Chapter 20, Problem 1M

Summary Introduction

Case study:

Person SW, thepresident of H industries, has been exploring many ways to increase the financial performance of the company. The sales of H industries were slow. However due to the expansion in the economy, the sales might increase in the future. Person SW has asked Person AP to examine the credit policy of H industries and bring about changes to increase the profitability.

Characters in the case:

• H industries: The manufacturing industry of office equipment
• Person SW: The president of H industries
• Person AP: The company’s treasurer

To discuss: The credit policy of H industries.

Answer to Problem 1M

Company H should select Option 1 because it has the highest net present value (NPV) of $27,800,163.54 compared to other two options.

Explanation of Solution

Adequate information:

Credit policy refers to a set of procedures that include terms and conditions for providing goods on credit and principles for making collections. The company has a policy of net 30. The default rate on credit is 1.6%. Person AP came with 3 available options. H industries’ variable cost of production are 45% of sales, the interest rate is 6% of effective annual rate.

Option: 1

To relax the decision of the company to grant credit

Option: 2

To increase the credit period to net 45

Option: 3

Combination of relaxed policy and extension of credit period

Explanation:

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

$\text{Average daily sales under current policy = }\left(\frac{\text{Annual sales}}{\text{Days in a year}}\right)$

Compute the average daily sales under current policy:

$\begin{array}{c}\text{Average daily sales under current policy}=\left(\frac{\text{Annual sales}}{\text{Days in a year}}\right)\\ =\frac{\$120,000,000}{365}\\ =\$328,767.12\end{array}$

Hence, the average sales under current policy are $328,767.12.

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

$\begin{array}{l}\text{Average daily variable }\\ \text{costs under current policy}\end{array}\}=\left[\frac{45\%ofsales}{\text{Days in a year}}\right]$

Compute the average daily variable costs under current policy:

$\begin{array}{c}\begin{array}{l}\text{Average daily variable }\\ \text{costs under current policy}\end{array}\}=\left[\frac{45\%ofsales}{\text{Days in a year}}\right]\\ =\left[\frac{0.45\left(\$120,000,000\right)}{365}\right]\\ =\$147,945.205\end{array}$

Hence, the variable costs under current policy are $147,945.205.

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

$\begin{array}{l}\text{Average daily default}\\ \text{under current policy }\end{array}\}=\left(\frac{\text{Default rate}\times \text{Annual sales }}{\text{ Days in a year}}\right)$

Compute the average daily default under the current policy:

$\begin{array}{c}\begin{array}{l}\text{Average daily default}\\ \text{under current policy }\end{array}\}=\left(\frac{\text{Default rate}\times \text{Annual sales }}{\text{ Days in a year}}\right)\\ =\frac{0.016\times \$120,000,000}{365}\\ =\$5,260.27\end{array}$

Hence, the average daily default under current policy is $5,260.27.

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

$\begin{array}{l}\text{Average daily administrative }\\ \text{costs}\text{under}\text{current policy }\end{array}\}=\left[\frac{\text{Administrative costs}\times \text{Annual sales}}{\text{Days in a year}}\right]$

Compute the average daily administrative cost under the current policy:

$\begin{array}{c}\begin{array}{l}\text{Average daily administrative }\\ \text{costs}\text{under}\text{current policy }\end{array}\}=\left[\frac{\text{Administrative costs}\times \text{Annual sales}}{\text{Days in a year}}\right]\\ =\left[\frac{0.022\times \$120,000,000}{365}\right]\\ =\$7,232.87\end{array}$

Hence, the average administrative costs under current policy are $7,232.87.

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

$\text{Interest rate}=\left[{\left(\text{1}+\frac{\text{Annual interest rate}}{365}\right)}^{\text{Receivable period}}-1\right]$

Compute the interest rate:

$\begin{array}{c}\text{Interest rate}={\left(\text{1}+\frac{\text{Annual interest rate}}{365}\right)}^{\text{Receivable period}}-1\\ ={\left(1+\frac{\text{0}\text{.06 }}{\text{365}}\right)}^{\text{38}}–\text{ 1}\\ =0.0062\text{or 0}\text{.62\%}\end{array}$

Hence, the interest rate is 0.62%.

