26. Your firm\'s management of its cash position is based on the Miller-Orr mode

Question

26. Your firm's management of its cash position is based on the Miller-Orr model. The weekely standard deviation of the disbursements is $8.600. The applicable weekly interest rate is 0.054 percent and the fixed cost of transferring funds is S65. Suppose your firm's target cash balance, C 68,830. (i) What lower cash balance limit (L) is consistent with this information. (ii) Find U', the firm's implied maximum cash balance limit. (iii) Find your firm's average cash balance held over time. (iv)Using your answer to part (ii), find the average dollar cost incurred by the firm from holding cash over a two-week period.

Explanation / Answer

Solution: As per Miller Orr model,

C* = L + (3/4 x F x s^2/R)^(1/3) ....(i) Target Cash Balance

U* = 3 x C* - 2xL .... (ii) Maximum Cash Balance

Average Cash Balance = (4 x C* -L)/3 .... (iii)

Here, C* = Target Cash Balance, L = Lower Limit, F = Transaction Cost, s=Std Dev per period, R=Interest Rate per period

Given- C*=$68,830, IR = 0.00054, F=$65, s=$8600

Now putting all the given values in (i)

68,830 = L + (3/4 x 65 x 8600^2/0.00054) ^(1/3)

68,830 = L + (18,830)

L= $50,000

Now, putting all in (ii)

U* = 3 x 68,830 - 2 x 50,000

U* = $106,490

Now, putting all in (iii)

Avg Cash Balance = (4 x 68,830 - 50,000)/3 = $75,107

To, calculate averge dollar cost over two week period, multiply the Avg Cah Balance with two week Interest Rate.

Avg Dollar Cost = $75,107 x (2x0.00054) = $ 81.12

Hope it helps!

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.