monte carlo - cash budget models outline and correlations

7/28/2019 Monte Carlo - Cash Budget Models Outline and Correlations

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Monte Carlo Simulation Cash Budgeting Models Outline

1 Spreadsheet Modeling Dr. Grayson

Simulation applied to Cash Flow applications

Simulation has been applied to many financial applications. Thislesson covers applying Monte Carlo simulation to cash budgeting.

Example: Cash Budgeting at Butson Stores(Example, Powell & Baker, chapter 9, pp. 285-288.)

Butson Stores faces a problem maintaining sufficient cash balances foroperations over the first six months of the year. Each month, theymust pay certain fixed costs and taxes, as well as materials costs thatrun about 80 percent of the current months sales. Monthly cashreceipts consist of revenues from the previous months sales, as wellas 0.5 percent interest on short-term cash balances. The companyenters the six-month period with a cash balance of $250,000 andwishes to maintain at least that balance each month in order to covercash needs. December sales of $1.54 million have just been recorded.

If Butson finishes a month with less than $250,000 in cash, thecompany can take out a one-month loan at 1 percent interest. Theprincipal and interest are repaid in the following month. Butsonsmarketing department has made estimates for the mean and standarddeviation of sales in each of the next six months. Given theuncertainty in sales, Butson would like to know how large theirmaximum monthly loan is likely to be, and how likely they are toexceed their current credit limit of $750,000. Finally, the company

would like to know how much they will have to pay in interest costs forloans.

Our spreadsheet model is shown below:


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Named ranges:COGS ='9.24'!$C$9

InitCash ='9.24'!$C$13

Interest_return_on_cash ='9.24'!$C$12

IntRateCash ='9.24'!$C$12

IntRateLoan ='9.24'!$C$11

Loans ='9.24'!$E$29:$J$29

MinCashBal ='9.24'!$C$14


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Model logic:

Look at the month of February, cells F18 to F30.

Cash inflows in February come from three sources: the cash balance

available from the previous month, interest earned on that balance,and sales receipts (previous months sales).

The cash available at the end of each month must cover the cashoutflows: fixed costs and taxes (cell F24: =E8), cost of sales (80% ofthe current months sales), and repayment of the previous monthsloan (loan principal and interest on previous months loan if any).

Cash balance before loan is found by subtracting the uses of cash(costs) from the sources of cash (cash and receipts).

A loan is necessary if the cash balance before loan is less than$250,000, and the loan amount would be the amount necessary toobtain the required minimum balance.

Final cash balance is cash balance before loan plus the loan amount.

The uncertainty in this model is the sales in each month and this isdetermined by a random sample from a normal distribution with meanand standard deviation as shown for each month in rows 6 and 7.

Forecast cells are set up for maximum loan and loan interest.


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Results and Interpretation:


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Example: Everglade(Example, Hillier & Hillier, chapter 16.)

Assume the Everglade problem (described below) was solved for theoptimal solution to the two types of loans available to meet cash flow

problems with a solution as also shown below.

The Everglade Golden Years Company operates upscale retirement communities incertain parts of southern Florida. The company was founded in 1946, and enjoyedmany successful years. Unfortunately, the past few years have been difficult ones.The demand for retirement community housing has been light, and Everglade hasbeen unable to maintain full occupancy. However, the market has picked up recentlyand the future is looking brighter. Everglade has recently broken ground for theconstruction of a new retirement community and has more new construction plannedover the next 10 years.

Julie Lee is the CFO at Everglade, and has been trying to come to grips with theimminent cash flow problem. Her projection of cash flows for the next 10 years isshown in the table below. With less money currently coming in than would beprovided by full occupancy, and with all the construction costs for the new retirementcommunity, Everglade will have negative cash flow for the next few years. With only$1 million in cash reserves, it appears that Everglade will need to take out someloans in order to meet financial obligations. Also, to protect against uncertainty,company policy dictates maintaining a balance of at least $500,000 in cash reservesat all times.