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

$\text{NPV =}\left[\begin{array}{l}-\text{Average daily variable cost +}\\ \frac{\left(\begin{array}{l}\text{Average daily sales}-\\ \text{Average daily variable cost}-\\ \text{Average daily default}-\\ \text{Average daily administrative costs}\end{array}\right)}{\text{Interest rate}}\end{array}\right]$

Compute the net present value under the current policy:

$\begin{array}{c}\text{NPV =}\left[\begin{array}{l}-\text{Average daily variable cost +}\\ \frac{\left(\begin{array}{l}\text{Average daily sales}-\\ \text{Average daily variable cost}-\\ \text{Average daily default}-\\ \text{Average daily administrative costs}\end{array}\right)}{\text{Interest rate}}\end{array}\right]\\ =\left[-\$147,945.205+\frac{\left(\begin{array}{l}\$328,767.12-\$147,945.205\\ -\$5,260.27-\$7,232.87\end{array}\right)}{0.0062}\right]\\ \text{NPV }=-\$147,945.205+27,149,802.41\\ =27,001,857.205\end{array}$

Hence, the NPV under current policy is $27,001,857.205.

Option 1:

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

$\text{Average daily sales under option 1}=\left(\frac{\text{Annual sales}}{\text{Number of days in a year}}\right)$

Compute the average daily sales under option 1:

$\begin{array}{c}\text{Average daily sales under option 1}=\left(\frac{\text{Annual sales}}{\text{Number of days in a year}}\right)\\ =\frac{\$140,000,000}{365}\\ =\$383,561.64\end{array}$

Hence, the average daily sale under option 1 is $383,561.64.

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

$\begin{array}{l}\text{Average daily variable }\\ \text{ costs under option 1}\end{array}\}=\left[\frac{45\%ofsales}{\text{Number of days in a year}}\right]$

Compute the average daily variable costs under option 1:

$\begin{array}{c}\begin{array}{l}\text{Average daily variable }\\ \text{ costs under option 1}\end{array}\}=\left[\frac{45\%ofsales}{\text{Number of days in a year}}\right]\\ =\left[\frac{0.45\left(\$140,000,000\right)}{365}\right]\\ =\$172,602.73\end{array}$

Hence, the average daily variable cost under option 1 is $172,602.73.

The formula to calculate average daily default under option 1:

$\begin{array}{l}\text{Average daily default}\\ \text{under option 1 }\end{array}\}=\left(\frac{\text{Default rate}\times \text{Annual sales }}{\text{Number of days in a year}}\right)$

Compute the average daily default under option 1:

$\begin{array}{c}\begin{array}{l}\text{Average daily default}\\ \text{under option 1 }\end{array}\}=\left(\frac{\text{Default rate}\times \text{Annual sales }}{\text{Number of days in a year}}\right)\\ =\frac{0.025\times \$140,000,000}{365}\\ =\$9,589.04\end{array}$

Hence, the average daily default under option 1 is $9,589.04.

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

$\begin{array}{l}\text{Average daily administrative }\\ \text{costs}\text{under}\text{option 1 }\end{array}\}=\left[\frac{\text{Administrative costs}\times \text{Annual sales}}{\text{Number of days in a year}}\right]$

Compute the average daily administrative cost under option 1:

$\begin{array}{c}\begin{array}{l}\text{Average daily administrative }\\ \text{costs}\text{under}\text{option 1 }\end{array}\}=\left[\frac{\text{Administrative costs}\times \text{Annual sales}}{\text{Number of days in a year}}\right]\\ =\left[\frac{0.032\times \$140,000,000}{365}\right]\\ =\$12,273.97\end{array}$

Hence, the average daily administrative costs under option 1 are $12,273.97.

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

$\text{Interest rate}={\left(\text{1}+\frac{\text{Annual interest rate}}{365}\right)}^{\text{Receivable period}}-1$

Compute the interest rate for the collection period:

$\begin{array}{c}\text{Interest rate}={\left(\text{1}+\frac{\text{Annual interest rate}}{365}\right)}^{\text{Receivable period}}-1\\ {\left(1+\frac{\text{0}\text{.06 }}{\text{365}}\right)}^{41}–\text{1}\\ =0.00676\text{or 0}\text{.676}\%\end{array}$

Hence, the interest rate is 0.676%.

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

$\text{NPV}=\left[\begin{array}{l}-\text{Average daily variable cost}+\\ \frac{\left(\begin{array}{l}\text{Average daily sales}-\\ \text{Average daily variable cost}-\\ \text{Average daily default}-\\ \text{Average daily administrative costs}\end{array}\right)}{\text{Interest rate}}\end{array}\right]$

Compute the net present value (NPV) under option 1:

$\begin{array}{c}\text{NPV}=\left[\begin{array}{l}-\text{Average daily variable cost}+\\ \frac{\left(\begin{array}{l}\text{Average daily sales}-\\ \text{Average daily variable cost}-\\ \text{Average daily default}-\\ \text{Average daily administrative costs}\end{array}\right)}{\text{Interest rate}}\end{array}\right]\\ =\left[-\$172,602.73+\frac{\left(\begin{array}{l}\$383,561.64-\$172,602.73\\ -\$9,589.04-\$12,273.97\end{array}\right)}{0.00676}\right]\\ \text{NPV}=-\$172,602.73+\text{\$27,972,766}\text{.27}\\ =\text{\$27,800,163}\text{.54}\end{array}$

Hence, the NPV under option 1 is $27,800,163.54.

