Abstract
<title>Abstract</title> <p> Discounted cash flow valuation assigns most of a firm’s value to its terminal value, yet practice reports that value as a single point obtained by inserting point estimates of growth and the discount rate into a Gordon perpetuity. We show this convention is systematically biased and supply a closed-form correction. Because the perpetuity is convex in the spread between the discount rate and growth, the point estimate departs from the mean by, to second order, the squared coefficient of variation of the spread, which diverges as the spread narrows. Two results overturn the naive intuition: the required positive comovement of growth and the discount rate attenuates the bias, so independent-draw simulation overstates it; and once growth is financed by reinvestment, the bias reverses sign according to whether the return on invested capital exceeds the cost of capital. Our central contribution is the convexity-corrected terminal value, a closed-form, sign-aware estimator that removes the bias without simulation, complemented by a fragility metric that partitions valuation variance. In exact and simulated illustrations the correction removes about ninety percent of an error that ranges from six to fourteen percent and reverses sign with value creation. The estimator applies to any twice-differentiable terminal-value function and overlays a standard valuation model without simulation, making corrected and auditable terminal values practical for equity valuation, fairness opinions, and litigation support. <bold>JEL classification:</bold> G12; G17; G32; C63. </p>