Chapter 11, Problem 13P

1.

To determine

Calculate the total expenses that are included in the income statement of company A for 2016.

Explanation of Solution

Depreciation expense: Depreciation expense is a non-cash expense, which is recorded on the income statement reflecting the consumption of economic benefits of long-term asset on account of its wear and tear or obsolesces.

Depletion: Depletion is a process in which the cost of natural resources like oil reserves, mineral deposits, and timber tracts, is allocated equally over the extraction or harvesting period of the asset. When a resource is depleted, the value of resource is decreased and the value of extracted inventory obtained is increased. So, depletion is recorded on the balance sheet, and not on the income statement. But the Cost of Goods Sold expense is recorded when the extracted inventory is sold.

Calculate the amount of total expenses that would be included in the income statement of company A for 2016 as follows:

$\begin{array}{c}\text{Total expense =}\left(\begin{array}{l}\text{ Total expense of coal per ton }\times \\ \text{Number of tons sold}\end{array}\right)+\text{Accretion}\\ =\left(\$10.95\text{ per tons (5) }\times \text{54,000 tons (4) }\right)\text{+\$15,000 (3) }\\ \text{=\$606,300}\end{array}$

Working note (1):

Calculate the depletion rate per ton.

$\begin{array}{c}\text{Depleption rate = }\frac{\left[\begin{array}{l}\left(\text{Cost}-\text{Residual value}\right)\text{ +}\\ \text{Present value}\end{array}\right]}{\text{Estimated capacity of coal}}\\ =\frac{\left(\$2,000,000-\$100,000\right)+\$300,000}{800,000\text{ tons}}\\ =\$2.75\text{ per ton}\end{array}$

Working note (2):

Calculate the depreciation rate per ton.

$\begin{array}{c}\text{Depreciation rate = }\frac{\text{Cost}-\text{Residual value}}{\text{Estimated capacity of coal}}\\ =\frac{\left(\$170,000-\$10,000\right)}{800,000\text{ tons}}\\ =\$0.20\text{ per ton}\end{array}$

Working note (3):

Calculate the value of accretion.

$\begin{array}{c}\text{Accretion =}\left[\begin{array}{l}\text{ Present value }\times \text{Discount rate }\times \\ \frac{\text{Number of months between July to December}}{\text{Months in a year}}\end{array}\right]\\ =\$300,000\times \frac{10}{100}\times \frac{6}{12}\\ =\$15,000\end{array}$

Working note (4):

Calculate number of tons sold.

$\begin{array}{c}\text{Number of tons sold =}\left(\begin{array}{l}\text{ Number of tons sold per month }\times \\ \text{Number of months between July to December}\end{array}\right)\\ =9,000\text{ ton per month }\times \text{ 6 months}\\ \text{=54,000 tons}\end{array}$

Working note (5):

Calculate the total expense of coal per ton.

$\begin{array}{c}\text{Total expense =}\left[\begin{array}{l}\text{Depletion rate per unit + }\\ \text{Depreciation rate per unit+}\\ \text{Production cost per unit }\end{array}\right]\\ \text{=}\left(\begin{array}{l}\text{\$2}\text{.75 per ton (1) + \$0}\text{.20 per ton (2)+ }\\ \text{\$8}\text{.00 per ton}\end{array}\right)\\ =\$10.95\text{ per ton}\end{array}$

Conclusion

Therefore, the total expense of Company A for 2016 is $606,300.

2.

To determine

Calculate the cost of inventory of Company A for the year ended December 31, 2016.

Explanation of Solution

Calculate the cost of inventory of Company A for the year ended December 31, 2016 as follows:

$\begin{array}{c}\text{Cost of inventory = }\left(\begin{array}{l}\left[\begin{array}{l}\text{Total tons of coal produced}-\\ \text{Total tons of coal sold during the year}\end{array}\right]\\ \text{Total expense per ton}\times \end{array}\right)\\ =\left(\begin{array}{l}60,000\text{ tons (6)}-\\ 54,000\text{ tons (4) }\end{array}\right)\times \$10.95\text{ per ton (5)}\\ \text{=6,000 tons }\times \$10.95\text{ per ton}\\ \text{=\$67,500}\end{array}$

Working note (6):

Calculate the total tons of coal produced during the year.

$\begin{array}{c}\text{Number of tons sold =}\left(\begin{array}{l}\text{ Number of tons produced per month }\times \\ \text{Number of months between July to December}\end{array}\right)\\ =10,000\text{ ton per month }\times \text{ 6 months}\\ \text{=60,000 tons}\end{array}$

3.