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The companys bank has offered two types of loans to Everglade. The first is a tenyear loan with interest only payments made annually and then the entire principalrepaid in a single balloon payment after ten years. The interest rate on the ten yearloan is a favorable 7 percent per year. The second option is a series of one yearloans. These loans can be taken out each year as needed, but each must be repaid(with interest) the following year. The interest rate for these short term loans is

projected to be 10 percent per year.

Year Projected Net CashFlow

(millions of dollars)

2003 -8

2004 -2

2005 -4

2006 3

2007 6

2008 3

2009 -4

2010 72011 -2

2012 10

The spreadsheet might be organized as follows:

Decision Variables: Long Term Loan and Short Term Loans

Objective Function: Maximize Ending Cash Balance

Constraints: Ending Balance >= Minimum Balance


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Key relationships:

LT Interest = - Long Term Interest Rate * Long Term LoanST Interest = - Short Term Interest Rate * Prior Period Short Term LoanLT Payback = - Long Term Loan (Dec Var)ST Payback = - Prior Period Short Term Loan (Dec Var)

Ending balance = Starting balance + Cash flow + Loans Interest payments Loanpaybacks


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Using the most likely cash flow in a deterministic model yields anending balance of $2.92. Our optimal solution was determinedassuming no deviation from the projected cash flows. Maintaining thissolution for the long term loan we want to incorporate uncertainty forthe cash flows and determine the likelihood of achieving a positive

cash balance at the end of the ten years.

We will model the uncertainty of the cash flows for each year using atriangular distribution with parameters as shown below:

We will incorporate the uncertainty into our model, identify our

forecast cell and run the simulation to answer the managementquestion about our risk.


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The result of our Monte Carlo analysis reveals there is about an 87%chance the ending balance will be positive:


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Correlations and Implications(based on Chapter 5, Charnes)

Suppose we have two assets with return characteristics as shown

below:

Further suppose the correlation between those can be set in D5.

We want to explore the impact of correlation on the portfolio returnassuming an equal mix of these two assets.

We will define correlation as a decision variable and then use aDecision Table to explore this relationship:


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Chart: Trend

Chart: Overlay (-0.75, 0.0, 0.75)


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Logic for Enston Company (upcoming lab problem)

The Entson Company believes that its monthly sales during the period fromNovember to July of the next year are normally distributed with means and standarddeviations given in the accompanying table. Each month Entson incurs fixed costs of$250,000. In March taxes of $150,000 and in June taxes of $50,000 must be paid.

Dividends of $50,000 must also be paid in June. Entson estimates that its receipts ina given month are a weighted sum of sales from the current month, the previousmonth, and two months ago with weights of 0.2, 0.6 and 0.2. In symbols, if Rt andSt represent receipts and sales in month t, then:

The materials and labor needed to produce a months sales must be purchased onemonth in advance, and the cost of these averages to 80% of the products sales. Forexample, if sales in February are $1,500,000, then the February materials and laborcosts are $1,200,000, but these must be paid in January.At the beginning of January Entson has $250,000 in cash. The company would liketo ensure that each months ending cash balance never dips below $250,000. This

means Entson might have to take out short-term (one month) loans. For example, ifthe ending cash balance at the end of March is $200,000, Entson will take out a loanfor $50,000, which it will then pay back (with interest) one month later. The interestrate on a short-term loan is 1% per month. At the beginning of each month, Entsonearns interest of 0.5% on its cash balance.

The company would like to use simulation to estimate the maximum loan it will needto take out to meet its desired minimum cash balance. It would also like to see howsensitive the results are to the sales data. In particular, considering this data as abase case, it would like to run a simulation in which the means are 20% below thevalues in the table and another simulation in which the means are 20% above thosein the table.

Chronological sequence:

Entson observes its beginning cash balance. Entson receives interest on its beginning cash balance. Receipts arrive and expenses are paid (including payback of the previous

months loan, if any, with interest). If necessary, Entson takes out a short-term loan.

The final cash balance is observed, which becomes next months beginningcash balance.

ttttSSSR *2.0*6.0*2.0

12++=


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Given information incorporated into spreadsheet model:

monte carlo - cash budget models outline and correlations

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