Elaborate on why the net present value (NPV) of a relatively long-term project is more sensitive to changes in the cost of capital than is the NPV of a short-term project.
Provide two examples of NPV calculations that support your position.
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Elaborate on why the net present value (NPV) of a relatively long-term project
Full Answer Section
The Net Present Value (NPV) of a relatively long-term project is more sensitive to changes in the cost of capital than is the NPV of a short-term project primarily due to the compounding effect of discounting over extended periods.
Here's a breakdown of the reasoning:
Why Long-Term Projects' NPV is More Sensitive to Cost of Capital
The NPV formula is:
Where:
- = Cash flow at time
- = Discount rate (cost of capital)
- = Time period
- = Total number of periods (project life)
The core reason for the increased sensitivity lies in the exponent () in the denominator, .
-
Exponential Impact of Discounting:
Sample Answer
The Net Present Value (NPV) of a relatively long-term project is more sensitive to changes in the cost of capital than is the NPV of a short-term project primarily due to the compounding effect of discounting over extended periods.
Here's a breakdown of the reasoning:
Why Long-Term Projects' NPV is More Sensitive to Cost of Capital
The NPV formula is:
Where:
- = Cash flow at time
- = Discount rate (cost of capital)
- = Time period
- = Total number of periods (project life)
The core reason for the increased sensitivity is the exponent in the denominator, .
-
Exponential Impact of Discounting:
- When (the cost of capital) changes, its effect is magnified by the exponent . For short-term projects, is small, so even a slight change in doesn't significantly alter the denominator.
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