Option 2:

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

$\text{Average daily sales under option 2}=\left(\frac{\text{Annual sales}}{\text{Number of days in a year}}\right)$

Compute the average daily sales under option 2:

$\begin{array}{c}\text{Average daily sales under option 2}=\left(\frac{\text{Annual sales}}{\text{Number of days in a year}}\right)\\ =\frac{\$137,000,000}{365}\\ =\$375,342.46\end{array}$

Hence, the average daily sales under option 2 are $375,342.46.

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

$\begin{array}{l}\text{Average daily variable }\\ \text{ costs under option 2}\end{array}\}=\left[\frac{45\%ofsales}{\text{Number of days in a year}}\right]$

Compute the average daily variable costs under option 2:

$\begin{array}{c}\begin{array}{l}\text{Average daily variable }\\ \text{ costs under option 2}\end{array}\}=\left[\frac{45\%ofsales}{\text{Number of days in a year}}\right]\\ =\left[\frac{0.45\left(\$137,000,000\right)}{365}\right]\\ =\$168,904.10\end{array}$

Hence, the average daily variable costs under option 2 are $168,904.10.

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

$\begin{array}{l}\text{Average daily default}\\ \text{under option 2 }\end{array}\}=\left(\frac{\text{Default rate}\times \text{Annual sales }}{\text{Number of days in a year}}\right)$

Compute the average daily default under option 2:

$\begin{array}{c}\begin{array}{l}\text{Average daily default}\\ \text{under option 2 }\end{array}\}=\left(\frac{\text{Default rate}\times \text{Annual sales }}{\text{Number of days in a year}}\right)\\ =\frac{0.018\times \$137,000,000}{365}\\ =\$6,756.16\end{array}$

Hence, the average daily default under option 2 is $6,756.16.

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

$\begin{array}{l}\text{Average daily administrative }\\ \text{costs}\text{under}\text{option 2 }\end{array}\}=\left[\frac{\text{Administrative costs}\times \text{Annual sales}}{\text{Days in a year}}\right]$

Compute the average daily administrative cost under option 2:

$\begin{array}{c}\begin{array}{l}\text{Average daily administrative }\\ \text{costs}\text{under}\text{option 2 }\end{array}\}=\left[\frac{\text{Administrative costs}\times \text{Annual sales}}{\text{Days in a year}}\right]\\ =\left[\frac{0.024\times \$137,000,000}{365}\right]\\ =\$9,008.21\end{array}$

Hence, the average daily administrative costs under option 2 are$9,008.21.

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

$\text{Interest rate}={\left(\text{1}+\frac{\text{Annual interest rate}}{365}\right)}^{\text{Receivable period}}-1$

Compute the interest rate:

$\begin{array}{c}\text{Interest rate}={\left(\text{1}+\frac{\text{Annual interest rate}}{365}\right)}^{\text{Receivable period}}-1\\ ={\left(1+\frac{\text{0}\text{.06 }}{\text{365}}\right)}^{51}–\text{1}\\ =0.00841\text{or 0}\text{.841}\%\end{array}$

Hence, the interest rate is 0.841%.

The formula to calculate NPV under option 2:

$\text{NPV}=\left[\begin{array}{l}-\text{Average daily variable cost }+\\ \frac{\left(\begin{array}{l}\text{Average daily sales}-\\ \text{Average daily variable cost}-\\ \text{Average daily default}-\\ \text{Average daily administrative costs}\end{array}\right)}{\text{Interest rate}}\end{array}\right]$

Compute the NPV under option 2:

$\begin{array}{c}\text{NPV}=\left[\begin{array}{l}-\text{Average daily variable cost }+\\ \frac{\left(\begin{array}{l}\text{Average daily sales}-\\ \text{Average daily variable cost}-\\ \text{Average daily default}-\\ \text{Average daily administrative costs}\end{array}\right)}{\text{Interest rate}}\end{array}\right]\\ =\left[-\$168,904.10+\frac{\left(\begin{array}{l}\$375,342.46-\$168,904.10\\ -\$6,756.16-\$9,008.21\end{array}\right)}{0.00841}\right]\\ \text{NPV}=-\$168,904.10+\$22,672,293.69\\ =\$22,503,389.59\end{array}$

Hence, the NPV under option 2 is $22,503,389.59.

