Chapter 15, Problem 1P

Summary Introduction

To determine: The cash conversion cycle, the new cash conversion cycle, the amount of cash that would be freed up and the effect on pretax profits.

Introduction:

Cash Conversion Cycle:

The cash conversion cycle refers to the time period which starts from the production of the products to selling of the products and lasts until the time the customer receives the cash.

Explanation of Solution

Given information:

The amount of sales is $12 million.

The amount of inventories is $3 million.

The amount of receivables is $3.25 million.

The amount of payables is $1.25 million.

Cost of goods sold is 75% of sales.

The rate of interest on bank loans is 8%.

Calculation of the cash conversion cycle:

The formula to calculate the cash conversion cycle is,

$\begin{array}{c}\text{Cash}\text{Conversion}\text{Cycle}=\text{Inventory}\text{conversion}\text{period}\\ +\text{Average}\text{collection}\text{period}\\ -\text{Payment}\text{deferral}\text{period}\end{array}$

Substitute 60.83 days for inventory conversion period, 73 days for the average collection period and 30.41 days for the payables deferral period (refer working note) in the above formula.

$\begin{array}{c}\text{Cash}\text{Conversion}\text{Cycle}=121.67\text{ days}+98.85\text{ days}-50.69\text{ days}\\ =169.83\text{days}\end{array}$

The cash conversion cycle is 169.83 days or 170 days.

Now,

The inventories are reduced by 10%.

The receivables are reduced by 10%.

The payables are increased by 10%.

Calculation of the new cash conversion cycle:

The formula to calculate the cash conversion cycle is,

$\begin{array}{c}\text{Cash}\text{Conversion}\text{Cycle}=\text{Inventory}\text{conversion}\text{period}\\ +\text{Average}\text{collection}\text{period}\\ -\text{Payment}\text{deferral}\text{period}\end{array}$

Substitute 109.5 days for inventory conversion period, 88.97 days for the average collection period and 55.76 days for the payables deferral period (refer working note) in the above formula.

$\begin{array}{c}\text{Cash}\text{Conversion}\text{Cycle}=109.5\text{ days}+88.97\text{ days}-55.76\text{ days}\\ =143\text{days}\end{array}$

The new cash conversion cycle is 143 days.

Calculation of the total amount of cash freed up:

The formula to calculate the total amount of cash freed up is,

$\begin{array}{c}\text{Total}\text{cash}\text{freed}\text{up}=\text{Cash}\text{freed}\text{up}\text{for}\text{inventory}\\ +\text{Cash}\text{freed}\text{up}\text{for}\text{accounts}\text{receivable}\\ +\text{Cash}\text{freed}\text{up}\text{for}\text{accounts}\text{payable}\end{array}$

Substitute $300,082.14 for cash freed up for inventory, $324,821.89 for cash freed up for accounts receivable and (-$125,013.68) for cash freed up for accounts payable (refer working note) in the above formula.

$\begin{array}{c}\text{Total}\text{cash}\text{freed}\text{up}=\$300,082.14+\$324,821.89+\left(\$125,013.68\right)\\ =\$499,890.35\end{array}$

The total cash freed up is $499,890.35.

Calculation of the pre-tax profit:

The formula to calculate the pre-tax profit is,

$\text{Pre-tax}\text{profit}=\text{Total}\text{freed}\text{up}\text{cash}\times \text{Interest}\text{rate}$

Substitute $499,890.35 for the total cash freed up and 8% for the interest rate in the above formula.

$\begin{array}{c}\text{Pre-tax}\text{profit}=\$499,890.35\times 8\%\\ =\$39,991.228\end{array}$

The pre-tax profit is $39,991.228.

Working note:

Calculation of the cost of goods sold:

$\begin{array}{c}\text{Cost}\text{of}\text{goods}\text{sold}=\text{Sales}\times \text{Cost}\text{of}\text{goods}\text{sold}\text{percentage}\\ =\text{\$12,000,000}\times 75\text{\%}\\ =\text{\$9,000,000}\end{array}$

The cost of goods sold is $9,000,000.

Calculation of the inventory conversion period:

$\begin{array}{c}\text{Inventory}\text{conversion}\text{period}=\frac{\text{Inventory}}{\text{Cost}\text{of}\text{goods}\text{sold}\text{per}\text{day}}\\ =\frac{\$3,000,000}{\frac{\$9,000,000}{365}}\\ =\frac{\$2,000,000}{\$32,876.71}\\ =121.67\text{days}\end{array}$

The inventory conversion period is 121.67 days.

Calculation of the average collection period:

$\begin{array}{c}\text{Average}\text{collection}\text{period}=\frac{\text{Accounts}\text{receivable}}{\text{Sales}\text{per}\text{day}}\\ =\frac{\text{Accounts}\text{receivable}}{\frac{\text{Sales}}{\text{365}}}\\ =\frac{\$3,250,000}{\frac{\$12,000,000}{365}}\\ =98.85\text{days}\end{array}$

The average collection period is 98.85 days.

