Chapter 2, Problem 52P

Cost Assignment, Direct Costs

Harry Whipple, owner of an inkjet printer, has agreed to allow Mary and Natalie, two friends who are pursuing master’s degrees, to print several papers for their graduate courses. However, he has imposed two conditions. First, they must supply their own paper. Second, they must pay Harry a fair amount for the usage of the ink cartridge. Harry’s printer takes two types of cartridges, a black one and a color one that contains the inks necessary to print in color. Black replacement cartridges cost $25.50 each and print approximately 850 pages. The color cartridge replacement cost $31 and prints approximately 310 color pages. One ream of paper costs $2.50 and contains 500 sheets. Mary’s printing requirements are for 500 pages, while Natalie’s are for 1,000 pages.

Required:

1. 1. Assuming that both women write papers using text only (i.e., black ink), what is the total amount owed to Harry by Mary? By Natalie?
2. 2. What is the total cost of printing (ink and paper) for Mary? For Natalie?
3. 3. Now suppose that Natalie illustrates her writing with many large colorful pie charts and pictures and that about 20% of her total printing is primarily color. Mary uses no color illustrations. What is the total amount owed to Harry by Natalie? What is the total cost of printing (ink and paper) for Natalie?

To determine

Calculate the amount owed to Person H by Person M and Person N.

Answer to Problem 52P

The amount owed to person H by Person M and Person N is $15 and $30 respectively.

Explanation of Solution

Cost:

Cost can be defined as the cash and cash equivalent which is incurred against the products or its related services which will benefit the organization in the future. There are two types of costs that are direct and indirect costs.

Use the following formula to calculate the amount owed to Person H by Person M:

$\text{Amount owed to Person H by Person M}=\left(\begin{array}{c}\text{Number of printing pages}\\ \times \text{Cost per page of black ink}\end{array}\right)$

Substitute 500 pages for the number of printing pages and $0.03 for cost per page for black ink in the above formula.

$\begin{array}{c}\text{Amount owed to Person H by Person M}=500\text{pages}\times \$0.03\\ =\$15\end{array}$

Therefore, the amount owed to person H by Person M is $15.

Use the following formula to calculate the amount owed to Person H by Person N:

$\text{Amount owed to Person H by Person N}=\left(\begin{array}{c}\text{Number of printing pages}\\ \times \text{Cost per page for black ink}\end{array}\right)$

Substitute 1,000 pages for the number of printing pages and $0.03 for cost per page for black ink in the above formula.

$\begin{array}{c}\text{Amount owed to Person H by Person N}=1,000\text{pages}\times \$0.03\\ =\$30\end{array}$

Therefore, the amount owed to person H by Person N is $30.

Working Note:

Calculation of cost of printing per page of black ink:

$\begin{array}{c}\text{Cost of printing per page}=\frac{\text{Cost of cartridge}}{\text{Number of pages that can be printed}}\\ =\frac{\$25.50}{850}\\ =\$0.03\end{array}$

Hence, the amount of cost of printing per page for black ink is $0.03.

To determine

Calculate the amount of printing cost for Person M and N.

Answer to Problem 52P

The total printing cost for Person M and Person N is $17.50 and $35 respectively.

Explanation of Solution

Use the following formula to calculate the total printing cost for Person M:

$\begin{array}{c}\text{Total printing cost for Person M}=\text{Number of printing pages}\\ \times \left(\begin{array}{l}\text{Cost per page for black ink}\\ +\text{Cost of one sheet}\end{array}\right)\end{array}$

Substitute 500 pages for the number of printing pages, $0.03 for cost per page for black ink and $0.005 for the cost of one sheet in the above formula.

$\begin{array}{c}\text{Total printing cost for Person M}=500\text{pages}\times \left(\$0.03+\$0.005\right)\\ =500\text{pages}\times \$0.035\\ =\$17.5\end{array}$

Therefore, the total printing cost for Person M is $17.50.

Use the following formula to calculate the total printing cost for Person N:

$\begin{array}{c}\text{Total printing cost for Person N}=\text{Number of printing pages}\\ \times \left(\begin{array}{l}\text{Cost per page for black ink}\\ +\text{Cost of one sheet}\end{array}\right)\end{array}$

Substitute 1,000 pages for the number of printing pages, $0.03 for cost per page for black ink and $0.005 for the cost of one sheet in the above formula.

