Optimizing Liquidity Sources Under Cash Flow and Borrowing Constraints
Summary
The document frames a multi-period funding problem: choose among borrowing sources to cover forecast cash shortfalls while minimizing interest expense. The example includes fixed-rate borrowing with a short maturity, a capped source available across a range of maturities, and floating-rate borrowing with a spread. Borrowed funds must later be repaid, so funding decisions affect future cash balances and costs.
Two operational constraints make the problem more complex: a maximum amount can mature on any one day, and each source can be tapped only a limited number of times per week. The author recognizes that solving each day independently will not account for these linked decisions and asks how to model the full horizon. No optimization model or solution is provided; the natural direction is a constrained multi-period formulation, but the document leaves decision variables, exact interest conventions, and treatment of uncertain cash flows unspecified.
Key ideas
- Funding decisions should cover cash deficits across the full forecast horizon, including repayments.
- The objective is to minimize interest expense across a mix of liquidity sources.
- Maturity amounts and borrowing frequency impose constraints that couple decisions across days.
- Daily optimization alone cannot capture the effect of borrowing and repayment on later cash needs.
- The document poses the modeling problem but does not provide a solution or empirical results.
Tags
Full text
# Interest Expense Optimization # Interest Expense Optimization So I have a problem I need to solve and no idea how to approach it. Its a verbal problem without any specific numbers given except for those below. So it is up to me to determine how to structure the problem and solve it. In a nutshell the goal is that I need a way to find the optimal mix of sources of liquidity that minimize interest expense but also adheres to the restrictions below. I know its not much to go on but maybe this example will help understand the problem. Ex. Say I have a time series of future cash flows for the next 120 days. Some days are positive cash in the bank and other days I go negative. I don't want to go negative as the interest of overdrawing the bank account is 4% so I can borrow money from the following sources of liquidity cheaper than I can from overdrawing the bank account. Source 1: 1.5% for any amount of $ but has a 30 day maturity Source 2: 0.8% for up to $250 mil from 1 day up to 270 days maturity Source 3: Libor rate + spread (ex. 1.25%) for any amount of $ but has a 90 day maturity Restriction 1: Cannot have more than $250 mil maturing on any single day Restriction 2: Cannot borrow more than 3 times a week from any single source With that said this problem is clearly a time series. I can solve this easily for any single day. But for a 120 days of cashflows and with the restrictions on # of borrowings per week and amount of $ maturing per day are making me pull my hair out. I can take future cash needs into account, find the days that will be negative and borrow the $ needed to stay above $0 without caring much about minimizing interest expense. But how do I borrow money such that I minimize interest expense in the long run by using a mixture of the 3 sources listed above and also keep track of the 2 restrictions listed above and also any funding needs to repay the amounts borrowed in the future. Any ideas on how I can tackle such a problem? I have python experience so I can code an algorithm if needed but don't know how to start. I'm thinking of doing some sort of a random walk algorithm and try and brute force a solution over thousands of iterations and settling on a random solution that results in the least interest expense over said iterations but that sounds computationally expensive. There must be a mathematical way of modelling this right?
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