Gemini Inc.'s optimal cash transfer amount, using the Baumol model, is $60,000.The firm's fixed cost per cash transfer of marketable securities to cash is $180, and the total cash needed for transactions annually is $960,000.On what opportunity cost of holding cash was this analysis based?
A) 19.2%
B) 10.4%
C) 6.3%
D) 12.1%
E) 9.6%

Question

Quizplus · Accepted Answer

The Baumol model of cash management is used to determine the optimal cash conversion amount to minimize the sum of the holding cost and the transaction cost. The formula to calculate the optimal cash transfer amount (C*) is given by:$$ C* = \sqrt{\frac{2FB}{i}} $$where:- $ C* $ is the optimal cash transfer amount,- $ F $ is the fixed cost per cash transfer,- $ B $ is the total cash needed for transactions annually,- $ i $ is the opportunity cost of holding cash (as a decimal).Given that $ C* = \$60,000 $, $ F = \$180 $, and $ B = \$960,000 $, we can rearrange the formula to solve for $ i $:$$ i = \frac{2FB}{C*^2} $$Plugging in the given values:$$ i = \frac{2 \times 180 \times 960,000}{60,000^2} = \frac{345,600,000}{3,600,000} = 0.096 $$Converting $ i $ to a percentage gives us 9.6%.