Chapter 20, Problem 2M

Summary Introduction

To evaluate: The credit policy of the firm

Introduction:

Credit policy refers to a set of procedures that include the terms and conditions for providing goods on credit and principles for making collections.

Answer to Problem 2M

It is plausible, when the administrative costs and default probability rate of option 2 are lesser than option 3. Option 2 extends the period of credit and Option 3 extends the period of credit and relaxes the policy.

This relaxation may increase the default probability rate because it will include firms with lesser credit ratings who are less likely to pay. As a result, it will increase the costs of administration of managing the fraudulent accounts.

Explanation of Solution

The formula to calculate the average daily sales under current policy:

$\begin{array}{c}\text{Average daily sales under current policy = }\left(\frac{\text{Annual sales}}{\text{Days in a year}}\right)\\ =\frac{\$144,000,000}{365}\\ =\$394,520.55\end{array}$

Hence, the average sales under current policy is $394,520.55.

The formula to calculate average daily variable costs under current policy:

$\begin{array}{c}\begin{array}{l}\text{Average daily variable }\\ \text{costs under current policy}\end{array}\}\text{ =}\left[\frac{45\%ofsales}{\text{Days in a year}}\right]\\ =\left[\frac{.45\left(\$144,000,000\right)}{365}\right]\\ =\$177,534.25\end{array}$

Hence, the variable costs under current policy is $177,534.25.

The formula to calculate the average daily default under current policy:

$\begin{array}{c}\begin{array}{l}\text{Average daily default}\\ \text{under current policy }\end{array}\}\text{= }\left(\frac{\text{Default rate}\times \text{Annual sales }}{\text{ Days in a year}}\right)\\ =\frac{.016\times \$144,000,000}{365}\\ =\$6,312.33\end{array}$

Hence, the average daily default under current policy is $6312.33.

The formula to calculate average daily administrative cost under current policy:

$\begin{array}{c}\begin{array}{l}\text{Average daily administrative }\\ \text{costs}\text{under}\text{current policy }\end{array}\}\text{= }\left[\frac{\text{Administrative costs}\times \text{Annual sales}}{\text{Days in a year}}\right]\\ =\left[\frac{.022\times \$144,000,000}{365}\right]\\ =\$8,679.45\end{array}$

Hence, the average administrative costs under current policy is $8,679.45.

The formula to calculate the interest rate for the collection period:

$\begin{array}{c}\text{Interest rate =}{\left(\text{1+}\frac{\text{Annual interest rate}}{365}\right)}^{\text{Receivable period}}-1\\ {\left(1+\frac{\text{0}\text{.06 }}{\text{365}}\right)}^{\text{37}}\text{– 1}\\ =0.0061\text{or }\text{.61\%}\end{array}$

Hence, the interest rate is 0.61%.

The formula to calculate the net present value (NPV) under current policy:

$\begin{array}{c}\text{NPV =}\left[\begin{array}{l}-\text{Average daily variable cost +}\\ \frac{\left(\begin{array}{l}\text{Average daily sales}-\\ \text{Average daily variable cost}-\\ \text{Average daily default}-\\ \text{Average daily administrative costs}\end{array}\right)}{\text{Interest rate}}\end{array}\right]\\ =\left[-\$177,534.25+\frac{\left(\begin{array}{l}\$394,520.55-\$177,534.25\\ -\$6,312.33-\$8,679.45\end{array}\right)}{0.0061}\right]\\ \text{NPV = \$32,936,321}\text{.48}\end{array}$

Hence, the NPV under current policy is $32,936,321.48.

Option 1:

The formula to calculate the average daily sales under option 1:

$\begin{array}{c}\text{Average daily sales under option 1 = }\left(\frac{\text{Annual sales}}{\text{Number of days in a year}}\right)\\ =\frac{\$168,000,000}{365}\\ =\$460,273.97\end{array}$

Hence, the average daily sales under option 1 is $460,273.97.

The formula to calculate average daily variable costs under option 1:

$\begin{array}{c}\begin{array}{l}\text{Average daily variable }\\ \text{ costs under option 1}\end{array}\}\text{ =}\left[\frac{45\%ofsales}{\text{Number od days in a year}}\right]\\ =\left[\frac{.45\left(\$168,000,000\right)}{365}\right]\\ =\$207,123.29\end{array}$

Hence, the average daily variable costs under option 1 is $207,123.29.

