Question

Which of the following methods of depreciation calculations results in book values greater than those obtained with straight line method?

• A. Multiple straight-line method
• B. Sinking fund method
• C. Declining balance method
• D. Sum of the years digit method

Hint:

The sinking fund method results in higher book values than straight-line because it depreciates more slowly in early years, assuming interest accumulation.

Answer 1

The Correct Option is B

Step 1: Understand depreciation methods and book value. 
Depreciation is the allocation of an asset’s cost over its useful life. The book value at any time is the initial cost minus accumulated depreciation: \[ \text{Book Value} = \text{Initial Cost} - \text{Accumulated Depreciation}. \] A method that results in greater book values than the straight-line method means it depreciates the asset more slowly (lower accumulated depreciation at any given time). Straight-line method: Depreciates the asset at a constant rate: \[ \text{Annual Depreciation} = \frac{\text{Cost} - \text{Salvage Value}}{\text{Useful Life}}. \] For an asset with cost \( C \), salvage value \( S \), and life \( n \), the book value at year \( t \) is: \[ \text{Book Value}_{\text{SL}} = C - t \times \frac{C - S}{n}. \] Multiple straight-line method: Not a standard term, but likely a variation of the straight-line method (e.g., applied in segments). Assumed to be similar to straight-line for comparison.
Sinking fund method: Assumes depreciation is set aside as if the asset’s value is recovered through a sinking fund earning interest. Depreciation is lower in early years and increases over time, resulting in slower depreciation and higher book values compared to straight-line.
Declining balance method: An accelerated method where depreciation is a fixed percentage of the remaining book value each year, leading to higher depreciation in early years and lower book values than straight-line.
Sum of the years’ digits method: An accelerated method where depreciation is higher in early years, calculated as a fraction based on the remaining life, leading to lower book values than straight-line.
Step 2: Compare depreciation rates and book values. 
Straight-line: Depreciates evenly, so book value decreases linearly.
Sinking fund method: Depreciation is calculated as if the asset’s cost is recovered through a sinking fund with compound interest. Early depreciation is lower because it assumes the fund grows with interest, so accumulated depreciation is less than straight-line in early years, resulting in higher book values.
Declining balance: Depreciates more in early years, so book value decreases faster than straight-line, resulting in lower book values.
Sum of the years’ digits: Also an accelerated method, depreciating more in early years, so book value is lower than straight-line.
The sinking fund method results in higher book values because it depreciates the asset more slowly in the early years compared to the straight-line method. 
Step 3: Evaluate the options. 
(1) Multiple straight-line method: Incorrect, as it is likely similar to straight-line and would not result in higher book values. Incorrect.
(2) Sinking fund method: Correct, as it depreciates more slowly in early years, leading to higher book values than the straight-line method. Correct.
(3) Declining balance method: Incorrect, as it is an accelerated method, resulting in lower book values than straight-line. Incorrect.
(4) Sum of the years’ digits method: Incorrect, as it is also an accelerated method, resulting in lower book values than straight-line. Incorrect. 
Step 4: Select the correct answer. 
The sinking fund method results in book values greater than those obtained with the straight-line method, matching option (2).