Equity Optimization Calculator

Two questions, one page. The Time to target tab answers how long your equity takes to grow from its current value to a target at a steady annual growth rate, with projected values at 5, 10, 15, and 20 years. The ROE gap tab measures the distance between your actual performance and your target return on equity: the optimization gap in dollars.

Quick Answer

Worked examples, checked against this exact tool

Time to target: $100,000 growing to $500,000 at 15% a year takes 11.52 years: ln(500,000 ÷ 100,000) ÷ ln(1.15) = 1.6094 ÷ 0.1398. Projections: $201,136 after 5 years, $404,556 after 10, $1,636,654 after 20. ROE gap: $2,000,000 of equity with an 18% target ROE needs $360,000 of income; actual net income of $250,000 leaves a $110,000 shortfall (actual ROE 12.5%).

The time-to-target formula

Compound growth says target = current × (1 + g)^t. Solving for t: t = ln(target ÷ current) ÷ ln(1 + g). The logarithm base does not matter as long as it is the same top and bottom: natural log and base-10 both give 11.52 years in the example. (An earlier version of this page mixed ln on top with base-10 on the bottom and printed 26.38 years: the tool always computed 11.52, and the text is now corrected.) A quick sanity check: the rule of 72 says money doubles every ~4.8 years at 15%, and $100k needs about 2.3 doublings to reach $500k: 2.3 × 4.8 ≈ 11 years.

The ROE optimization gap

Gap = (Target ROE × Total equity) − Actual net income. A positive gap is the income shortfall to close: the business is under-earning its equity base. A negative gap means performance already exceeds the target. The gap turns a vague “improve ROE” goal into a dollar number: $110,000 more income, or the equivalent equity reduction, to hit 18%[2]. To decompose ROE into margin, turnover, and leverage, see the DuPont breakdown[7].

What equity means here

Equity is ownership value with growth potential: company shares, a business’s book equity, an investment portfolio, or property equity. The time-to-target tab fits anything with a projected steady growth rate; the ROE tab fits businesses measured on return on equity. The equity growth calculator projects the growth path alone, and the advisor equity calculator values equity stakes. For home-equity borrowing questions, see our equity home calculator, which handles loan-to-value limits instead.

What competing calculators miss

Rival pages each own one interpretation: time-to-target here, ROE gap at bravecalculator, portfolio allocation at calculatorultra, home equity at savvycalculator. None combine them. This page runs the two business interpretations side by side, adds the projection snapshots and target year the formula-only pages skip, and carries the corrected worked example.

Frequently asked questions