Cash Conversion Cycle Parramore Corp has $12 million of sales, $3 million of inventories, $3.25 million of receivables, and $1.25 million of payables. Its cost of goods sold is 75% of sales, and it finances working capital with bank loans at an 8% rate. What is Parramore’s cash conversion cycle (CCC)? If Parramore could lower its inventories and receivables by 10% each and increase its payables by 10%, all without affecting sales or cost of goods sold, what would be the new CCC, how much cash would be freed up, and how would that affect pretax profits?

1. Cash conversion circle = 122+99 - 51 = 170 days

2. Revised Cash conversion circle = 110+89 - 56 = 143 days

3. The amount of cash to be freed up = (0.1 x $3m) + (0.1 x $3.25) + (0.11 x $1.25) = $762,500

4. Pretax profits will be increased because lower inventory level leads to lower cost of sales and higher gross profit which means higher net profits

Explanation:

Cash conversion Cycle = Days Inventory Outstanding + Days Sales Outstanding - Days Payable Outstanding.

Days Inventory outstanding = Inventory / Cost of Sales x 365 = $3 million / (0.75 x $12 million) x 365 = 122 days

Days Sales outstanding = Account receivable / Sales x 365 = $3.25 million / $12 million x 365 = 99 days

Days Purchases Outstanding = Accounts Payable / Cost of Sales x 365 = $1.25 million /  (0.75 x $12 million) x 365 = 51 days

Therefore Cash conversion circle = 122+99 - 51 = 170 days

2. If Parramore could lower its inventories and receivables by 10% each and increase its payables by 10%, all without affecting sales or cost of goods sold, what would be the new CCC,

Days Inventory outstanding = Inventory / Cost of Sales x 365 = [( 0.9 x $3 million) / (0.75 x $12 million)] x 365 = 110 days

Days Sales outstanding = Account receivable / Sales x 365 = [(0.9 x $3.25 million) / $12 million] x 365 = 89 days

Days Purchases Outstanding = Accounts Payable / Cost of Sales x 365 = [(1.1 x $1.25 million) /  (0.75 x $12 million)] x 365 = 56 days

Therefore revised Cash conversion circle = 110+89 - 56 = 143 days

3. The amount of cash to be freed up = (0.1 x $3m) + (0.1 x $3.25) + (0.11 x $1.25) = $762,500

4. Pretax profits will be increased because lower inventory level leads to lower cost of sales and higher gross profit which means higher net profits

start by isolating the variable on one side by adding 43w^2 to both sides.   the equation will read:

25w^2+5=0

*subtract 5 from both sides*

25w^2=-5

*divide both sides by 25*

w^2=-1/5

*take the square root of both sides*

w=√(-1/5)

the square root of -1 is i.   the square root of 5 remains √5

the answer is i/√5.

hope this