Capital Turnover Explorer

How recycling rates translate into dollars deployed — the number of times a unit of capital is put to work, T(R) = 1/(1 − R), truncated at N cycles. ⚠️ This is not the System Value Multiplier, which counts value created rather than dollars deployed: SVM = γ·T_N(R). At R = 0.98 the two are 50× and 38.6× (γ = 1.7, N = 30), and the gap widens as R approaches 1.

Parameters

Recycling Rate (R): 80%

30%98%

Time Horizon: 30 years

Show theoretical limit

Turnover T(R), infinite horizon

5.00×

T(R) = 1 / (1 − 80%) — dollars deployed, not value generated

Deployed over 30 cycles

4.99×

99.9% of theoretical captured

Impact Example

A $100K gift with R=80% deploys $499K over 30 years.

The Math

SVM = 1 + R + R² + R³ + ... = 1/(1-R)

Each cycle, R% of capital returns. The sum of this geometric series gives total impact.

At R=80%, you need 21 cycles to capture 99% of theoretical SVM.

SVM Accumulation Over Time (Multiple R Factors)

SVM vs Recycling Rate

Non-Linear Growth

SVM grows exponentially as R approaches 100%. Moving from 80% to 90% R doubles the multiplier (5× to 10×).

Practical vs Theoretical

Most impact (90%+) is captured within 20-30 years for typical R factors. The theoretical limit is approached asymptotically.

R Factor	T(R), infinite	10 cycles	30 cycles	Years to 90%
50%	2.00×	2.00×	2.00×	4
60%	2.50×	2.48×	2.50×	5
70%	3.33×	3.24×	3.33×	7
80%	5.00×	4.46×	4.99×	11
90%	10.0×	6.51×	9.58×	22
95%	20.0×	8.03×	15.7×	45