FV at t=17 = PV at t=0 * (1 + EAR)^17 FV at t=17 = $2,560,750.37 * (1.0404)^17 FV at t=17 = $2,560,750.37 * 1.960676 = $5,020,801.88. This result is confirmed by directly summing the future value of each of the 15 individual contributions, compounded from its own payment date to t=17, which yields the same total. The option reflecting the direct use of the stated annual rate (4.00%) in the future value calculation, rather than the effective annual rate (4.04%), is incorrect because it fails to convert the semi-annual compounding to an annual basis, thereby understating the actual growth of the investment: using the same method with r=4.00% yields approximately $5,005,896.91. The option reflecting a value equal to the simple sum of contributions ($250,000 * 15 = $3,750,000) is incorrect because it entirely disregards the impact of compounding interest over the long investment horizon, failing to apply time value of money principles correctly. The option reflecting a significantly higher value results from incorrectly compounding the initial present value (at t=0) for an excessive number of periods, specifically 20 years instead of the correct 17 years, thereby overstating the final accumulated value at approximately $5,654,238.39.

Rationale:
To determine the bond equivalent yield (BEY) for a U.S. Treasury Bill, it is necessary to convert the bank discount yield (BDY) by adjusting for two key factors: the yield basis and the day count convention. The BDY is based on the face value of the instrument and uses a 360-day year, whereas the BEY is based on the purchase price and uses a 365-day year. First, calculate the dollar discount from the face value: Discount = Face Value * BDY * (Days to Maturity / 360) Discount = $1,000,000 * 0.0275 * (180 / 360) = $1,000,000 * 0.0275 * 0.5 = $13,750. Next, calculate the purchase price of the T-bill: Purchase Price = Face Value - Discount = $1,000,000 - $13,750 = $986,250. Then, calculate the holding period yield (HPY), which is based on the purchase price rather than the face value: HPY = Discount / Purchase Price = $13,750 / $986,250 = 1.394170%. Finally, annualize the HPY using a 365-day year to arrive at the bond equivalent yield: BEY = HPY * (365 / Days to Maturity) = 1.394170% * (365 / 180) = 2.8271%. The 90-day T-bill yield and the standard deviation of excess returns for corporate debt are distractors and are not used in converting the bank discount yield to a bond equivalent yield. An answer of 2.7883% results from annualizing the holding period yield using a 360-day year instead of the 365-day year required for the bond equivalent yield basis: HPY * (360 / 180) = 1.394170% * 2 = 2.7883%. This fails to make the full conversion from the 360-day bank discount basis to the 365-day bond equivalent basis. An answer of 2.7931% reflects a computational error of similar magnitude in applying the day count or annualization adjustment, rather than a distinct, cleanly identifiable conceptual misapplication of the BEY formula. An answer of 2.7500% simply restates the quoted bank discount rate itself without any conversion at all, ignoring both the shift from a face-value basis to a purchase-price basis and the shift from a 360-day to a 365-day year, both of which are required to properly compare a T-bill's yield to instruments quoted on a bond equivalent basis.

Rationale:
The shift towards modular product architectures and standardized component interfaces fundamentally alters the competitive landscape. This development typically leads to products becoming more commoditized, which intensifies rivalry among existing firms and drives down prices. Furthermore, standardized interfaces reduce the costs and complexities for customers to switch between different suppliers, thereby increasing buyer bargaining power. Both intensified rivalry and increased buyer power exert downward pressure on prices and profit margins, leading to a sustained erosion of average industry profitability over the long term. The idea of enhanced operational efficiencies, while potentially true, overlooks the crucial impact of competitive forces. While modularity can reduce costs, if competition drives prices down even faster, overall industry profitability will decline, not increase. The claim of elevated barriers to entry is incorrect; modularity and standardization typically *lower* barriers to entry by allowing new entrants to assemble products from readily available components without needing to develop every part in-house, reducing the capital and R&D expenditure required. Finally, the notion of strengthened supplier bargaining power due to specialization is a common misinterpretation in this context. While some niche modular component suppliers might gain, the overall trend of standardization often leads to a more fragmented supply base and reduced switching costs for manufacturers, thereby *weakening* supplier power or at least not making it the dominant factor driving down overall industry profitability compared to the combined effects of buyer power and rivalry.