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Cash Management
Meeting 4
• 1. Explain the concept of cash management.
• 2. Explain how to improve cash management efficiency.
• 3. Explain the benefits of cash management, speed up cash income
and slow down cash expenditures.
• 4. Ability to calculate optimal cash balance (Baumol model, and
Miller-Orr model).
Concept of cash
• Though cash hold the smallest portion of total current assets.
However, cash is both the beginning and end of working capital cycle
– cash, inventories, receivables and cash.
• It is the cash, which keeps the business going. Hence, every
enterprises has to hold necessary cash for its existence.
• Moreover, steady and healthy circulation of cash throughout the
entire business operations is the basis of business solvency.
Concept of cash
• Cash may be interpreted under two concepts.
• In narrow sense, cash is very important business asset, but although
coin and paper currency can be handled, the major part of the cash of
most enterprises is in the form of bank checking accounts, which
represent claims to money rather than tangible property.
• While in broader sense, cash consists of legal tender, cheques, bank
drafts, money orders and demand deposits in banks.
Cash Management
• Is a process of:
• collecting cash
• managing cash
• using cash for investing
Cash
Deficit Surplus
Borrow Invest
Motivation for Holding Cash
Transaction Motive
• Companies need to be
able to pay bills
• Companies need a cash
reserve in order to
balance short-term cash
inflows and outflows
since these are not
perfectly matched
• Measure: quick ratio
Precautionary motive
• Companies need to avoid
uncertainty in future
• Companies need a cash
reserve in case there will be
unexpected demands for
cash in future
• Measure: volatility of
operating cash flows
Speculative motive
• Companies need cash
reserves for any
investment
opportunities
• Companies need to get
profit making
opportunities from
fluctuations in
commodity prices,
security prices, interest
rates, and foreign
exchange rates.
Transaction Motive
• Firms need cash to meet their transaction needs.
• The collection of cash (from sale of goods and services) is not
perfectly synchronised with the payment of cash (for purchase of
goods and services).
• Hence, some cash balance is required as a buffer.
Precautionary Motive
• There may be some uncertainty about the cash inflows from sale of
goods and services.
• Likewise, there may be uncertainty about cash outflows on account of
purchases.
• To protect itself against such uncertainties, a firm may require some
cash balance.
Speculative motive
• Companies may build up cash reserves in order to take advantage of
any attractive investment opportunities that may arise.
• These opportunities may include fluctuations in commodity prices,
security prices, interest rates, and foreign exchange rates.
• If a company has significant speculative cash reserves for which it
cannot see an advantageous use, it may choose to enhance
shareholder value by returning them to shareholders (dividends)
Investing surplus cash
• If a firm’s need to hold cash is reduced, the funds can be invested in a
number of different short-term securities
• Including Treasury bills, certificates of deposit, commercial paper,
repurchase agreements, banker’s acceptances, and short-term tax
exempts
INVESTMENT OF SURPLUS FUNDS
• Companies often have surplus funds for short periods of time before
they are required for capital expenditures, loan repayment, or some
other purpose.
• Instead of allowing these surplus funds to accumulate in current
account where they earn no interest, companies invest them in a
variety of short-term instruments like term deposits with banks,
money market mutual funds, and so on.
• Managing the investment of surplus funds is a very important
responsibility of the financial manager. This has become more so in
recent years, thanks to higher corporate liquidity and wider range of
investment options.
Investment Portfolio: Three Segments
The ready cash
segment
reserves for the
company's cash
account to meet
operational needs
The controllable cash
segment
outflows like taxes,
dividend, interest
payments, and
repayments of
borrowings
The free cash
segment
surplus funds invested
in short-term
instruments to
generate income
Investment Portfolio: Three Segments
• The ready cash segment represents a reserve for the company's cash
account. It is meant to increase the cash resources of the company to meet
unanticipated operational needs. Investments in this segment must
necessarily be highly liquid in nature.
