# Improved Methods for Predicting the Financial Vulnerability of Nonprofit Organizations

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Outline of the Hazard Analysis Procedure

_{i}(Wang 2005).

#### 2.2. Methods for Time-At-Risk Estimation

#### 2.3. Using the Results for Predicting Financial Vulnerability

#### 2.4. Testing the Robustness and Optimization Procedure

_{0}is the length of time that elapses from the first break in obtaining grants until the NPO fails or until the end of the period of interest whichever comes first while N

_{1}represents the number of no-grant periods of one or more years within that time period.

## 3. Example of Results

_{2}constant while varying the value of k

_{1}. The calculations were repeated for several different values of k

_{2}. The results are presented in Figure 2.

_{1}and k

_{2}in some optimal way.

## 4. Conclusions

## Acknowledgements

## Conflicts of Interest

## Appendix A. Definitions of Generalized Time-At-Risk

_{0}, T

_{1}, T

_{2}, and T

_{3}Burde (2012) are considered. T

_{0}is the simplest way to define the time-at-risk, and does so by equating it with the length of time that elapses from the first break in obtaining grants until the NPO fails or until the end of the period of interest (N

_{0}), whichever comes first i.e., T

_{0}= N

_{0}. This definition does not reflect many situations faced by NPOs. For instance, it fails to differentiate between a situation in which an NPO fails to obtain grants only once versus numerous times during the studied period. Additionally, several consecutive no-grant years are potentially riskier for an NPO than a single year without a grant if the NPO successfully obtains grants throughout the rest of the relevant period. Consequently, the second definition for time-at-risk, e.g., ${T}_{1}$ is introduced by

_{0}is as defined above, whilst Y is defined as follows:

_{1}represents the number of no-grant periods of one or more years, N

_{2}the number of no-grant periods of two or more years, and so on. The coefficients k

_{1}and k

_{2}of N

_{0}and Y in Equation (10), as well as additional coefficients k

_{3}, k

_{4}and so on within the definition of Y, serve as weighting factors that consider the cumulative effect of consecutive years of failure with respect to government funding. To reduce the number of parameters that take part in the optimization procedure the coefficients k

_{3}, k

_{4}and so on can be parameterized using one parameter k

_{0}, as follows

_{2}) was developed to account for a scenario in which an NPO experiences periods without grants that alternate with grant-funded years. In this scenario, the number of years from the first break in grants to the end of the period (i.e., N

_{0}) is of lesser importance, and thus N

_{0}can be replaced with Y to yield the following formula for T

_{2}

_{3}that comes closest to the notion of state funding instability, could be

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**MDPI and ACS Style**

Burde, G.
Improved Methods for Predicting the Financial Vulnerability of Nonprofit Organizations. *Adm. Sci.* **2018**, *8*, 3.
https://doi.org/10.3390/admsci8010003

**AMA Style**

Burde G.
Improved Methods for Predicting the Financial Vulnerability of Nonprofit Organizations. *Administrative Sciences*. 2018; 8(1):3.
https://doi.org/10.3390/admsci8010003

**Chicago/Turabian Style**

Burde, Gila.
2018. "Improved Methods for Predicting the Financial Vulnerability of Nonprofit Organizations" *Administrative Sciences* 8, no. 1: 3.
https://doi.org/10.3390/admsci8010003