Answer-first summary for fast verification
Answer: 12.0%.
**Explanation:** The time-weighted rate of return (TWRR) measures the compound growth rate of $1 initially invested over the measurement period. It is calculated by taking the geometric mean of the holding period returns (HPRs). 1. **HPR for Year 0 to Year 1:** - Initial investment: $100 - End value: $110 (price of the second share) + $10 (dividend) = $120 - HPR₁ = ($120 - $100) / $100 = 20% 2. **HPR for Year 1 to Year 2:** - Initial investment: $220 (value of two shares at $110 each) - End value: $230 (proceeds from selling two shares) - HPR₂ = ($230 - $220) / $220 ≈ 4.545% 3. **Annualized TWRR:** - TWRR = [(1 + HPR₁) × (1 + HPR₂)]^(1/2) - 1 - TWRR = [(1 + 0.20) × (1 + 0.04545)]^(1/2) - 1 ≈ 12.0% Option A (9.7%) is incorrect because it represents the money-weighted rate of return (MWRR), which is similar to the internal rate of return (IRR). Option C (12.3%) is incorrect as it calculates the arithmetic average of the HPRs, not the geometric mean required for TWRR.
Author: LeetQuiz Editorial Team
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An investor summarizes end-of-year cash outlays and proceeds from a two-year investment in a company's shares as follows:
Year | Outlays | Proceeds
0 | $100 to purchase the first share | ---
1 | $110 to purchase the second share | $10 dividend received from first share (not reinvested)
2 | --- | $230 received from selling two shares at $115 per share
The annualized time-weighted rate of return of the investment over the two-year period is closest to:
A
9.7%.
B
12.0%.
C
12.3%.