Calculation of the payable deferral period:

$\begin{array}{c}\text{Payment}\text{deferral}\text{period}=\frac{\text{Accounts}\text{payable}}{\text{Cost}\text{of}\text{goods}\text{sold}\text{per}\text{day}}\\ =\frac{\text{Accounts}\text{payable}}{\frac{\text{Cost}\text{of}\text{goods}\text{sold}}{\text{365}}}\\ =\frac{\$1,250,000}{\frac{\$9,000,000}{365}}\\ =50.69\text{days}\end{array}$

The payment deferral period is 50.69 days.

Calculation of the new amount of inventories:

$\begin{array}{c}\text{New}\text{inventories}=\text{Inventories}\times \left(1-\text{Reduced}\text{percentage}\right)\\ =\$3,000,000\times \left(1-0.10\right)\\ =\$2,700,000\end{array}$

The new amount of inventories is $2,700,000.

Calculation of the new amount of receivables:

$\begin{array}{c}\text{New}\text{receivables}=\text{Receivables}\times \left(1-\text{Reduced}\text{percentage}\right)\\ =\$3,250,000\times \left(1-0.10\right)\\ =\$2,925,000\end{array}$

The new amount of receivables is $2,925,000.

Calculation of the new amount of payables:

$\begin{array}{c}\text{New}\text{payables}=\text{Payables}\times \left(1+\text{Increased}\text{percentage}\right)\\ =\$1,250,000\times \left(1+0.10\right)\\ =\$1,375,000\end{array}$

The amount of new payables is $1,375,000.

Calculation of the new inventory conversion period:

$\begin{array}{c}\text{Inventory}\text{conversion}\text{period}=\frac{\text{Inventory}}{\text{Cost}\text{of}\text{goods}\text{sold}\text{per}\text{day}}\\ =\frac{\$2,700,000}{\frac{\$9,000,000}{365}}\\ =109.5\text{days}\end{array}$

The inventory conversion period is 109.5 days.

Calculation of the average collection period:

$\begin{array}{c}\text{Average}\text{collection}\text{period}=\frac{\text{Accounts}\text{receivable}}{\text{Sales}\text{per}\text{day}}\\ =\frac{\text{Accounts}\text{receivable}}{\frac{\text{Sales}}{\text{365}}}\\ =\frac{\$2,925,000}{\frac{\$12,000,000}{365}}\\ =88.97\text{days}\end{array}$

The average collection period is 88.97 days.

Calculation of the payable deferral period:

$\begin{array}{c}\text{Payment}\text{deferral}\text{period}=\frac{\text{Accounts}\text{payable}}{\text{Cost}\text{of}\text{goods}\text{sold}\text{per}\text{day}}\\ =\frac{\text{Accounts}\text{payable}}{\frac{\text{Cost}\text{of}\text{goods}\text{sold}}{\text{365}}}\\ =\frac{\$1,375,000}{\frac{\$9,000,000}{365}}\\ =55.76\text{days}\end{array}$

The payment deferral period is 55.76 days.

Calculation of the cash freed up for inventory:

$\begin{array}{c}\text{Cash}\text{freed}\text{up}\text{for}\text{inventory}=\text{Change}\text{in}\text{inventory}\times \text{Cost}\text{of}\text{goods}\text{sold}\text{per}\text{day}\\ \text{=}\left(\text{121}\text{.67 days}-109.5\text{ days}\right)\times \frac{\$9\text{million}}{365}\\ =12.17\times \$24,657.53\\ =\$300,082.14\end{array}$

The cash freed up for inventory is $300,082.14.

Calculation of the cash freed up for accounts receivable:

$\begin{array}{c}\text{Cash}\text{freed}\text{up}\text{for}\text{accounts}\text{receiavble}=\text{Change}\text{in}\text{accounts}\text{receivable}\times \text{Sales}\text{per}\text{day}\\ \text{=}\left(\text{98}\text{.85 days}-88.97\text{ days}\right)\times \frac{\$12\text{million}}{365}\\ =9.88\text{days}\times \$32,876.71\\ =\$324,821.89\end{array}$

The cash freed up for accounts receivables is $324,821.89.

Calculation of the cash freed up for accounts payable is:

$\begin{array}{c}\text{Cash}\text{freed}\text{up}\text{for}\text{accounts}\text{payable}=\left(\begin{array}{c}\text{Change}\text{in}\text{accounts}\text{payable}\\ \times \text{Cost}\text{of}\text{goods}\text{sold}\text{per}\text{day}\end{array}\right)\\ \text{=}\left(\text{50}\text{.69 days}-55.76\text{ days}\right)\times \frac{\$9\text{million}}{365}\\ =-5.07\text{days}\times \$24,657.53\\ =\left(\$125,013.68\right)\end{array}$

The cash freed up for accounts payable is ($125,013.68).

Conclusion

Thus, the cash conversion cycle is 170 days, the new cash conversion cycle is 143 days, the total cash freed up is $499,890.35 and the pre-tax profit is $39,991.228.