Tim Legler requires an estimate of the cost of goods lost by a fire on March 9. Merchandise on hand on January 1 was $38,490. Purchases since January 1 were $93,260; freight-in, $4,700; purchase returns and allowances, $3,000. Sales are made at 33 1/3% above cost and totaled $143,400 to March 9. Goods costing $12,120 were left undamaged by the fire; remaining goods were destroyed.(a) Compute the cost of goods destroyed.(b) Compute the cost of goods destroyed, assuming that the gross profit is 33 1/3% of sales. (Round ratios for computational purposes to 5 decimal places, e. g. 78.72345% and final answer to 0 decimal places, e. g. 28,987.)

(a) Cost of goods destroyed = $13,780

(b) Cost of goods destroyed = $25,730

Explanation:

(a) Compute the cost of goods destroyed.

Markup = Percentage at which sales are made above cost = 33 1/3% = 33.33333%

Margin = Markup / (1 + Markup) = 33.33333% / (1 + 33.33333%) = 25%

Sales = Cost of goods sold * (100% + Markup) (1)

Substituting relevant value into equation (1) and solve for Cost of goods sold, we have:

$143,400 = Cost of goods sold * (100% + 33.33333%)

Cost of goods sold = $143,400 / (100% + 33.33333%) = $107,550

Cost of goods available for sale = Merchandise on hand on January 1 + Purchases since January 1 + Freight-in + Purchase returns and allowances = $38,490 + $93,260 + $4,700 - $3,000 = $133,450

Closing stock = Cost of goods available for sale - Cost of goods sold = $133,450 - $107,550 = 25,900

Cost of goods destroyed = Closing stock - Cost of goods left undamaged = $25,900 - $12,120 = $13,780

(b) Compute the cost of goods destroyed, assuming that the gross profit is 33 1/3% of sales. (Round ratios for computational purposes to 5 decimal places, e.g. 78.72345% and final answer to 0 decimal places, e.g. 28,987.)

Margin = gross profit percentage of sales = 33 1/3% = 33.33333%

Markup = Margin / (1 - Margin) = 33.33333% / (1 - 33.33333%) = 50%

Sales = Cost of goods sold * (100% + Markup) (1)

Substituting relevant value into equation (1) and solve for Cost of goods sold, we have:

$143,400 = Cost of goods sold * (100% + 50%%)

Cost of goods sold = $143,400 / (100% + 50%) = $95,600

Cost of goods available for sale = $133,450

Closing stock = Cost of goods available for sale - Cost of goods sold = $133,450 - $95,600 = 37,850

Cost of goods destroyed = Closing stock - Cost of goods left undamaged = $37,850 - $12,120 = $25,730