Option 3:

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

$\text{Average daily sales under option 3}=\left(\frac{\text{Annual sales}}{\text{Number of days in a year}}\right)$

Compute the average daily sales under current policy:

$\begin{array}{c}\text{Average daily sales under option 3}=\left(\frac{\text{Annual sales}}{\text{Number of days in a year}}\right)\\ =\frac{\$150,000,000}{365}\\ =\$410,958.90\end{array}$

Hence, the average daily sales under option 3 are $410,958.90.

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

$\begin{array}{l}\text{Average daily variable }\\ \text{ costs under option 3}\end{array}\}=\left[\frac{45\%ofsales}{\text{Number od days in a year}}\right]$

Compute the average daily variable costs under option 3:

$\begin{array}{c}\begin{array}{l}\text{Average daily variable }\\ \text{ costs under option 3}\end{array}\}=\left[\frac{45\%ofsales}{\text{Number od days in a year}}\right]\\ =\left[\frac{0.45\left(\$150,000,000\right)}{365}\right]\\ =\$184,931.50\end{array}$

Hence, the average daily variable costs under option 3 are $184,931.50.

The formula to calculate the average daily default under option 3:

$\begin{array}{l}\text{Average daily default}\\ \text{under option 3 }\end{array}\}=\left(\frac{\text{Default rate}\times \text{Annual sales }}{\text{Number of days in a year}}\right)$

Compute the average daily default under option 3:

$\begin{array}{c}\begin{array}{l}\text{Average daily default}\\ \text{under option 3 }\end{array}\}=\left(\frac{\text{Default rate}\times \text{Annual sales }}{\text{Number of days in a year}}\right)\\ =\frac{0.022\times \$150,000,000}{365}\\ =\$9,041.09\end{array}$

Hence, the average daily default under option 3 is $9,041.09.

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

$\begin{array}{l}\text{Average daily administrative }\\ \text{costs}\text{under}\text{option 3 }\end{array}\}=\left[\frac{\text{Administrative costs}\times \text{Annual sales}}{\text{Days in a year}}\right]$

Compute the average daily administrative cost under option 3:

$\begin{array}{c}\begin{array}{l}\text{Average daily administrative }\\ \text{costs}\text{under}\text{option 3 }\end{array}\}=\left[\frac{\text{Administrative costs}\times \text{Annual sales}}{\text{Days in a year}}\right]\\ =\left[\frac{0.03\times \$150,000,000}{365}\right]\\ =\$12,328.76\end{array}$

Hence, the average daily administrative costs under option 3 are $12,328.76.

The formula to calculate the interest rate for collection period:

$\text{Interest rate}={\left(\text{1}+\frac{\text{Annual interest rate}}{365}\right)}^{\text{Receivable period}}-1$

Compute the interest rate for collection period:

$\begin{array}{c}\text{Interest rate}={\left(\text{1}+\frac{\text{Annual interest rate}}{365}\right)}^{\text{Receivable period}}-1\\ ={\left(1+\frac{\text{0}\text{.06 }}{\text{365}}\right)}^{49}–\text{1}\\ =0.00808\text{or 0}\text{.808\%}\end{array}$

Hence, the interest rate is 0.808%.

The formula to calculate NPV under option 3:

$\text{NPV}=\left[\begin{array}{l}-\text{Average daily variable cost +}\\ \frac{\left(\begin{array}{l}\text{Average daily sales}-\\ \text{Average daily variable cost}-\\ \text{Average daily default}-\\ \text{Average daily administrative costs}\end{array}\right)}{\text{Interest rate}}\end{array}\right]$

Compute the net present value under option 3:

$\begin{array}{c}\text{NPV}=\left[\begin{array}{l}-\text{Average daily variable cost +}\\ \frac{\left(\begin{array}{l}\text{Average daily sales}-\\ \text{Average daily variable cost}-\\ \text{Average daily default}-\\ \text{Average daily administrative costs}\end{array}\right)}{\text{Interest rate}}\end{array}\right]\\ =\left[-\$184,931.50+\frac{\left(\begin{array}{l}\$410,958.90-\$184,931.50\\ -\$9,041.09-\$12,328.76\end{array}\right)}{0.00808}\right]\\ \text{NPV }=-\$184,931.50+\$25,328,904.70\\ =\$25,143,973.2\end{array}$

Hence, the NPV under option 3 is $25,143,973.202.