Important mathematical tools/techniques for appraisal of business projects under certainty, risk and uncertainty conditions are discussed in this paper, including certainty equivalent method, risked adjusted discount rate method, expected monetary value (EMV) method, expected opportunity loss (EOL) method, criterion of optimism, criterion of pessimism and criterion of realism. Under Certainty equivalent and risked adjusted discount rate methods net present value (NPV) of the project/investment project is find out to enable the decision maker or the project manager whether to continue or reject or select the best among the alternatives. In cases of the business decision making under risk or probabilistic decision situations EMV and EOL are suitably used. In the absence of knowledge about the probability of any state of nature (future) occurring, the decision maker must base his decision only on the actual conditional pay off values. In such situations criterion of optimism, criterion of pessimism and criterion of realism as Hurwicz criterion are usefully applied.