After the examination of the pertinent considerations and cost that determine cash needs, the next aspect relates to the determination of cash needs. There are two approaches to derive an optimal cash balance. namely, (a) minimising cost cash models and (b) cash budget. Cash ManaJement/Conversion Models While it is true that financial managers need not necessarily follow cash management models exactly but a familiarity with them provides an insight into the normative framework as to how  cash management should be conducted. This section, therefore, attempts to outline the following analytical models for cash management: (j) Baumol Model, (ii) Miller-Orr Model and (iii) Orgler's Model. The Control Theory Mode: Approach is highly mathematical and outside the scope of this book."

Baumol ModelS The purpose of this model is to determine the minimum cost amount of cash that a financial manager can obtain by convening securities to cash, considering the cost of conversion and the counter-balancing cost of keeping idle cash balances which otherwise could have been invested in marketable securities. The total cost associated with cash management, according to this model, has two elements: (i) cost of ccnverting marketable securities into cash and (ii) the lost opportunity cost. lhe' contersion costs are incurred each time marketable securities are convened into cash. Symbolically,

Total conversion cost per period = TB/C

Where b = cost per conversion assumed to be independent of the size of the transaction
T = total transaction cash needs for the period
C=·value of marketable securities sold at each conversion.

The opportunity cost is derived from the lost/forfeited interest rate W that could have been earned on the investment of cash balances. The total opportuniry cost is the interest rate times the average cash balance kept by the firm. The model assumes a constant and a certain pattern of cash outflows. At the beginning of each period. the firm starts with a cash balance which it gradually spends until at the end of the period it has a zero cash balance and must replenish its each supply to the level of cash balan!=ein the beginning. Symbolically. the average lost opponunity cost.


Where i= interest rate that could have been earned.
02 = the average cash balance that is, the beginning cash (0 plus the ending cash balance
of the period (zero) divided by 2.

The total cost associated with cash management comprising total conversion cost plus opportunity cost of not investing cash until needed in interest-bearing instruments can be symbolically expressed as:

I(C/2)+ (TB/C)

To minirnise the cost, therefore. the model attempts to determine the optimal conversion amount. that is. the cash withdrawal which costs the least. The reason is that a firm should notkeep'tbe total beginning cash balance during the entire period as it is not needed a~e beginning of the period. For example, if the period were one thirty day month, only one-thirtieth of ihe opening cash balance each day will be required. This means if only one-thirtieth of the entire amountIs withdrawn. the rest could be left invested in interest-earning marketable se~rities. As a result, on the one-thirtieth of the cash not needed to the last day of the month, twenty-nine day's interest could be earned by the fimf~nd ;;0 on. Symbolically, the optimal' conversion amount (C),


The model in te.rns of of Eq. 29.4 has important implications. first, as the total cash needs for transaction rises becauSe' of expension/diversiticstion, the oplimal wilhdra w,,1 increases less than proportionately. This is the result of economy of scale in cash management. Each project cloe» no  need its own additional cash balances. It only needs enough additions to the general cash balance of the firm to facilitate expanded operations, Secondly, as the opportunity interest rate (r) increases, the optimal cash withdrawal decreases. This is so because as (I) increases it IS more costly to forfeit the investment opportunity and financial managers want to keep as much cash invested in securities for as long as possible. They can afford to do this at the higher interest .rates because at those higher rate shortfall cost caused by a lower withdrawal are offset. In sum, the Baumol Model of cash management is very simplistic. Further, its assumptions of certainty and regularity of withdrawal of cash do not re.uistically reflect the actual situation in any firm. Also, the model is concerned only with transaction balances and not with precautionary balances. In addition, the assumed fixed nature of the cash withdrawals is also not realistic. Nevertheless, the model does clearly and concisely demonstrate the economies of scale and the counteracting nature of the conversion and opportunity costs which are undoubtedly majo considerations in any financial manager's cash management strategy. lbe ABC ud requires Rs 30 lakh in cash 10 meet its transaction needs duritig the next three-month cash planning period. It holds marketable securities of an equal amou.nt. The annual yield on these marketable 'Securities is 20 per cent. The conversion oi these securities inlO cash entails a fixed cost oi Rs 3,000 pel transaction. Using Baumol model, compute the amount oi marketable securities converted into cash order. Assuming ABC can sell its marketable securities in any of the five lot sizes: 1.50,000, 3.00, 6,00,000, 7,50,000 and 15.00,000. prepare a table indicating the economic lot size using numerical analysis.

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