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Reconcile three private-capital multiples

Paid-in 100, distributions 40 and residual value 110 give 0.4× DPI, 1.1× RVPI and 1.5× TVPI.

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Check the common basis

The original fictional amounts describe one investor population and one reporting date in one currency. The case has no recallable or recycling adjustment, and all inputs are supplied on the same selected cost basis.

Calculate each component

Distributions divided by paid-in are 40/100 = 0.4×. Residual divided by paid-in is 110/100 = 1.1×. Total entered value is 40+110 = 150, giving TVPI 150/100 = 1.5×.

Original multiple bridge
MetricNumeratorDenominatorResult
DPI401000.4×
RVPI1101001.1×
TVPI1501001.5×

Check the identity and units

0.4+1.1 = 1.5 because all three ratios share paid-in 100. The ratios are multiples without a time unit. The 50 value above paid-in includes residual appreciation under the inputs; it is not 50 of cash profit already paid.

State what remains unknown

No transfer dates are supplied, so an annualized investor return is not calculated. Future realized proceeds can differ from the residual valuation. A useful report keeps those limits next to the multiple rather than turning 1.5× into an unspecified annual rate.

Further references