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CA Intermediate · Financial Management and Strategic Management · Treasury and Cash Management

In the Baumol model of cash management, which of the following changes would increase the optimal transaction size of cash conversion (C), other things remaining unchanged?

A fall in the interest rate on marketable securities increases the optimal conversion size in the Baumol model. Since C equals the square root of 2UP divided by S, a lower opportunity cost of holding cash makes larger, less frequent conversions cheaper than frequent small ones.

  1. AA fall in the fixed cost per conversion of marketable securities into cash
  2. BA fall in the annual interest rate earned on marketable securitiesCorrect
  3. CA fall in the total cash requirement for the period
  4. DA rise in the annual interest rate earned on marketable securities

Explanation

Baumol's model gives C = sqrt(2 x U x P / S), where U is cash need, P is cost per conversion and S is the opportunity cost rate. C rises when U or P rises, or when S falls. A lower interest rate makes holding cash cheaper, so larger conversions are optimal. A rise in the rate would reduce C, so that option is wrong.

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