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# Relationships Between the Internal Rate of Return (IRR), Cost of Capital, and Net Present Value (NPV)

Note by James R. Martin, Ph.D., CMA
Professor Emeritus, University of South Florida

Citation: Martin, J. R. Not dated. Relationship between the internal rate of return (IRR), cost of capital, and net present value (NPV). Management And Accounting Web. https://maaw.info/IRRNPVandCostofCapital.htm

Traditional cash flow analysis (payback) and the accounting rate of return (ROI) fail to consider the time value of money. The internal rate of return (IRR) considers the time value of money and is frequently referred to as the time adjusted rate of return. The IRR is defined as the discount rate that makes the present value of the cash inflows equal to the present value of the cash outflows in a capital budgeting analysis, where all future cash flows are discounted to determine their present values.

The relationships are presented below. The cost of capital represents the minimum desired rate of return (i.e., a weighted average cost of debt and equity capital).

The net present value (NPV) is the difference between the present value of the expected cash inflows and the present value of the expected cash outflows.

If the present value of the expected cash outflows is greater than the present value of the expected cash inflows then NPV < 0.

If the present value of the expected cash outflows is equal to the present value of the expected cash inflows then NPV = 0.

If the present value of the expected cash outflows is less than the present value of the expected cash inflows then NPV > 0.

In these three cases the relationships between the NPV, IRR and Cost of Capital are illustrated in the following table along with the decisions based on the cash flow perspective.

 IF Then Capital Budgeting Decision NPV < 0 IRR < Cost of Capital Reject the investment from the cash flow perspective. Other factors could be important. NPV = 0 IRR = Cost of Capital Provides the minimum return. Probably reject from the cash flow perspective. Others factors could be important. NPV > 0 IRR > Cost of Capital Screen in for further analysis. Other investments may provide better returns and capital should be rationed, i.e., go to the most profitable projects. Others factors could be important.

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Related summaries:

Gold, B. 1976. The shaky foundations of capital budgeting. California Management Review (Winter): 51-60. (Summary).

Hayes, R. H. and W. J. Abernathy. 2007. Managing our way to economic decline. Harvard Business Review (July-August): 138-149. (This is a reprint of their 1980 article with a retrospect by Hayes on page 141). (Summary).

Kite, D. 1995. Capital budgeting: Integrating environmental impact. Journal of Cost Management (Summer): 11-14. (Summary).

Martin, J. R. Not dated. Chapter 14: Investment Centers, Return on Investment, Residual Income and Transfer Pricing. Management Accounting: Concepts, Techniques & Controversial Issues. Management And Accounting Web. https://maaw.info/Chapter14.htm

Martin, J. R. Not dated. Comparing Dupont's ROI with Goldratt's ROI. Management And Accounting Web. https://maaw.info/ComparingDupontGoldrattROI.htm

Martin, J. R. Not dated. Investment management. Management And Accounting Web. (Summary).