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How to use Miller Orr Model?

Cash is essential to meet day to day requirement for smoothly running a business. And managing the cash is also necessary because if cash is less than requirement level then company have to borrow the fund which increases the company’s interest paying burden and if more cash is available in comparison to required level in that case the unnecessary cash is acted as wastage for a company. To manage day to day cash and fulfil the requirement of the business Miller Orr Model is used.  

In this model the idle cash and the cash level is maintained properly. The below diagram explain the model briefly:

In above diagram the vertical line shows cash in rupees and horizontal line shows time period. The L line shows the minimum level or limited level of cash beyond which cash doesn’t go. Or you can say the safety level of company.  The Z line or point shows the target level or return point of cash should be available in a company. The H line shows the excess level of cash available in a company. The cash between H and Z is idle and to manage this cash efficiently it is used by purchasing the marketable securities. If the cash is below from Z point or level then those marketable securities which are purchased earlier are sold to meet the cash requirement of the company. So, that company does not need any borrowed funds to meet the cash requirement.

Formula:

Return point = Limited amount + 1/3 spread

Spread = 3[(3*transaction cost*variance of cash flows)/4*Daily Interest rate] ^1/3

OR

Spread = 3[(3*transaction cost*variance of cash flows)/4*annual Interest rate/365] ^1/3

Upper limit = 3z – 2l

Variance of cash = σ2 or (standard deviation) 2

Example: Company PQR has decided to maintain limited amount of cash which is Rs.25, 000. The cash variance is 5,7,60,000 (standard deviation 2400). The selling and purchasing cost of marketable securities is Rs. 5,000. The annual interest rate is 6.2% Find out the targeted return point.

Solution:  Optimal return point = Limited amount + 1/3 (3[(3/4*transaction cost*variance of cash flows)/Interest rate] ^1/3)

= 25,000 + 1/3 (3[(3*5000*5760000)/4*(0.062/365)] ^1/3)

= 25,000 + 1/3 *(3[86, 40, 00, 00,000/0.00068]^1/3)

= 25,000 + 1/3 *(3[12, 70, 58, 82, 35, 29, 411.76] ^1/3)

= 25,000 + 1/3 * 1, 50,819.047

= 25,000 + 50,273.016

= Rs.75, 273.016

Example: Mehta & Sons wants to maintain minimum Rs.10, 000 cash balance. The daily variance of cash is Rs. 50, 00,000 and transaction cost for purchasing and selling securities is Rs. 150. The daily interest rate is 0.007%. Find out the return point and upper limit of cash balance with the help of Miller Orr model.

Solution: Optimal return point = Limited amount + 1/3 (3[(3/4*transaction cost*variance of cash flows)/Interest rate] ^1/3)

= 10,000 + 1/3 (3[(3*150*50, 00,000)/4*0.00007] ^1/3)

= 10,000 + 1/3 (3[2, 25, 00, 00, 000/0.00028] ^1/3)

= 10,000 + 1/3 (3*[80, 35, 71, 42, 85,714.29] ^1/3)

= 10,000 + 1/3* 60,089.15

= 10,000 + 20,029.72

= 30,029.72

Upper limit = 3z-2l

= 3*30, 029.72 – 2*10,000

= 90, 089.16 – 20, 000

= 70, 089.16

 

 

 

 

 

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