• The controllable cash segment represents that part of the investment
portfolio which is meant to meet the needs of knowable outflows like
taxes, dividend, interest payments, and repayments of borrowings. Ideally,
investments in this segment must be matched in size and maturity to
known future outflows.
• The free cash segment represents that part of the investment portfolio
which is meant neither to increase unforeseen current cash needs nor to
meet known future outflows. It essentially represents surplus funds with
the firm which has been invested in short-term instruments to generate
income, without much concern for liquidity or maturity.
Criteria for Evaluating Investment Instruments
Safety
Refers to the probability of
getting back the amount
invested
Liquidity
Refers to the ability of the
investor to convert instrument
into cash without loss
Yield
the return earned from
instrument by way of
interest or dividend
Maturity
refers to the life of the
instrument
Criteria for Evaluating Investment Instruments
• Safety refers to the probability of getting back the amount invested. Treasury bills may be
regarded as the safest of all the instruments as they represent the obligations of the
government. The safety of the other instruments depends on the type of the instrument
and the issuer. A high degree of safety is essential for an instrument to be considered for
inclusion in the short-term investment portfolio of the firm.
• Liquidity refers to the ability of the investor to convert it into cash on short notice
without incurring a loss. An instrument may be quite safe if it is held till maturity, but it
may not be possible to sell it prematurely without suffering a loss. For a traded
instrument, a large and active secondary market ensures liquidity. For a non-traded
instrument, liquidity is high if the penalty for premature liquidation is negligible.
• Yield is the return earned from it by way of interest, dividend, and capital appreciation.
Some instruments like Treasury bills and commercial paper do not pay interest, but they
are sold at a discount and redeemed at face value. Yield has to be measured in post-tax
terms, taking into account the tax rate applicable to the returns earned by the
investment instrument.
• Maturity refers to the life of the instrument. While some instruments (like Treasury bills)
have fixed original maturities, others (like certificates of deposit) can have tailormade
maturity. Generally, the longer the maturity, the greater the yield.
Investment Options
• Fixed Deposits with Banks
• Mutual Fund Schemes
• Treasury Bills
• G-Secs
• Commercial Paper
• Certificates of Deposits
• Inter-Corporate Deposits
• Ready Forwards
Investment
instruments
T-bills (short term)
G-secs (long term) - risk ↓ return ↓
Deposits - risk average return average
Futures/options (derivatives) - risk ↑ return ↑
Efficient Cash Management Strategies
Delaying and stretching
Accounts Payables
by paying accounts
payable as late as possible
and cash discounts
Plus (better bigger)
Speeding up collection of
Accounts Receivables
by changes in credit terms
and cash discounts
Minus (better smaller)
Efficient Inventory-
Production
Management
by increasing the raw
materials and finished
turnover, and decreasing
the production cycle
(better planning)
Minus (better smaller)
Delaying and stretching Accounts Payables
• The firm should pay its accounts payable as late as possible without
damaging its credit standing.
• But the firm should take advantage of cash discount, if any, offered by
suppliers for prompt payment.
• The reason is that, the cost of not taking a discount will work out
more than the cost of delaying payment.
Speeding up collection of Accounts Receivables
• By speeding up the collection of accounts receivables, the cash cycle would
come down, thereby resulting in saving a cost to the firm.
• But it should be done very carefully so that the customers are not lost.
• The average collection period of receivables can be reduced by changes in
credit terms, credit standards and collection policies.
• Cash discounts should be given for immediate payments or payments
within 10 days of invoice to encourage customers to speed up the
payments.
Efficient Inventory-Production Management
• Increasing the raw materials turnover by using more efficient
inventory control techniques.
• Decreasing the production cycle through better production planning,
scheduling and control techniques, which will lead to an increase in
the work-in-progress inventory turnover.
• Increasing the finished goods turnover through better forecasting of
demand and a better planning of production.
