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