Answer: 51.4%.

**Time-Weighted Rate of Return Calculation:** **Step 1: Calculate Holding Period Returns for Each Period** **Year 1 (t=0 to t=1):** - Initial investment: $50.00 - Dividend received: $5.00 - Ending value: $75.00 (price at which additional share is purchased) - HPR1 = (Ending Value + Dividend - Beginning Value) / Beginning Value - HPR1 = ($75.00 + $5.00 - $50.00) / $50.00 = $30.00 / $50.00 = 0.60 or 60% **Year 2 (t=1 to t=2):** - Beginning value: $75.00 × 2 shares = $150.00 (2 shares at $75 each) - Dividends received: $7.50 × 2 shares = $15.00 - Ending value: $100.00 × 2 shares = $200.00 - HPR2 = (Ending Value + Dividends - Beginning Value) / Beginning Value - HPR2 = ($200.00 + $15.00 - $150.00) / $150.00 = $65.00 / $150.00 = 0.4333 or 43.33% **Step 2: Calculate Time-Weighted Return** - Time-weighted return = [(1 + HPR1) × (1 + HPR2)]^(1/2) - 1 - TWR = [(1 + 0.60) × (1 + 0.4333)]^(1/2) - 1 - TWR = [(1.60) × (1.4333)]^(1/2) - 1 - TWR = [2.2933]^(1/2) - 1 - TWR = 1.5143 - 1 = 0.5143 or 51.43% **Step 3: Compare with Options** - 51.43% rounds to 51.4%, which matches option C **Why not the other options?** - **Option A (23.2%):** This is too low and might be a simple average of the two returns - **Option B (51.7%):** This is close but slightly higher than the correct calculation **Key Points:** 1. Time-weighted return eliminates the effect of cash flows (additional investments/withdrawals) 2. It's calculated by geometrically linking the holding period returns 3. The required return of 35.0% is irrelevant for calculating the actual time-weighted return 4. Dividends must be included in the holding period return calculations

Author: LeetQuiz Editorial Team