Efficient Cash Management
• Cash conversion cycle CCC = Average age of Inventory + Average
collection period - Average Accounts Payable period
• Cash turnover = Number of times cash is used during the year =
365/Cash cycle
• Minimum operating cash = It is the level of opening cash balance at
which a firm would meet all obligations and is computed by dividing
total annual outlays by the cash turnover
• Or total operating cashflow divided by cash turnover
Example:
• Let us assume that a firm currently takes 40 days to pay its suppliers,
allows 75 days to collect receivables and a gap of 90 days between
purchase of raw materials and the sale of finished goods. Total
operating annual outlay = $250 000.
• So, current cash cycle =
• 90 days + 75 days - 40 days = 125 days
• So, cash turnover =
• 365/125 = 2.92 or 3 days
• So, minimum operating cash =
• $250,000/2.92 days = $85,616.44
Example:
• Now what if:
• Accounts payable increases by 15 days
• Average age of inventory reduces by 20 days
• Speeds up collection by 25 days.
• New cash cycle, new cash turnover, new minimum operating cash?
New cash cycle, new cash turnover, new
minimum operating cash:
• The new cash cycle would be => (90-20) + (75-25) - (40+15)
• => 70 + 50 - 55 => 65 days
• So, the new cash turnover would be = 365/65 = 5.6 days
• So, the new minimum operating cash requirement = $250,000/5.6
days = $44,642.86 or $44,643
Efficient cash management: result
• Difference in minimum operating cash requirement =>
• $85,616 (old) - $44,643 (new) = $40,973 – we could this amount of
cash
• This is the result of efficient cash management
Cash balance
• Surplus cash – large cash balance – buying securities (investing) – few
transactions - but higher opportunity costs of maintaining cash
• Optimal cash – can invest excess cash for return and have enough
cash for future
• Lack of cash – small cash balance – selling securities – many
transactions
Optimal cash balance by Baumol and
Miller-Orr models
• The main objective of cash management is an optimal cash balance
• Optimal balance means a position when the cash balance amount is
on the most invest the excess cash for a return and at the same time
have sufficient liquidity for future needs
• The question is how to determine the optimal cash balance?
• By Baumol and Miller-Orr offer cash models
The Baumol model is based on the following
assumptions:
• The firm is able to forecast cash requirements
• The firm’s payouts are constant
• The opportunity cost of holding is constant
• Transaction costs for all conversions of securities into cash are
constant
• A company sells securities and realises cash, and this cash is used to
make payments.
• As the cash balance decreases and reaches a point, the financial
manager tops up its cash balance by selling marketable securities
available with it and this pattern continues.
The Baumol model
• Financial Manager decisions:
• If cash balance ↓ - selling securities - making payments -
• cash balance ↓ again … =//=
Limitations of the Baumol Model
• The model assumes constant rate of use of cash which is a
hypothetical assumption and is not possible in practice by a firm.
• The model assumes fixed nature of cash withdrawal which is Cash
payments are not often predictable also not realistic.
• Transaction cost is also difficult to measure in advance since it
depends on the type of investment as well as the maturity period.
• This model is concerned only with transaction balances and not with
precautionary balances.
Baumol Model
• The model can determine the optimum amount of cash for a company to
hold under conditions of certainty. The objective is to minimize the sum of
the fixed costs of transactions and the opportunity cost of holding cash
balances that do not yield a return.
• The optimal level of cash is determined using the following formula:
• Optimal level of cash = 𝑂𝐶𝐿 = 2𝐹 𝑇 𝐼
F = Fixed costs of a transaction
T = Total cash required for the specified time period
I = Interest rate on marketable securities
Baumol Example:
• A Company estimates a cash requirement of $2,000,000 for a 1 month
period. The opportunity interest rate is 6% per annum, which works out to
0.5 percent per month. The transaction cost for borrowing or withdrawing
funds is $150.
• Optimal level of cash = √(2 x $150 x $2,000,000) / 0.005 => $346,410.16
• With the above optimal transaction size, we can now find the number of
transactions required.
