It Is January 1, 2011, Beth Is The Finance Manager At The Gl

Question

It Is January 1 2011 Beth Is The Finance Manager At The Glop Foundat It is January 1, 2011. Beth is the finance manager at the Glop Foundation, which has $75,000 in cash in its checking account. The Foundation must make annual cash payments for 2011, 2012, and 2013: $25,000, $25,000, and $26,000 respectively. Funds required each year must be withdrawn at the beginning of that year. The Foundation plans to shut down on January 1, 2014, at which point any remaining cash will be distributed to beneficiaries. The Foundation’s bank offers two savings options: a 2-year Certificate of Deposit (CD) earning 3% interest annually and a 3-year CD earning 5% annually, both available in any amount with no early withdrawal. Any funds not invested in the CDs remain in the checking account, which yields 2% interest annually. Interest from both the checking account and CDs is deposited on January 1 each year and can be used for that year's payments. Beth aims to develop a financing strategy maximizing the final amount paid to beneficiaries on January 1, 2014, while satisfying the payment requirements in each of the first three years. This involves creating a linear optimization model to determine the optimal investment approach.

Dr. Jack HW Helper · Accepted Answer

Introduction Effective financial planning for nonprofit foundations requires strategic allocation of available funds to maximize legacy disbursements while ensuring compliance with expenditure commitments. The Glop Foundation’s scenario presents a classical linear programming problem involving cash management, investment decisions, and interest accruals over multiple periods. Developing an optimal financing strategy entails decisions about how much to invest in short-term or long-term CDs versus holding cash, considering interest rates and cash flow obligations. Model Formulation Decision Variables The decision variables include: - $ x_{2}(0) $: Amount invested in the 2-year CD at the start (January 1, 2011) - $ x_{3}(0) $: Amount invested in the 3-year CD at the start (January 1, 2011) - $ C_{1} $: Cash available at the beginning of 2012 (after interest and deductions) - $ C_{2} $: Cash available at the beginning of 2013 - $ C_{3} $: Cash available at the beginning of 2014 (end of the period) Additional variables, such as interest earned from CDs and cash, are implicit in the modeling through formulas and constraints. Objective Function The goal is to maximize the amount available for beneficiaries on January 1, 2014: $$ \text{Maximize } C_{3} $$ which depends on the initial investments, interest earnings, and payments made during the period. Constraints The constraints ensure: 1. Initial cash allocation: $$ x_{2}(0) + x_{3}(0) + C_{0} = 75,000 $$ where $ C_{0} $ is the initial cash remaining after CD investments. 2. Payment obligations each year: - At beginning of 2011: $$ \text{Cash available} \geq 25,000 $$ - At beginning of 2012: $$ C_{1} \geq 25,000 $$ - At beginning of 2013: $$ C_{2} \geq 26,000 $$ 3. Interest calculations: - Cash earns 2% interest annually if not invested. - CDs accrue interest based on their respective rates: $$ \text{Interest from 2-year CD} = x_{2}(0) \times 3\% $$ $$ \text{Interest from 3-year CD} = x_{3}(0) \times 5\% $$ 4.

It Is January 1, 2011, Beth Is The Finance Manager At The Gl

It Is January 1 2011 Beth Is The Finance Manager At The Glop Foundat

Paper For Above instruction

Introduction

Model Formulation

Decision Variables

Objective Function

Constraints

Implementation in Excel

Results and Optimal Strategy

Conclusion

References