Question

The following information is available concerning a firm’s cash

       Total amount of cash needed for transaction balances      : $2,600,000/month

       Current interest rate on marketable securities            : 10 percent

       Cost per transaction of buying and selling securities : $1,000

       Assume the firm does not carry any safety cash balances. Find the optimal cash     balances, average cash balances and the total cost of carry cash using Baumol model.

Draw and explain the model using your numbers and indicate decisions concerning buying and selling securities.

Answer 1

Holding Cost = k*(C/2)

K= Current interest rate on marketable securities =10 percent=0.1

C=Amount of cash replaced

C/2=Average Cash Balance

Transaction Cost = c*(T/C)

c=Cost per transaction=$1000

T=Total amount of cash needed per year=$2600000*12=$31,200,000

For Optimum Cash balance (minimum total cost:

Holding Cost = Transaction Cost

0.1*(C/2)=1000*(31,200,000/C)

C^2=(1000*2/0.1)*31,200,000=20000*31,200,000

C=SQRT(20000*31,200,000)

C=$789,937

Optimal Cash Balance=C/2=$394,968

Total Cost = Holding Cost + Transaction Cost =k*C=0.1*$789,937=$78,994

X=(C/2)	A=0.1*X	B=1000*31.2million/(2X)	C=A+B
Average Cash Balance	Holding Cost	Transaction Cost	Total Cost
$100,000	$10,000	$156,000	$166,000
$200,000	$20,000	$78,000	$98,000
$300,000	$30,000	$52,000	$82,000
$394,968	$39,497	$39,497	$78,994
$500,000	$50,000	$31,200	$81,200
$600,000	$60,000	$26,000	$86,000
$700,000	$70,000	$22,286	$92,286

Note: Total Cost is MINIMUM when Holding Cost=Transaction Cost