Question

A firm earns 5% on its marketable securities. It costs $500 in commissions to convert the securities into cash. If the firm has annual cash disbursements of $20,000,000. What is the optimal conversion amount? What is the total cost of carrying cash?

Answer #1

**Solution)** According to the Banmol Model,
Optimal Conversion amount = Sqrt(2*b*T/r)

where, b = cost of conversion = $500

T = Total amount of cash = $20,000,000

r = interest rate earned = 5%

Therefore, **Optimal Conversion amount =
Sqrt(2*500*20000000/5%) = $632,455.53**

Total number of conversions = Total cash/Optimal Conversion amount = 20000000/632,455.53 = 31.622

= 32

Average cash balance = $632,455.53/2 = $316,227.77

Total cost of carrying cash = 32*500 + 316,227.77*5%

= 16000 + 15811.3885

**Total cost of carrying cash = $31811.3885 =
$31,811.39**

**Please comment in case of any doubts or clarifications
required.**

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