A mean-risk index model for uncertain capital budgeting

Abstract

This paper discusses the capital budgeting problem of projects using annual cash inflows, cash outflows and initial investment outlays given by experts’ evaluations when no historical data are available. Uncertain variables are used to describe the projects’ parameters. A profit risk index and a capital risk index are proposed, and a mean-risk index model is developed for optimal project selection. In addition, the deterministic forms of the model are given and a solution algorithm is provided. For the sake of illustration, a numerical example is also presented. The results of the example show that both profit risk index and capital risk index are important in investment risk control. However, when the profit risk control requirement is strong, the selected project portfolio may be insensitive to the capital risk constraint; when the profit risk control requirement is moderate, the capital risk constraint plays an important role. The results also show the tendency that when either the tolerable profit risk level or the tolerable capital risk level becomes higher, the obtained expected net present value of the project portfolio becomes larger, which is in agreement with the investment rule that the higher the risk, the higher the return.

Keywords:

• capital budgeting
• project selection
• uncertain programming
• risk index

Acknowledgements

This work has been supported by National Natural Science Foundation of China Grants No. 70871011 and No. 71171018, the Program for New Century Excellent Talents in Universities, and the Fundamental Research Funds for Central Universities. The authors thank anonymous reviewers and the editor-in-chief for their valuable comments and Dr Mark Buck for his help in the revision of the manuscript.

Notes

1 To be exact, the sentence is valid when the NPV graph is monotonically decreasing. In general, the rate of return of a project will be a lending rate in some periods and a borrowing rate in other periods.