The formula to calculate average daily default under option 1:

$\begin{array}{c}\begin{array}{l}\text{Average daily default}\\ \text{under option 1 }\end{array}\}\text{= }\left(\frac{\text{Default rate}\times \text{Annual sales }}{\text{Number of days in a year}}\right)\\ =\frac{.025\times \$168,000,000}{365}\\ =\$11,506.85\end{array}$

Hence, average daily default under option 1 is $11,506.85.

The formula to calculate average daily administrative cost under option 1:

$\begin{array}{c}\begin{array}{l}\text{Average daily administrative }\\ \text{costs}\text{under}\text{option 1 }\end{array}\}\text{= }\left[\frac{\text{Administrative costs}\times \text{Annual sales}}{\text{Number of days in a year}}\right]\\ =\left[\frac{.032\times \$168,000,000}{365}\right]\\ =\$14,728.77\end{array}$

Hence, the average daily administrative costs under option 1 is $14,728.77.

The formula to calculate interest rate for the for collection period:

$\begin{array}{c}\text{Interest rate =}{\left(\text{1+}\frac{\text{Annual interest rate}}{365}\right)}^{\text{Receivable period}}-1\\ {\left(1+\frac{\text{0}\text{.06 }}{\text{365}}\right)}^{40}\text{– 1}\\ =0.00659\text{or }\text{.659}\%\end{array}$

Hence, the interest rate is 0.659%.

The formula to calculate the net present value (NPV) under option 1:

$\begin{array}{c}\text{NPV =}\left[\begin{array}{l}-\text{Average daily variable cost +}\\ \frac{\left(\begin{array}{l}\text{Average daily sales}-\\ \text{Average daily variable cost}-\\ \text{Average daily default}-\\ \text{Average daily administrative costs}\end{array}\right)}{\text{Interest rate}}\end{array}\right]\\ =\left[-\$207,123.29+\frac{\left(\begin{array}{l}\$460,273.97-\$207,123.29\\ -\$11,506.85-\$14,728.77\end{array}\right)}{0.00659}\right]\\ \text{NPV = \$34,226,117}\text{.98}\end{array}$

Hence, the NPV under option 1 is $34,226,117.98.

Option 2:

The formula to calculate the average daily sales under option 2:

$\begin{array}{c}\text{Average daily sales under option 2 = }\left(\frac{\text{Annual sales}}{\text{Number of days in a year}}\right)\\ =\frac{\$165,000,000}{365}\\ =\$452,054.79\end{array}$

Hence, the average daily sales under option 2 is $452,054.79.

The formula to calculate average daily variable costs under option 2:

$\begin{array}{c}\begin{array}{l}\text{Average daily variable }\\ \text{ costs under option 2}\end{array}\}\text{ =}\left[\frac{45\%ofsales}{\text{Number od days in a year}}\right]\\ =\left[\frac{.45\left(\$165,000,000\right)}{365}\right]\\ =\$203,424.66\end{array}$

Hence, the average daily variable costs under option 2 is $203,424.66.

The formula to calculate average daily default under option 2:

$\begin{array}{c}\begin{array}{l}\text{Average daily default}\\ \text{under option 2 }\end{array}\}\text{= }\left(\frac{\text{Default rate}\times \text{Annual sales }}{\text{Number of days in a year}}\right)\\ =\frac{.018\times \$165,000,000}{365}\\ =\$8,136.99\end{array}$

Hence, the average daily default under option 2 is $8,136.99.

The formula to calculate average daily administrative cost under option 2:

$\begin{array}{c}\begin{array}{l}\text{Average daily administrative }\\ \text{costs}\text{under}\text{option 2 }\end{array}\}\text{= }\left[\frac{\text{Administrative costs}\times \text{Annual sales}}{\text{Days in a year}}\right]\\ =\left[\frac{.024\times \$165,000,000}{365}\right]\\ =\$10,849.32\end{array}$

Hence, the average daily administrative costs under option 2 is $10,849.32.