• Number of transactions required = $2,000,000 / $346,410.16 => 5.77 or 6
transactions during the month.
Baumol Question 1:
• Find out the optimum cash balance using Baumol's Model?
• Annual cash needed $4.800.000
• Transaction cost $90 per conversion
• Interest rate 9%
Baumol Answer 1:
• As per Baumol's Model
• C = Cash required each time to restore balance to minimum cash
• F= Total cash required during the year = $4.800.000
• T= Cost of each transaction between cash and marketable securities = $90
• I = Rate of interest on marketable securities = 9%
• 𝑂𝐶𝐿 = 2𝐹 𝑇 𝐼 = $ 97.979.59
Miller-Orr model
• When the cash payments are uncertain, Miller-Orr model can be used
• This model places upper and lower limits on cash balances
• When the upper limit is reached, a transfer of cash to marketable
securities is made; when the lower limit is reached, a transfer from
securities to cash is made.
• As long as the cash balance stays within the limits, no transaction
occurs.
Miller-Orr model
• Upper limit of cash balance is reached - a transfer of cash to
marketable securities is made (buying securities)
• Lower limit is reached - a transfer from securities to cash is made
(selling securities)
Miller-Orr model
• The various factors in this model are fixed costs of a securities
transaction (F) which is assumed to be the same for buying and
selling, the daily interest rate on marketable securities (I) and
variance of the daily net cash flows, represented by σ2.
Miller-Orr model
• This model assumes that the cash flows are random.
• According to this model, the optimal cash balance z is computed as
follows:
• Z = 3√(3FV)/ 4I
• The various factors in this model are fixed costs of a securities
transaction (F), the daily interest rate on marketable securities (I) and
variance of the daily net cash flows, represented by V.
Miller-Orr Example:
• Fixed cost of a securities transaction = $5
• Variance of daily net cash flows = $25
• Daily interest rate on securities = 0.0003 (10% per annum, so
10%/360 days = 0.0003 daily)
• Optimal cash balance OCB = ?
• 3√(3 x $5 x $25) / (4 x 0.0003) => $67.86
• (or) $68 rounded off

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Meeting 4 - Cash management (Financial Management)

  • 2. • 1. Explain the concept of cash management. • 2. Explain how to improve cash management efficiency. • 3. Explain the benefits of cash management, speed up cash income and slow down cash expenditures. • 4. Ability to calculate optimal cash balance (Baumol model, and Miller-Orr model).
  • 3. Concept of cash • Though cash hold the smallest portion of total current assets. However, cash is both the beginning and end of working capital cycle – cash, inventories, receivables and cash. • It is the cash, which keeps the business going. Hence, every enterprises has to hold necessary cash for its existence. • Moreover, steady and healthy circulation of cash throughout the entire business operations is the basis of business solvency.
  • 4. Concept of cash • Cash may be interpreted under two concepts. • In narrow sense, cash is very important business asset, but although coin and paper currency can be handled, the major part of the cash of most enterprises is in the form of bank checking accounts, which represent claims to money rather than tangible property. • While in broader sense, cash consists of legal tender, cheques, bank drafts, money orders and demand deposits in banks.
  • 5. Cash Management • Is a process of: • collecting cash • managing cash • using cash for investing
  • 6.
  • 8. Motivation for Holding Cash Transaction Motive • Companies need to be able to pay bills • Companies need a cash reserve in order to balance short-term cash inflows and outflows since these are not perfectly matched • Measure: quick ratio Precautionary motive • Companies need to avoid uncertainty in future • Companies need a cash reserve in case there will be unexpected demands for cash in future • Measure: volatility of operating cash flows Speculative motive • Companies need cash reserves for any investment opportunities • Companies need to get profit making opportunities from fluctuations in commodity prices, security prices, interest rates, and foreign exchange rates.
