Which method involves multiplying a depreciation rate by the asset's beginning-period book value?

The declining balance method of depreciation is characterized by multiplying a fixed depreciation rate by the asset's beginning-period book value. This method results in a higher depreciation expense in the earlier years of an asset's life and gradually decreases the amount of depreciation expense in subsequent years. The formula typically involves taking the book value of the asset at the start of each period and applying a constant rate, which is often based on the asset's useful life.

In contrast, the straight line method involves dividing the cost of the asset minus its salvage value by its useful life, resulting in equal depreciation expenses each period. The sum-of-the-years'-digits method accelerates depreciation similarly but uses a formula based on the remaining life of the asset, which is more complex than the simple multiplication used in the declining balance method. Lastly, the historical cost method refers to the price paid for an asset at its acquisition and is not a method for calculating depreciation.

Thus, the declining balance method is specifically designed to apply a depreciation rate to the book value of an asset at the start of each accounting period, distinguishing it from other methods.