Question

(Depletion Computations—Timber) Forda Lumber Company owns a 7,000-acre tract of timber purchased in 2003 at a cost of \(1,300 per acre. At the time of purchase, the land was estimated to have a value of \)300 per acre without the timber. Forda Lumber Company has not logged this tract since it was purchased. In 2017, Forda had the timber cruised. The cruise (appraiser) estimated that each acre contained 8,000 board feet of timber. In 2017, Forda built 10 miles of roads at a cost of \(7,840 per mile. After the roads were completed, Forda logged and sold 3,500 trees containing 850,000 board feet.

Instructions

1. Determine the cost of timber sold related to depletion for 2017.
2. If Forda depreciates the logging roads on the basis of timber cut, determine the depreciation expense for 2017.
3. If Forda plants five seedlings at a cost of \)4 per seedling for each tree cut, how should Forda treat the reforestation?

Short answer

Answer

1. Cost of timber = $106,250
2. Depreciation = $1,190
3. Cost of reforestation = $70,000

Step-by-step solution

Meaning of Depreciation 

Depreciation is an accounting procedure that is used to know the exact value of the asset as the time passes and when the asset becomes obsolete. A company has different options for analyzing depreciation, with the straight-line method being the most common one.

(a) Determining the cost of timber sold related to depletion for 2017

Determining the cost of timber

$\begin{array}{rcl}\text{Cost} \text{of}\text{timber}& =& \left(\text{Timber}\text{cost}-\text{Estimated}\text{value}\text{of}\text{land}\right)\times \text{Total}\text{timber}\text{area}\\ & =& \left(\$1,300-\$300\right)\times 7,000\\ & =& \$1,000\times 7,000\\ & =& \$7,000,000\\ & & \end{array}$

Determining depletion of timber

$\begin{array}{rcl}\text{Depletion}\text{timber}& =& \text{Timber}\text{area}\times \text{Estimated}\text{acres}\text{of}\text{timber}\\ & =& 7,000\times 8,000\\ & =& \$56,000,000\end{array}$

Calculation depletion rate

$\begin{array}{rcl}\text{Depletion} \text{rate}& =& \frac{\text{Cost}\text{of}\text{timber}}{\text{Depletion} \text{timber}}\\ & =& \frac{\$7,000,000}{\$56,000,000}\\ & =& 12.50\%\end{array}$

Calculating the cost of timber

$\begin{array}{rcl}\text{Cost}\text{of}\text{timber}& =& \text{Board}\text{fleet}\times \text{Depletion} \text{rate}\\ & =& 850,000\times 12.50\%\\ & =& \$106,250\end{array}$

(b) Determining the depreciation expenses for 2017 

Calculating the cost of road

$\begin{array}{rcl}\text{Cost} \text{of}\text{road}& =& \text{Road} \text{per}\text{mile}\text{cost}\times \text{Total}\text{miles}\\ & =& 7,480\times 10\\ & =& 74,800\end{array}$

Calculating depletion of timber

$\begin{array}{rcl}\text{Depletion}\text{timber}& =& \text{Timber}\text{area}\times \text{Estimated}\text{acres}\text{of}\text{timber}\\ & =& 7,000\times 8,000\\ & =& \$56,000,000\\ & & \end{array}$

Calculating depreciation for 2017

$\begin{array}{rcl}\text{Depreciation}& =& \text{Cost} \text{of}\text{road}\times \frac{\text{Board}\text{fleet}}{\text{Depletion}\text{timber}}\\ & =& \$74,800\times \frac{850,000}{56,000,000}\\ & =& \$1,190\end{array}$

(b) Determining the treatment of the reforestation 

Calculating the cost of reforestation

$\begin{array}{rcl}\text{Cost}\text{of}\text{reforetation}& =& \text{Number}\text{of}\text{plants}\times \text{Cost}\text{per}\text{seed}\times \text{Trees}\text{sold}\\ & =& 5\times 4\times 3,500\\ & =& \$70,000\end{array}$