To determine

Calculate the total expense of Company A for 2017, and assume the new estimation of the company indicates that the capacity of the mine is 500,000 tons.

Explanation of Solution

Calculate the amount of total expense of Company A for 2017, and assume the new estimation of the company indicates that the capacity of the mine is 500,000 tons as follows:

$\begin{array}{c}\text{Total expense =}\left(\begin{array}{l}\text{ Cost of inventory + }\\ \left[\begin{array}{l}\left(\begin{array}{l}\text{Number of tonss sold during the year (12)}\\ -\text{Begining inventory in tons}\end{array}\right)\times \\ \text{Total expense per ton (11) }\end{array}\right]\end{array}\right)+\text{Accretion (10)}\\ =\left[\$65,700+\left(\left(\begin{array}{l}120,000\text{ tons }-\\ \text{6,000 tons}\end{array}\right)\times \$12.366\right)\right]\text{+\$33,000 (3) }\\ \text{=\$65,700+\$1,409,724+\$33,000}\\ \text{=\$1,508,424}\end{array}$

Working note (7):

Calculate the new depletion rate per ton.

$\begin{array}{c}\text{Depletion rate = }\frac{\left[\begin{array}{l}\left(\left(\begin{array}{l}\text{Cost}-\text{Depletion expense }\\ \text{for sold items}\end{array}\right)-\text{Residual value}\right)\text{ +}\\ \text{Present value}\end{array}\right]}{\text{Estimated capacity of coal}}\\ =\frac{\left(\left(\begin{array}{l}\$2,000,000-\\ \$165,000\end{array}\right)-\$100,000\right)+\$300,000}{500,000\text{ tons}}\\ =\$4.07\text{ per ton}\end{array}$

Note: The depletion expense for sold item is $165,000$\left(\$2.75\times \text{60,000 tons}\right)$.

Working note (8):

Calculate the depreciation rate per ton.

$\begin{array}{c}\text{Depreciation rate = }\frac{\left(\begin{array}{l}\text{Cost}-\text{Depreciation }\\ \text{expense for sold items}\end{array}\right)-\text{Residual value}}{\text{Estimated capacity of coal}}\\ =\frac{\left(\left(\$170,000-\$12,000\right)-\$10,000\right)}{500,000\text{ tons}}\\ =\$0.296\text{ per ton}\end{array}$

Note: The depreciation expense for sold item is $12,000$\left(\$0.20\times \text{60,000 tons}\right)$.

Working note (9):

Calculate the present value of mine for 2017.

$\begin{array}{c}\text{Present value =Present value for 2016 + }\left[\begin{array}{l}\text{ Present value }\times \\ \text{Discount rate}\end{array}\right]\\ =\$300,000+\left(\$300,000\times \frac{10}{100}\right)\\ =\$300,000+\$30,000\\ =\$330,000\end{array}$

Note: Assume the present value of mine is increased by 10%.

Working note (10):

Calculate the value of accretion for 2017.

$\begin{array}{c}\text{Accretion =}\left[\begin{array}{l}\text{ Present value for 2017 (9) }\times \text{Discount rate }\times \\ \frac{\text{Number of months between January to December}}{\text{Months in a year}}\end{array}\right]\\ =\$330,000\times \frac{10}{100}\times \frac{12}{12}\\ =\$33,000\end{array}$

Working note (11):

Calculate the total expense of coal per ton.

$\begin{array}{c}\text{Total expense =}\left[\begin{array}{l}\text{Depletion rate per unit + }\\ \text{Depreciation rate per unit+}\\ \text{Production cost per unit }\end{array}\right]\\ \text{=}\left(\begin{array}{l}\text{\$4}\text{.07 per ton (8) + \$0}\text{.296 per ton (9)+ }\\ \text{\$8}\text{.00 per ton}\end{array}\right)\\ =\$12.366\text{ per ton}\end{array}$

Working note (12):

Calculate number of tons sold.

$\begin{array}{c}\text{Number of tons sold =}\left(\begin{array}{l}\text{ Number of tons sold per month }\times \\ \text{Number of months from January to December}\end{array}\right)\\ =10,000\text{ ton per month }\times \text{ 12 months}\\ \text{=120,000 tons}\end{array}$

Conclusion

Therefore, the total expense of Company A for 2017 is $1,508,424.