Reducing Balance Depreciation

Reducing balance depreciation refers to a decrease of an item’s book value by a rate (that is a percentage of the previous book value of the good) each time interval.

The Formula

$BV_T=P(1-\dfrac r{100})^T$

Example 1

Nick purchased a new computer for $1,300. He depreciates the computer using the reducing balance method at a rate of 15% per annum. What will the computer’s total depreciation and book value be after three years?

State the information we are provided with in the question.

$P=1,300$
$r=15$
$T=3$

Substitute these values into the formula to find the book value after three years.

$BV_T=P(1-\dfrac r{100})^T$
$BV_3=1,300(1-\dfrac 15{100})^3$
$BV_3=1,300(0.85)^3$
$BV_3=798.3625$

Use the book value to calculate the total depreciation.

Total depreciation $=P-BV$
Total depreciation $=1,300-798.3625$
Total depreciation $=501.6375$

The book value of the computer after three years will be $798.36 and the total depreciation will be $501.64.

Remember

Reducing balance depreciation is also known as diminishing value depreciation so look out for both of these terms in the question.
When an item’s book value equals zero, it will be written off.
Scrap value refers to the book value of the item when it will no longer be used.

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