$\begin{array}{c}\text{Total printing cost for Person N}=1,000\text{pages}\times \left(\$0.03+\$0.005\right)\\ =1,000\text{pages}\times \$0.035\\ =\$35\end{array}$

Therefore, the total printing cost for Person N is $35.

Working Note:

Calculation of cost of one sheet:

$\begin{array}{c}\text{Cost of one sheet}=\frac{\text{Cost of one ream of paper}}{\text{Number of pages included in one ream}}\\ =\frac{\$2.50}{500}\\ =\$0.005\end{array}$

Hence, the amount of cost of one sheet is $0.005.

To determine

Calculate the amount owed to Person H by Person N if the proportion of primary color is 20%. Also, calculate the amount of total printing cost for Person N.

Answer to Problem 52P

The amount owned to Person H by Person N is $44 and the total printing cost for Person N is $49.

Explanation of Solution

Use the following formula to calculate the amount owed to Person H by Person N is,

$\begin{array}{c}\text{Amount owed to Person H by Person N}=\left(\begin{array}{c}\text{Number of black ink pages}\\ \times \text{Cost per page for black ink}\end{array}\right)\\ +\left(\begin{array}{c}\text{Number of color ink pages}\\ \times \text{Cost per page for color ink}\end{array}\right)\end{array}$

Substitute 800 pages for black ink pages, $0.03 for cost per page for black ink, 200 pages for color ink pages and $0.10 for cost per page for color ink in the above formula.

$\begin{array}{c}\text{Amount owed to Person H by Person N}=\left(800\text{pages}\times \$0.03\right)\\ +\left(200\text{pages}\times \$0.10\right)\\ =\$24+\$20\\ =\$44\end{array}$

Therefore, the amount owned to Person H by Person N is $44.

Use the following formula to calculate total printing cost for Person N is,

$\begin{array}{c}\text{Total printing cost}=\left[\left(\begin{array}{l}\text{Cost per page for black ink}\\ +\text{Cost per sheet}\end{array}\right)\times \text{Number of black ink pages}\right]\\ =\left[\left(\begin{array}{l}\text{Cost per page for color ink}\\ +\text{Cost per sheet}\end{array}\right)\times \text{Number of color ink pages}\right]\end{array}$

Substitute $0.03 for the cost per page for black ink, $0.005 for cost per sheet, 800 pages for the number of black ink pages, $0.10 for the cost per page for color ink, $0.005 for cost per sheet, 200 pages for the number of color ink pages in the above formula.

$\begin{array}{c}\text{Total printing cost}=\left[\left(\$0.03+\$0.005\right)\times 800\text{pages}\right]\\ =\left[\left(\$0.10+\$0.005\right)\times 200\text{pages}\right]\\ =\left(\$0.035\times 800\text{pages}\right)+\left(\$0.105\times 200\text{pages}\right)\end{array}$

$\begin{array}{c}\text{Total printing cost}=\$28+\$21\\ =\$49\end{array}$

Therefore, the total printing cost for Person N is $49.

Working Notes:

Calculation of cost per page of color ink:

$\begin{array}{c}\text{Cost per page of color ink}=\frac{\text{Cost of color cartridge}}{\text{Number of pages }}\\ =\frac{\$31}{310}\\ =\$0.10\end{array}$

Hence, the cost per page of color ink is $0.10.

Calculation of the number of color ink pages:

$\begin{array}{c}\text{Number of color ink pages}=\text{Number of pages of Person N}\\ \times \text{Proportion of color ink}\\ =1,000\text{pages}\times \text{20\%}\\ =200\text{pages}\end{array}$

Therefore, the numbers of color ink pages are 200.

Calculation of the number of black ink pages:

$\begin{array}{c}\text{Number of black ink pages}=\left(\begin{array}{c}\text{Number of pages of Person N}\\ -\text{Number of color ink pages}\end{array}\right)\\ =1,000\text{pages}-200\text{pages}\\ =800\text{pages}\end{array}$

Therefore, the numbers of black ink pages are 800.