  • 9. Transaction Motive • Firms need cash to meet their transaction needs. • The collection of cash (from sale of goods and services) is not perfectly synchronised with the payment of cash (for purchase of goods and services). • Hence, some cash balance is required as a buffer.
  • 10. Precautionary Motive • There may be some uncertainty about the cash inflows from sale of goods and services. • Likewise, there may be uncertainty about cash outflows on account of purchases. • To protect itself against such uncertainties, a firm may require some cash balance.
  • 11. Speculative motive • Companies may build up cash reserves in order to take advantage of any attractive investment opportunities that may arise. • These opportunities may include fluctuations in commodity prices, security prices, interest rates, and foreign exchange rates. • If a company has significant speculative cash reserves for which it cannot see an advantageous use, it may choose to enhance shareholder value by returning them to shareholders (dividends)
  • 12. Investing surplus cash • If a firm’s need to hold cash is reduced, the funds can be invested in a number of different short-term securities • Including Treasury bills, certificates of deposit, commercial paper, repurchase agreements, banker’s acceptances, and short-term tax exempts
  • 13. INVESTMENT OF SURPLUS FUNDS • Companies often have surplus funds for short periods of time before they are required for capital expenditures, loan repayment, or some other purpose. • Instead of allowing these surplus funds to accumulate in current account where they earn no interest, companies invest them in a variety of short-term instruments like term deposits with banks, money market mutual funds, and so on. • Managing the investment of surplus funds is a very important responsibility of the financial manager. This has become more so in recent years, thanks to higher corporate liquidity and wider range of investment options.
  • 14. Investment Portfolio: Three Segments The ready cash segment reserves for the company's cash account to meet operational needs The controllable cash segment outflows like taxes, dividend, interest payments, and repayments of borrowings The free cash segment surplus funds invested in short-term instruments to generate income
  • 15. Investment Portfolio: Three Segments • The ready cash segment represents a reserve for the company's cash account. It is meant to increase the cash resources of the company to meet unanticipated operational needs. Investments in this segment must necessarily be highly liquid in nature. • The controllable cash segment represents that part of the investment portfolio which is meant to meet the needs of knowable outflows like taxes, dividend, interest payments, and repayments of borrowings. Ideally, investments in this segment must be matched in size and maturity to known future outflows. • The free cash segment represents that part of the investment portfolio which is meant neither to increase unforeseen current cash needs nor to meet known future outflows. It essentially represents surplus funds with the firm which has been invested in short-term instruments to generate income, without much concern for liquidity or maturity.
  • 16. Criteria for Evaluating Investment Instruments Safety Refers to the probability of getting back the amount invested Liquidity Refers to the ability of the investor to convert instrument into cash without loss Yield the return earned from instrument by way of interest or dividend Maturity refers to the life of the instrument
  • 17. Criteria for Evaluating Investment Instruments • Safety refers to the probability of getting back the amount invested. Treasury bills may be regarded as the safest of all the instruments as they represent the obligations of the government. The safety of the other instruments depends on the type of the instrument and the issuer. A high degree of safety is essential for an instrument to be considered for inclusion in the short-term investment portfolio of the firm. • Liquidity refers to the ability of the investor to convert it into cash on short notice without incurring a loss. An instrument may be quite safe if it is held till maturity, but it may not be possible to sell it prematurely without suffering a loss. For a traded instrument, a large and active secondary market ensures liquidity. For a non-traded instrument, liquidity is high if the penalty for premature liquidation is negligible. • Yield is the return earned from it by way of interest, dividend, and capital appreciation. Some instruments like Treasury bills and commercial paper do not pay interest, but they are sold at a discount and redeemed at face value. Yield has to be measured in post-tax terms, taking into account the tax rate applicable to the returns earned by the investment instrument. • Maturity refers to the life of the instrument. While some instruments (like Treasury bills) have fixed original maturities, others (like certificates of deposit) can have tailormade maturity. Generally, the longer the maturity, the greater the yield.
