To calculate the loss from shrinkage, we need to find the difference between the expected inventory value based on retail prices and the actual year-end inventory value. Let's break down the calculation step by step.
1. Find the expected inventory value based on retail prices:
Subtract the retail inventory value of $78,550 from the retail value of year-end inventory (84,700):
Expected retail value = 84,700 - 78,550 = $6,150
2. Calculate the loss from shrinkage at retail:
Subtract the actual retail inventory value (78,550) from the expected retail value (6,150):
Loss from shrinkage at retail = 6,150 - 78,550 = -$72,400
Note: A negative value indicates a loss.
3. Calculate the loss from shrinkage at cost:
To calculate the loss from shrinkage at cost, we need to determine the cost-to-retail ratio. Divide the year-end inventory at cost ($55,902) by the year-end inventory at retail ($84,700):
Cost-to-retail ratio = 55,902 / 84,700 ≈ 0.66
Multiply the loss from shrinkage at retail by the cost-to-retail ratio to get the loss from shrinkage at cost:
Loss from shrinkage at cost = -72,400 * 0.66 ≈ -$47,784
Therefore, the company's loss from shrinkage is approximately -$72,400 at retail and approximately -$47,784 at cost.