A novel approach to legacy donations with long‐term benefits supported by mathematical analysis

Abstract

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.

Mathematical results for the ‘Master Fund Strategy’ for legacy donations under the assumption of annual compounding

“…The Master Fund also grows at a rate g, and pays yearly the same fraction r of its beginning-of-year balance to the Charity Fund. Solow et al (2024) inductively prove that the impact of the bequest on Charity Fund balance and net present value of all payments respectively are…”

“…We apply annual compounding to the model described by Solow et al (2024) in which an amount p is earmarked as a bequest aimed at generating a (yearly) stream of funds to one non-profit organisation. In the traditional approach, the amount of money p will be used to set up a 'Charity Fund' (or will be added to such a fund), from which yearly payments will be made to the receiving organisation.…”

“…Finally, note that to determine the transition year t T , it is necessary to find numerically the first value of t so that Equation 6 is positive: Solow et al (2023) provide an excellent example of such an approach. Solow et al (2023Solow et al ( , 2024 propose a novel way to structure a legacy donation, the Master Fund Strategy (MFS). Under continuous compounding and rather general conditions, they prove the MFS to be more beneficial in net present value terms than a traditional strategy (TFS), while also presenting, in their 2023 article, numerical results under yearly compounding.…”

“…If NPV(∞) turns out to be larger than NPV(∞), this inevitably implies the existence of a transition year somewhere after t*, defined as the first year, say t T , in which NPV(t) > NPV(t). This year is the 'annual compounding' version of the variable of interest in the Break-even Theorem proposed by Solow et al (2024) under continuous compounding (defined as the value of t BE for which NPV(t BE )…”