Example 15.6 Managing Cash Flows at Fun Toys A Dynamic Financial Model

Objective To use LP to find the loan amounts that maintain a minimum cash balance each month and minimize the cash balance at the end of the planning horizon.

Background Information A small toy store, Fun Toys, projects the monthly cash inflows listed below (in thousands of dollars) during the year 2000.

Background Information -- continued A negative cash flow means that cash outflow exceed cash inflows to the business - bills exceed revenues. Fun Toys begins the year with a cash balance of $6500. To pay its bills, Fun Toys will need to borrow money early in the year. The company can borrow money in two ways. First, it can obtain a long-term 1-year loan and receive the total amount in January. Beginning in February, 1% interest will be charged each month on this loan. The loan must be paid back by January 2001.

Background Information -- continued Second, each month Fun Toys can borrow money from a short term bank line of credit with a monthly interest rate of 1.5%. All short term loans must be paid back by the beginning of January 2001. At the end of each month excess cash earns Fun Toys 0.4% interest. Fun Toys wants to maximize its cash on hand at the beginning of January 2001, after paying back all loans.Also Fun Toys’ policy is to have a cash balance of at least $5000 at the end of each month.

Solution This example is interesting from a modeling point of view. There are different - and probably reasonable - ways to model the problem, and these lead to different solutions. We will cover one possible approach, but depending on the assumptions you make, you could argue for another approach.

Solution -- continued We make the following timing assumptions. Cash at the end of the previous month is carried forward, with interest, to the beginning of the next month. At the beginning of each month, short-term loans are paid back with interest and new short-term loans are taken out. The cash balance after these activities must be nonnegative. During any month bills are paid and/or revenues are received. The cash balance at the end of the month, after these activities occur, must be at least as large as the minimum cash balance specified by Fun Toys. At the beginning of January 2001, Fun Toys pays back any outstanding loans with interest. The cash balance after doing so is the amount Fun Toys wants to maximize.

CASHBALANCE.XLS The spreadsheet model for Fun Toys’ problem is shown on the next slide. This file contains the setup which should be used to develop the model.

Developing the Model To set up the spreadsheet, proceed as follows. Inputs. Enter the given inputs (interest rates, minimal required cash balance, initial cash balance, and monthly cash inflows/outflows) in the appropriate shaded cells. Loan amounts. Enter any trial value in the LTLoan cell for the long-term loan, and enter any trial values in the STLoan range for the short-term loans. Beginning cash balance each month. Row 19 is used to keep track of the cash balance from the previous month. Begin by entering the formula =D15 in cell B19. Then enter the formula =SUM(B31,B35) in cell C19 (carryover from January to February), and copy it across row 19.

Developing the Model -- continued Interest on long-term loan. Row 22 contains the interest from the long-term loan each month. It is a constant, so we enter the formula =$B$10*LTLoan in cell B22 and copy it across row 22. Interest on short-term loan. The short-term loan interest amounts vary from month to month, depending on the current short-term loan amount. Enter the formula =$B$11*B21 in cell B23 and copy it across row 23.

Developing the Model -- continued Paybacks (Including interest) on loans. Rows 24 and 25 record the amounts paid back, including the loan amounts and interest. We assume each is paid back at the beginning of the month it is due. For the long term loan enter the formula =B22 in cell C24 and copy it across to cell M24. Then enter the formula=LTLoan+M20 in cell N24 to capture the long-term loan payback plus interest in January 2001. For short term loans enter the formula =SUM(B21,B23) in cell C25 and copy it across row 25.

Developing the Model -- continued Balance after loan activities. Row 26 captures the cash balance each month after the loan activities but before the revenues and bills in row 29. This is the beginning cash balance plus any loans taken out minus any loan/interest paybacks. Therefore, enter the formula =SUM(B19:B21)-SUM(B24:B25) in cell B26 and copy it across row 26. Also enter 0’s in row 28. Balance at end of month. Row 31 captures the cash balance at the end of the month.It is the cash balance in row 26 plus the inflow (or outflow if negative) in row 30. Enter the formula =B26+B30 in cell B31 and copy it across row 31. Then enter the formula =MinCashBal in cell B33 and copy it across row 33 to designate the required minimum monthly ending cash balance.

Developing the Model -- continued Interest earned on cash balances each month. Row 35 records the interest earned on the ending cash balance each month. Enter the formula =$B$12*B31 in cell B35 and copy it across row 35. Summary measures. We want to maximize the cash balance in January 2001, after loans have been paid back, so we record its value in the FinalBla cell (B39) with the formula =N26. Fun Toys might also like to know the total amount of interest it pays throughout the year, so calculate it in B38 with the formula =SUM(B22:M23).

Using Solver The Solver dialog box appears below. Fun Toys wants to maximize its final cash balance, subject to meeting its end-of-month minimum cash balance each month and also having nonnegative cash after settling its loan each month.

Using Solver -- continued Note that the nonnegativity constraint must be included in the list of constraints, even though the Assume Non-Negative box is checked in Solver’s Options. This is because the Assume Non-Negative box covers only changing cells, and the BalAfterLoan range is not part of the changing cell range.

Solver Solution The solution recommends a long-term loan of $30,344 plus a short-term loans of various amounts during the six months from April to September. At the beginning of January 2001, Fun Toys’ cash balance will be $19,267, and it will have paid $4,844 in interest.

Sensitivity Analysis Once the model is built, we can proceed in a number of directions. We can use the Solver/Table add-in with inputs such as interest rates and the minimal required ending cash balance each month. Another possible change we might consider is a change in the objective. Rather than maximizing the final cash balance in January 2001, we could minimize the total amount of interest paid throughout the year (that is, the value in cell B38).

Sensitivity Analysis -- continued Finally, we could omit the nonnegativity constraint on the cash balance after loan activities - that is, the BalAfterLoan >=0 constraint. This is simple to do. We highlight this constraint in the Solver dialog box, delete it and rerun Solver. The optimal solution is again quite close to the original optimal solution. However, we note the following: First, the objective value is larger than before ($19,380 instead of $19,267).

Sensitivity Analysis -- continued Second, we see from the original model that the constraints we omitted were binding only in June and September; all other months had a positive cash balance. We might have expected cash balances in June and September to be negative. June’s balance remains at 0, but September’s decreases to -$10,000. Of course, this negative cash balance in early September is more than made up by the large intake in the middle of September; so that by month’s end, the cash balance is a positive $5000.