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Define all three inputs
P is the selected cumulative paid-in capital, D the corresponding distributions, and V the residual value at the reporting date. Inputs share one population, date, currency and reporting basis. These definitions are part of the formula, not optional labels.
Separate the two value components
DPI measures the entered distributed component per unit of paid-in. RVPI measures the remaining valued component. Their sum equals TVPI because they use exactly the same positive denominator.
The identity depends on compatible inputs and a common P.
Check the original numbers
For P = 100, D = 40 and V = 110, DPI is 0.4×, RVPI 1.1× and TVPI 1.5×. Value above paid-in is 50. It is not an annual percentage, and 110 of the entered total remains residual rather than distributed.
Handle missing and zero data separately
Zero distributions or a known zero residual can be valid inputs. A zero paid-in denominator leaves these ratios undefined. A missing residual is not a known zero; it prevents a complete TVPI statement under this input set.