The formula to calculate interest rate for the for collection period:

$\begin{array}{c}\text{Interest rate =}{\left(\text{1+}\frac{\text{Annual interest rate}}{365}\right)}^{\text{Receivable period}}-1\\ {\left(1+\frac{\text{0}\text{.06 }}{\text{365}}\right)}^{50}\text{– 1}\\ =0.00825\text{or }\text{.825}\%\end{array}$

Hence, the interest rate is 0.852%.

The formula to calculate NPV under option 2:

$\begin{array}{c}\text{NPV =}\left[\begin{array}{l}-\text{Average daily variable cost +}\\ \frac{\left(\begin{array}{l}\text{Average daily sales}-\\ \text{Average daily variable cost}-\\ \text{Average daily default}-\\ \text{Average daily administrative costs}\end{array}\right)}{\text{Interest rate}}\end{array}\right]\\ =\left[-\$203,424.66+\frac{\left(\begin{array}{l}\$452,054.79-\$203,424.66\\ -\$8,136.99-\$10,849.32\end{array}\right)}{0.00825}\right]\\ \text{NPV = \$27,632,189}\text{.89}\end{array}$

Hence, the NPV under option 2 is $27,632,189.89.

Option 3:

The formula to calculate the average daily sales under current policy:

$\begin{array}{c}\text{Average daily sales under option 3 = }\left(\frac{\text{Annual sales}}{\text{Number of days in a year}}\right)\\ =\frac{\$180,000,000}{365}\\ =\$493,150.68\end{array}$

Hence, the average daily sales under option 3 is $493,150.68.

The formula to calculate average daily variable costs under option 3:

$\begin{array}{c}\begin{array}{l}\text{Average daily variable }\\ \text{ costs under option 3}\end{array}\}\text{ =}\left[\frac{45\%ofsales}{\text{Number od days in a year}}\right]\\ =\left[\frac{.45\left(\$180,000,000\right)}{365}\right]\\ =\$221,917.81\end{array}$

Hence, the average daily variable costs under option 3 is $221,917.81.

The formula to calculate average daily default under option 3:

$\begin{array}{c}\begin{array}{l}\text{Average daily default}\\ \text{under option 3 }\end{array}\}\text{= }\left(\frac{\text{Default rate}\times \text{Annual sales }}{\text{Number of days in a year}}\right)\\ =\frac{.022\times \$180,000,000}{365}\\ =\$10,849.32\end{array}$

Hence, the average daily default under option 3 is $10,849.32.

The formula to calculate average daily administrative cost under option 3:

$\begin{array}{c}\begin{array}{l}\text{Average daily administrative }\\ \text{costs}\text{under}\text{option 3 }\end{array}\}\text{= }\left[\frac{\text{Administrative costs}\times \text{Annual sales}}{\text{Days in a year}}\right]\\ =\left[\frac{.03\times \$180,000,000}{365}\right]\\ =\$14,794.52\end{array}$

Hence, the average daily administrative costs under option 3 is $14,794.52.

The formula to calculate interest rate for collection period:

$\begin{array}{c}\text{Interest rate =}{\left(\text{1+}\frac{\text{Annual interest rate}}{365}\right)}^{\text{Receivable period}}-1\\ {\left(1+\frac{\text{0}\text{.06 }}{\text{365}}\right)}^{48}\text{– 1}\\ =0.00792\text{or }\text{.792\%}\end{array}$

Hence, the interest rate is 0.792%.

The formula to calculate NPV under option 3:

$\begin{array}{c}\text{NPV =}\left[\begin{array}{l}-\text{Average daily variable cost +}\\ \frac{\left(\begin{array}{l}\text{Average daily sales}-\\ \text{Average daily variable cost}-\\ \text{Average daily default}-\\ \text{Average daily administrative costs}\end{array}\right)}{\text{Interest rate}}\end{array}\right]\\ =\left[-\$221,917.81+\frac{\left(\begin{array}{l}\$493,150.68-\$221,917.81\\ -\$10,849.32-\$14,794.52\end{array}\right)}{0.00792}\right]\\ \text{NPV = \$30,786,798}\text{.099}\end{array}$

Hence, the NPV under option 3 is $30,786,798.099.