  • 18. Investment Options • Fixed Deposits with Banks • Mutual Fund Schemes • Treasury Bills • G-Secs • Commercial Paper • Certificates of Deposits • Inter-Corporate Deposits • Ready Forwards
  • 19. Investment instruments T-bills (short term) G-secs (long term) - risk ↓ return ↓ Deposits - risk average return average Futures/options (derivatives) - risk ↑ return ↑
  • 20. Efficient Cash Management Strategies Delaying and stretching Accounts Payables by paying accounts payable as late as possible and cash discounts Plus (better bigger) Speeding up collection of Accounts Receivables by changes in credit terms and cash discounts Minus (better smaller) Efficient Inventory- Production Management by increasing the raw materials and finished turnover, and decreasing the production cycle (better planning) Minus (better smaller)
  • 21. Delaying and stretching Accounts Payables • The firm should pay its accounts payable as late as possible without damaging its credit standing. • But the firm should take advantage of cash discount, if any, offered by suppliers for prompt payment. • The reason is that, the cost of not taking a discount will work out more than the cost of delaying payment.
  • 22. Speeding up collection of Accounts Receivables • By speeding up the collection of accounts receivables, the cash cycle would come down, thereby resulting in saving a cost to the firm. • But it should be done very carefully so that the customers are not lost. • The average collection period of receivables can be reduced by changes in credit terms, credit standards and collection policies. • Cash discounts should be given for immediate payments or payments within 10 days of invoice to encourage customers to speed up the payments.
  • 23. Efficient Inventory-Production Management • Increasing the raw materials turnover by using more efficient inventory control techniques. • Decreasing the production cycle through better production planning, scheduling and control techniques, which will lead to an increase in the work-in-progress inventory turnover. • Increasing the finished goods turnover through better forecasting of demand and a better planning of production.
  • 24. Efficient Cash Management • Cash conversion cycle CCC = Average age of Inventory + Average collection period - Average Accounts Payable period • Cash turnover = Number of times cash is used during the year = 365/Cash cycle • Minimum operating cash = It is the level of opening cash balance at which a firm would meet all obligations and is computed by dividing total annual outlays by the cash turnover • Or total operating cashflow divided by cash turnover
  • 25. Example: • Let us assume that a firm currently takes 40 days to pay its suppliers, allows 75 days to collect receivables and a gap of 90 days between purchase of raw materials and the sale of finished goods. Total operating annual outlay = $250 000. • So, current cash cycle = • 90 days + 75 days - 40 days = 125 days • So, cash turnover = • 365/125 = 2.92 or 3 days • So, minimum operating cash = • $250,000/2.92 days = $85,616.44
  • 26. Example: • Now what if: • Accounts payable increases by 15 days • Average age of inventory reduces by 20 days • Speeds up collection by 25 days. • New cash cycle, new cash turnover, new minimum operating cash?
  • 27. New cash cycle, new cash turnover, new minimum operating cash: • The new cash cycle would be => (90-20) + (75-25) - (40+15) • => 70 + 50 - 55 => 65 days • So, the new cash turnover would be = 365/65 = 5.6 days • So, the new minimum operating cash requirement = $250,000/5.6 days = $44,642.86 or $44,643
  • 28. Efficient cash management: result • Difference in minimum operating cash requirement => • $85,616 (old) - $44,643 (new) = $40,973 – we could this amount of cash • This is the result of efficient cash management
  • 29. Cash balance • Surplus cash – large cash balance – buying securities (investing) – few transactions - but higher opportunity costs of maintaining cash • Optimal cash – can invest excess cash for return and have enough cash for future • Lack of cash – small cash balance – selling securities – many transactions
  • 30. Optimal cash balance by Baumol and Miller-Orr models • The main objective of cash management is an optimal cash balance • Optimal balance means a position when the cash balance amount is on the most invest the excess cash for a return and at the same time have sufficient liquidity for future needs • The question is how to determine the optimal cash balance? • By Baumol and Miller-Orr offer cash models
  • 31. The Baumol model is based on the following assumptions: • The firm is able to forecast cash requirements • The firm’s payouts are constant • The opportunity cost of holding is constant • Transaction costs for all conversions of securities into cash are constant • A company sells securities and realises cash, and this cash is used to make payments. • As the cash balance decreases and reaches a point, the financial manager tops up its cash balance by selling marketable securities available with it and this pattern continues.
