To calculate the book value of the Biologique Recherche facial machine after the first year using the straight-line depreciation method, we can use the following formula:
Book Value = Cost - (Depreciation Expense * Number of Years Depreciated)
In this case, the cost of the machine is $123,000, the useful life is 4 years, and the residual value is $42,500. We can use these values to calculate the annual depreciation expense as follows:
Annual Depreciation Expense = (Cost - Residual Value) / Useful Life
= ($123,000 - $42,500) / 4
= $30,375
To calculate the book value of the machine after the first year, we can plug these values into the formula above:
Book Value = $123,000 - ($30,375 * 1)
= $123,000 - $30,375
= $92,625
Therefore, the book value of the Biologique Recherche facial machine after the first year using the straight-line depreciation method would be $92,625.