Last Updated 07 May 2020

# NPV of Long and Short-Term Project

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* Explain why the NPV of a relatively long-term project defined as one for which a high percentage of its cash flows are expected in the distant future, is more sensitive to changes in cost of capital than is the NPV of a short-term project. NPV is sensitive to the discount rate (or cost of capital) more so for projects with higher proportion of cash flows at the end of the project compared to a similar project with the same cash flows occurring earlier in the project lifecycle.

This phenomenon is illustrated in the example below: The long term project is more sensitive to discount rate changes as a larger proportion of cash flows are discounted multiple times at the discount rate, reducing the overall NPV value. The cash flows generated from the project as assumed (by the NPV method) to be re-invested at the discount rate. Higher cash flows earlier in the project’s life allow more re-investment income to be generated and thus higher NPV. (McCrary, 2010)

* In addition, explain why, if two mutually exclusive projects are being compared, the short-term project might have the higher ranking under the NPV criterion if the cost of capital is high, but the long-term project might be deemed better if the cost of capital is low. Mutually exclusive projects are also affected by this phenomena and high cost of capital can make short term projects attractive and similarly low cost of capital can make long term projects attractive. The reason for this is the same, i. e. high cash flows are assumed to be re-invested at the cost of capital and thus compounded over the remaining life of the project.

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*Finally, would changes in the cost of capital ever cause a change in the IRR ranking of two such projects? No! IRR depends on the cash flow patterns and not the cost of capital. Thus changes in the cost of capital shall not have any impact on the IRR. However, during project selection, only projects with IRRs higher than their cost of capital are considered otherwise the project would have a negative NPV (i. e. unprofitable project).

References

McCrary, Stuart A. (2010). Mastering Corporate Finance Essentials; John Wiley & Sons, Inc. ISBN: 9780470393338

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