EQUILIBRIUM IN THE PRICING OF CAPITAL ASSETS.pdfVIP

JOURNAL OF FINANCIAL AND QUANTITATIVE ANALYSIS September 1972 EQUILIBRIUM IN THE PRICING OF CAPITAL ASSETS, RISK-BEARING DEBT INSTRUMENTS, AND THE QUESTION OF OPTIMAL CAPITAL STRUCTURE : A REPLY Robert A. Haugen and James L. Pappas* Although Imai and Rubenstein are correct that our proof — that the Miller- Modigliani (M-M) and Sharpe-Lintner-Mossin (S-L-M) capital asset pricing models are mutually consistent — is incomplete, their comments indicate some confusion about the relationships involved in the equilibrium pricing of assets in these models . Further, they seem to imply that Stiglitzs proof in terms of dollar returns is in some sense superior to a proof in terms of rates of return . This is erroneous . Accordingly, we shall further clarify the relationships inherent in the models and correct our presentation of the proof of the invariance of capital costs in the context of the S-L-M model . Consider the following set of equations which express the relationships that exist given the M-M valuation model . V (20)^ r = -^ (21) (22) V* (23) r* e e where : V = value of the assets of the unlevered firm at the beginning of the period; V = terminal value of the assets; termina] V, = value of the debt at the beginning of the period; *Both, University of Wisconsin. ^Equations 1-19 are in our original paper [3] 2005 V, = terminal value of the debt; r = one-period rate of return on the unlevered firms assets; and V* and r* = the i