If the total cash requirement of a company is ₹ 2 crore next year, the opportunity cost of funds is 15 percent per annum and the cost of conversion from securities to cash per transaction is ₹ 150, the optimum cash balance as per Baumol’s Model will be :
₹ 2 lakhs
Option 1 — ₹ 2 lakhs is correct.
Baumol's model treats cash management like inventory (EOQ) management: it balances the transaction cost of converting securities into cash against the opportunity cost of holding idle cash. The optimum (economic) cash balance is:
\( C^* = \sqrt{\dfrac{2 \times b \times T}{i}} \)
where \( T \) = total annual cash need, \( b \) = fixed cost per conversion, \( i \) = opportunity cost rate. Substituting \( T = 2{,}00{,}00{,}000 \), \( b = 150 \), \( i = 0.15 \):
\( C^* = \sqrt{\dfrac{2 \times 150 \times 2{,}00{,}00{,}000}{0.15}} = \sqrt{\dfrac{6{,}00{,}00{,}00{,}000}{0.15}} = \sqrt{4 \times 10^{10}} = 2{,}00{,}000 \)
So the firm should convert securities into cash in lots of ₹ 2 lakhs at a time. Raising cash in larger lots would cut transaction frequency but tie up more idle funds; \( C^* \) is the trade-off point that minimises total cost.
Takeaway: Feed the three inputs into the square-root formula to obtain the ₹ 2 lakh optimum lot size.
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