tutorial 1 - cash management

key information:

• company - barrow plc.

• objective - improve cash management strategy

• annual cash requirement [to pay obligations] - £15,000,000

• fixed transaction cost per cash raise - £700

• opportunity cost of holding cash - 10% per annum

• preferred buffer cash balance - £10,000

• daily variance of cash balance - £9,000,000

formula sheet:

a. applying the Baumol model to manage cash balances

the Baumol model is similar to the economic order quantity [EOQ] model but applied to cash management. it helps determine how much cash a company should withdraw at a time to minimise transaction and opportunity costs

given data:

• total cash requirement per yr [T] = 15,000,000

• fixed cost per transaction [F] = 700

• opportunity cost per rate [R] = 10%

• formula for optimal order quantity [i.e. the amount of cash withdrawn each time]:

a. i. compute optimal order quantity

substituting the given values:

this means barrow plc. should withdraw £458,257.57 each time they need cash

a. ii. compute the average cash balance

since cash is withdrawn in fixed amounts and spent over time, the average cash balance is simply:

so, the company will, on average, hold £229,128.78 in cash

a. iii. compute the no. of transaction per yr

the no. of times the company needs to withdraw cash annually is:

this means barrow plc. will need to withdraw cash about 33 times a yr

a. iv. compute the trading costs and opportunity costs

• total trading costs:

  • = fixed cost per transaction x no. of transactions

  • = 700 × 32.73 = 22,912.88

• total opportunity costs:

  • = average cash balance x opportunity cost rate

  • = 229,128.78 × 0.10 = 22,912.88

• total cost:

  • = trading costs + opportunity costs

  • = 22,912.88 + 22,912.88 = 45,825.76

so, the total cost of managing cash using the baumol model is £45,825.76 per yr

b. applying the Miller-Orr model

the miller-orr model is useful when cash inflows and outflows are uncertain. it sets upper and lower limits for cash balances and determines a target balance

given data:

• lower limit [L] = 10,000

• fixed cost per transaction [F] = 700

• opportunity cost rate [R] = 10%

• variance of daily cash flows = 9,000,000

• so, standard deviation of daily cash flows:

• constant K for miller-orr formula:

  • [1 + K]^365 = 1 + R

  • as R = 10%, when rearranged, K = 0.000261

b. i. compute target cash balance

the miller-orr target cash balance formula:

substituting the values:

so the target cash balance is £36,257.23

b. ii. compute the upper limit

the upper limit is given by:

b. iii. compute the average cash balance

the miller-orr average cash balance is:

b. iv. compute the spread

the spread in the miller-orr model is the difference between the upper limit and the lower limit, which is:

c. effect of a decrease in opportunity cost to 7%

if the opportunity cost of holding cash decreases to 7%, it impacts both models:

baumol model adjustments

miller orr model adjustments

new target cash balance:

d. evaluation of the usefulness of baumol and miller orr models

baumol model

strengths

• simply to apply and understand, making it easy for financial managers

• helps minimise transaction and opportunity costs by determining an optimal cash withdrawal amount

• suitable for firms with predictable and steady cash flows

limitations

• assumes constant cash outflows, which is unrealistic for a business with fluctuating cash needs

• requires regular and schedules withdrawals, which may not be practical for barrow plc.

• doesn’t account for uncertainty in cash flows, making it less useful in volatile environments

applicability to barrow plc:

• since barrow plc. likely has uncertain cash needs, the baumol model may not be the most effective choice

• it works well for planned cash management but lacks flexibility in real-world conditions

miller orr model

strengths

• designed to handle uncertain cash flows, making it more realistic for barrow plc.

• establishes upper and lower cash limits, allowing automatic decisions on cash transfers

• reduces unnecessary cash holdings while keeping a buffer for unexpected expenses

• helps balance transaction costs with the opportunity cost of holding excess cash

limitations

• more complex than the baumol model, requiring estimates of variance in cash flows

• requires constant monitoring to ensure cash stays within limits

• assumes a normal distribution of cash movements, which may not always be accurate

applicability to barrow plc:

• since barrows plc’s cash balance varies daily [variance = £9 mil.], the miller orr model is more suitable

• it allows barrow plc to adjust its cash balance dynamically based on inflows and outflows

final recommendation

• miller orr model is the better choice for barrow plc. due to its adaptability to fluctuating cash flows

• the baumol model may still be useful for forecasting and basic cash planning but lacks the flexibility required for real world conditions

• a combined approach [using baumol model for planning and miller ott for daily management] may be an effective strategy