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Zorluk: Çok zorRatio, Proportion, and Percent Calculations

The table below details capital allocation, exit valuations, active portfolio companies, and successful exits across five high-technology sectors for a venture capital firm in 2026.

SectorCapital Invested ($M)Realized Exit Valuation ($M)Active Portfolio CompaniesSuccessful Exits
AI Infrastructure4501,350186
Clean Energy320560164
Enterprise SaaS6001,5002510
Advanced Robotics250375103
BioHealth & Genomics400880125

Evaluate the following statement based on the data provided:

The overall return multiple (total realized exit valuation divided by total capital invested across all five sectors combined) is less than the percentage return on investment (net gain divided by capital invested) achieved by the BioHealth & Genomics sector.

Cevap: Cevap

Cevap

False. The overall return multiple across all five sectors (2.3094×2.3094\times, representing 230.94%230.94\%) is greater than the percentage ROI for BioHealth & Genomics (120%120\%).
The evaluated statement is False. Calculating the total sum of capital invested across all sectors yields $2,020M\$2,020\text{M}, and the total sum of realized exit valuations yields $4,665M\$4,665\text{M}. The overall return ratio is 46652020≈2.3094\frac{4665}{2020} \approx 2.3094 (or 230.94%230.94\%). In contrast, the percentage ROI for BioHealth & Genomics is calculated on its net gain: 880−400400=1.20\frac{880 - 400}{400} = 1.20 (or 120%120\%). Comparing the two values reveals that 2.3094>1.20002.3094 > 1.2000, contradicting the statement's claim that the overall multiple is less.

Adım Adım Çözüm

1
Calculate the total capital invested across all five sectors.
Total Capital Invested = 450+320+600+250+400=$2,020 million450 + 320 + 600 + 250 + 400 = \$2,020\text{ million}.
Aggregating the column provides the denominator for the combined return multiple.
2
Calculate the total realized exit valuation across all five sectors.
Total Exit Valuation = 1,350+560+1,500+375+880=$4,665 million1,350 + 560 + 1,500 + 375 + 880 = \$4,665\text{ million}.
Aggregating the column provides the numerator for the combined return multiple.
3
Compute the overall return multiple across all sectors.
Overall Multiple = $4,665M$2,020M≈2.3094\frac{\$4,665\text{M}}{\$2,020\text{M}} \approx 2.3094 (or 230.94%230.94\% of capital invested).
Determines the benchmark value stated in the prompt.
4
Calculate the percentage ROI for the BioHealth & Genomics sector.
BioHealth Net Gain = $880M−$400M=$480M\$880\text{M} - \$400\text{M} = \$480\text{M}. BioHealth ROI = $480M$400M×100%=120%\frac{\$480\text{M}}{\$400\text{M}} \times 100\% = 120\%.
Percentage ROI measures net profit relative to initial capital invested.
5
Compare the overall return multiple to the BioHealth percentage ROI.
2.3094>1.20002.3094 > 1.2000 (or 230.94%>120%230.94\% > 120\%). The statement claims the overall multiple is less than the BioHealth ROI, which is incorrect.
Direct comparison evaluates the truth value of the target statement.

Anahtar Kavram

Distinguishing Total Return Multiples from Net Percentage ROI and Aggregating Tabular Data
Tahmini Süre:2m 30s
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Ratio, Proportion, and Percent Calculations

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