  • 32. The Baumol model • Financial Manager decisions: • If cash balance ↓ - selling securities - making payments - • cash balance ↓ again … =//=
  • 33. Limitations of the Baumol Model • The model assumes constant rate of use of cash which is a hypothetical assumption and is not possible in practice by a firm. • The model assumes fixed nature of cash withdrawal which is Cash payments are not often predictable also not realistic. • Transaction cost is also difficult to measure in advance since it depends on the type of investment as well as the maturity period. • This model is concerned only with transaction balances and not with precautionary balances.
  • 34. Baumol Model • The model can determine the optimum amount of cash for a company to hold under conditions of certainty. The objective is to minimize the sum of the fixed costs of transactions and the opportunity cost of holding cash balances that do not yield a return. • The optimal level of cash is determined using the following formula: • Optimal level of cash = 𝑂𝐶𝐿 = 2𝐹 𝑇 𝐼 F = Fixed costs of a transaction T = Total cash required for the specified time period I = Interest rate on marketable securities
  • 35. Baumol Example: • A Company estimates a cash requirement of $2,000,000 for a 1 month period. The opportunity interest rate is 6% per annum, which works out to 0.5 percent per month. The transaction cost for borrowing or withdrawing funds is $150. • Optimal level of cash = √(2 x $150 x $2,000,000) / 0.005 => $346,410.16 • With the above optimal transaction size, we can now find the number of transactions required. • Number of transactions required = $2,000,000 / $346,410.16 => 5.77 or 6 transactions during the month.
  • 36. Baumol Question 1: • Find out the optimum cash balance using Baumol's Model? • Annual cash needed $4.800.000 • Transaction cost $90 per conversion • Interest rate 9%
  • 37. Baumol Answer 1: • As per Baumol's Model • C = Cash required each time to restore balance to minimum cash • F= Total cash required during the year = $4.800.000 • T= Cost of each transaction between cash and marketable securities = $90 • I = Rate of interest on marketable securities = 9% • 𝑂𝐶𝐿 = 2𝐹 𝑇 𝐼 = $ 97.979.59
  • 38. Miller-Orr model • When the cash payments are uncertain, Miller-Orr model can be used • This model places upper and lower limits on cash balances • When the upper limit is reached, a transfer of cash to marketable securities is made; when the lower limit is reached, a transfer from securities to cash is made. • As long as the cash balance stays within the limits, no transaction occurs.
  • 39. Miller-Orr model • Upper limit of cash balance is reached - a transfer of cash to marketable securities is made (buying securities) • Lower limit is reached - a transfer from securities to cash is made (selling securities)
  • 40. Miller-Orr model • The various factors in this model are fixed costs of a securities transaction (F) which is assumed to be the same for buying and selling, the daily interest rate on marketable securities (I) and variance of the daily net cash flows, represented by σ2.
  • 41. Miller-Orr model • This model assumes that the cash flows are random. • According to this model, the optimal cash balance z is computed as follows: • Z = 3√(3FV)/ 4I • The various factors in this model are fixed costs of a securities transaction (F), the daily interest rate on marketable securities (I) and variance of the daily net cash flows, represented by V.
  • 42. Miller-Orr Example: • Fixed cost of a securities transaction = $5 • Variance of daily net cash flows = $25 • Daily interest rate on securities = 0.0003 (10% per annum, so 10%/360 days = 0.0003 daily) • Optimal cash balance OCB = ? • 3√(3 x $5 x $25) / (4 x 0.0003) => $67.86 • (or) $68 rounded off