Corporate taxation creates interactions between the firm's activities and incremental capital investment. This chapter evaluates a number of commonly used methods of project appraisal and risk analysis in terms of shareholder wealth maximisation where complex tax situations exist. It also considers the role of financial project appraisal in the context of the firm's overall strategy, and reviews the empirical evidence on firms' capital budgeting techniques. Project appraisal is one part of the whole capital investment decision making process. The techniques developed for capital budgeting and project appraisal fall into two groups: the financial appraisal methods which generally treat projects in isolation, and the programming techniques developed in operational research. The financial appraisal methods involve payback period, net present value, and project yield. The operational research techniques comprise of linear and integer programming, dynamic programming, and network flow models.