This paper extends the fundamental theorem of share (or capital) valuation under conditions of certainty and purely competitive markets, to allow for the distinction between capital gains and income in the taxation of personal income. The objective is to develop the theorem for the tax case in a form general enough to allow for corporations both currently and not currently paying a dividend. However, the general derivation is sufficiently tedious to warrant a presentation which begins with less general cases. Accordingly, we will first develop the share valuation equation for a continuous discount version of the taxless case for corporations either paying or not paying a dividend. Then we turn to the effect of income and capital gains taxes for corporations currently paying a dividend; and finally the more general case. The derivations will be simplified by assuming a constant rate of interest over time, but all the theorems can be extended to deal with foreseen changes in interest over time.
Smith, Vernon L. “Taxes and Share Valuation in Competitive Markets.” Review of Economics and Statistics, 51.1 (1969): 96-99.