Interpolation

Definition

Interpolation is the process of estimating the value of a function or data point within a known range of values, based on the known values surrounding it. It is a mathematical technique used to approximate intermediate values when only a limited set of discrete data points is available.

5 Must Know Facts For Your Next Test

1. Interpolation is commonly used in capital investment decisions to estimate intermediate values of financial metrics, such as payback period and accounting rate of return.
2. The accuracy of interpolation depends on the number and distribution of known data points, as well as the underlying relationship between the variables.
3. Linear interpolation is the simplest form of interpolation, but it may not capture complex nonlinear relationships between variables.
4. Polynomial interpolation can better fit nonlinear relationships, but it requires more computational effort and may be more sensitive to the distribution of known data points.
5. Interpolation is a useful tool for making informed decisions when complete data is not available, but it should be used with caution and an understanding of its limitations.

Review Questions

• Explain how interpolation can be used to evaluate the payback period of a capital investment.
  • Interpolation can be used to estimate the payback period of a capital investment when the cash flows are not evenly distributed over time. By using the known cash flows at the beginning and end of the payback period, interpolation can be used to approximate the intermediate point where the cumulative cash flows equal the initial investment. This allows for a more accurate estimate of the payback period than simply dividing the initial investment by the average annual cash flow.
• Describe how the choice of interpolation method (e.g., linear vs. polynomial) can impact the evaluation of the accounting rate of return for a capital investment.
  • The choice of interpolation method can significantly affect the evaluation of the accounting rate of return (ARR) for a capital investment. Linear interpolation assumes a constant relationship between the investment and the returns, which may not accurately reflect the actual pattern of cash flows. Polynomial interpolation, on the other hand, can better capture nonlinear relationships and provide a more nuanced estimate of the ARR. However, polynomial interpolation requires more data points and computational effort, and may be more sensitive to the distribution of known values. The selection of the appropriate interpolation method should be based on the specific characteristics of the investment and the available data.
• Analyze the limitations of using interpolation in the evaluation of capital investment decisions, and discuss strategies for mitigating these limitations.
  • The primary limitation of using interpolation in the evaluation of capital investment decisions is the reliance on a limited set of known data points. Interpolation can be sensitive to the distribution and accuracy of these data points, and may not accurately capture complex relationships between variables. To mitigate these limitations, it is important to gather as much relevant data as possible, consider the use of more sophisticated interpolation methods (such as polynomial interpolation), and supplement the interpolation results with other analytical techniques (e.g., sensitivity analysis, scenario planning) to assess the robustness of the investment evaluation. Additionally, it is crucial to maintain a critical understanding of the assumptions and limitations of the interpolation process, and to use the results as one input among many in the overall capital investment decision-making process.

Related terms

Extrapolation: The process of estimating the value of a function or data point outside of a known range of values, based on the known values within the range.

Linear Interpolation: A simple form of interpolation where the intermediate values are estimated using a linear function connecting the known data points.

Polynomial Interpolation: A more complex form of interpolation where the intermediate values are estimated using a polynomial function that fits the known data points.