Each career path's annual earnings follow the Mincer earnings function, the standard human-capital model relating log-wages to schooling and work experience:
ln(w) = ln(w0) + b1·Exp + b2·Exp²
Exp = age − S − 6 (years since leaving school, S = years of schooling on THIS path)
where S is years of schooling and b1>0, b2<0 make earnings rise with experience but at a diminishing, then falling, rate — the familiar concave age-earnings profile. The return per year of schooling (the slider, r) is applied as a level multiplier exp(r·extraYears) on top of the experience curve, representing the wage premium the extra schooling itself buys.
Fix vs. the original 3D model: the source engine computed the extended path's experience using the baseline's 12 years of schooling for every setting of "extra years," which silently credited the extended-schooling worker with years of job experience they were still in the classroom for — inflating NPV by roughly 2–3× at typical settings (verified numerically). This 2D version uses the path's own actual schooling length, S = 12 + extraYears, when computing Exp, matching the formula this very panel documents.
The extended-schooling path spends its extra years in school (zero income, minus tuition) before starting work with the schooling bump. Its net present value against the baseline path is:
NPV = Σ_age [ Extended(age) − Baseline(age) ] / (1+d)^(age−18)
Break-even age is the first age where cumulative extended-path earnings (net of tuition and foregone wages) overtake cumulative baseline earnings — the real-world "payback period" on a degree. Approx. IRR is the discount rate at which NPV crosses zero, found by bisection on the same cash-flow stream. Real studies (Card, Mincer, Psacharopoulos) find r typically in the 7–10% range, which is why the slider defaults there.