Depreciation is the reduction in value of a long term asset due to wear and tear. There are various methods used to calculate depreciation one of which is the

reducing balance depreciation method often referred to as the declining balance depreciation method.

The reducing balance depreciation method involves applying a constant depreciation rate to the value of the asset at the start of each period.

The time value of money calculations can be used to calculate depreciation using the reducing balance depreciation method. To carry out the calculations we use the future value of a lump sum formula.

FV = PV x (1 + i)^{n}

**Variables used in the formula**

PV = Present Value

FV = Future Value

i = Discount rate

n = Number of periods

If we treat the present value (PV) as the original cost of the asset at the start of period 1, and the discount rate (i) as the reducing balance depreciation rate, then the future value of a lump sum formula can be used to give the value of the asset after depreciation (net book value) at the end of period n.

The variables in the formula above can be restated as follows:

FV = PV x (1 + i)^{n}

**Variables used in the formula**

PV = Original cost of the asset

FV = Net book value of the asset

i = Reducing balance depreciation rate per period

n = Number of periods

## Reducing Balance Depreciation Example

Suppose for example, a business purchases an asset for 100,000 (PV) and depreciates it using the declining balance method at the rate of 25% a year, then at the end of year 4, the net book value (FV) is given as follows:

PV = 100,000 n = 4 years i = -25% (rate is negative as the asset value is declining) FV = Net book value = PV x (1 + i)^{n}FV = Net book value = 100,000 x (1 - 25%)^{4}FV = 31,640.63

The time value of money calculations show that the net book value of the asset at the end of period 4 is 31,640.63 and the accumulated depreciation for the 4 years must be 100,000 – 31,640.63 = 68,359.37.

## Depreciation Calculation for a Specific Period

The reducing balance depreciation for any particular period can be found by calculating the future value at the start of the period, the future value at the end of the period, and taking the difference between the two.

Using the example above, if we want the reducing balance depreciation for period 8, we calculate the future value at the end of period 7 and deduct this from the future value at the end of period 8, the difference must be the reducing balance depreciation for period 8.

### Net book value at the end of period 7

PV = 100,000 n = 7 years i = -25% (rate is negative as the asset value is declining) FV = Net book value = PV x (1 + i)^{n}FV = Net book value = 100,000 x (1 - 25%)^{7}FV = 13,348.39

### Net book value at the end of period 8

PV = 100,000 n = 8 years i = -25% (rate is negative as the asset value is declining) FV = Net book value = PV x (1 + i)^{n}FV = Net book value = 100,000 x (1 - 25%)^{8}FV = 10,011.29

The reducing balance depreciation for period 8 is then 13,348.39 – 10,011.29 = 3,337.10