A Novel Approach to Legacy Donations with Long-Term Benefits Supported by Mathematical Analysis

A novel approach to legacy donations, called the “Master Fund Strategy,” is proposed. Potential long-term financial benefits for both donor and nonprofit organizations (NPOs) when compared to a “Traditional Fund Strategy” are established through mathematical analysis and computer simulations, providing nonprofit marketing and fundraising professionals an alternative way to lock in bequest funding. In particular, formulas are developed for computing relevant financial quantities associated with the two strategies. Conditions are presented under which the Master Fund Strategy is better than the Traditional Fund Strategy, in the sense that there is a point in time when the net present value of the distributions to the NPO under the Master Fund Strategy exceeds that of a Traditional Fund Strategy and continues to do so beyond that point. These analytical results are obtained under the assumption that the investment rates of return and the fund payouts rates are known constants; however, formulas for relaxing these restrictions are also developed and the consequences are examined with Monte Carlo simulations

A Novel Approach to Legacy Donations with Long-Term Benefits Supported by Numerical Illustrations

Philanthropic donors face challenges in matching the causes to which they donate, the time horizon—and thus impact—of their donations, and the charitable vehicles they choose for making contributions. Wealthier donors may elect to create their own foundations and customize their charitable support. Less wealthy donors have limited choices: they may contribute to a nonprofit\u27s current operations or to existing nonprofit endowments. We present a novel approach for making charitable donations, blending aspects of each of these strategies. Our approach has potential long-term financial benefits, allows donors to control their charitable donations in a convenient and easy-to-implement manner, can be established through an existing nonprofit organization, expands opportunities for more donors because it requires a smaller corpus contribution with lower management costs than creating a foundation, provides tax savings in the United States and other countries (e.g., the UK, Canada, and Australia) comparable to other planned giving vehicles, and may be implemented during one\u27s lifetime using donor advised funds or as part of a legacy plan through the donor\u27s estate documents, which is when the long-term benefits accrue

Mass and CO2

Each line provides information for one individual cricket (mass, percent time spent calling, and CO2 production). Data correspond to Figure 2

Mass, amplitude, and time spent calling

Sheet 1 contains the mass and percent of time spent calling. Sheet 2 contains mass and call amplitude. In both cases, each line represents a measurement on one cricket. Raw data for Figure 5

Data from: Signal diversification in Oecanthus tree crickets is shaped by energetic, morphometric, and acoustic trade-offs

Physiology, physics, and ecological interactions can generate trade-offs within species, but may also shape divergence among species. We tested whether signal divergence in Oecanthus tree crickets is shaped by acoustic, energetic, and behavioral trade-offs. We found that species with faster pulse rates, produced by opening and closing wings up to twice as many times per second, did not have higher metabolic costs of calling. The relatively constant energetic cost across species is explained by trade-offs between the duration and repetition rate of acoustic signals – species with fewer stridulatory teeth closed their wings more frequently such that the number of teeth struck per second of calling and the resulting duty cycle were relatively constant across species. Further trade-offs were evident in relationships between signals and body size. Calling was relatively inexpensive for small males, permitting them to call for much of the night, but at low amplitude. Large males produced much louder calls, reaching up to four times more area, but the energetic costs increased substantially with increasing size and the time spent calling dropped to only 20% of the night. These trade-offs indicate that the trait combinations that arise in these species represent a limited subset of conceivable trait combinations