# Simple depreciation

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## Introduction

In Grade 10, the ideas of simple and compound interest were introduced. In this chapter we will be extending those ideas, so it is a good idea to go back to the Finance chapter and revise what you learnt in Grade 10. If you master the techniques in this chapter, you will understand about depreciation and will learn how to determine which bank is offering the better interest rate.

## Depreciation

It is said that when you drive a new car out of the dealership, it loses 20% of its value, because it is now “second-hand”. And from there on the value keeps falling, or depreciating . Second hand cars are cheaper than new cars, and the older the car, usually the cheaper it is. If you buy a second hand (or should we say pre-owned !) car from a dealership, they will base the price on something called book value .

The book value of the car is the value of the car taking into account the loss in value due to wear, age and use. We call this loss in value depreciation , and in this section we will look at two ways of how this is calculated. Just like interest rates, the two methods of calculating depreciation are simple and compound methods.

The terminology used for simple depreciation is straight-line depreciation and for compound depreciation is reducing-balance depreciation . In the straight-line method the value of the asset is reduced by the same constant amount each year. In the compound depreciation method the value of the asset is reduced by the same percentage each year. This means that the value of an asset does not decrease by a constant amount each year, but the decrease is most in the first year, then by a smaller amount in the second year and by an even smaller amount in the third year, and so on.

## Depreciation

You may be wondering why we need to calculate depreciation. Determining the value of assets (as in the example of the secondhand cars) is one reason, but there is also a more financial reason for calculating depreciation - tax! Companies can take depreciation into account asan expense, and thereby reduce their taxable income. A lower taxable income means that the company will pay less income tax to the Revenue Service.

## Simple depreciation (it really is simple!)

Let us go back to the second hand cars. One way of calculating a depreciation amount would be to assume that the car has a limited useful life. Simple depreciation assumes that the value of the car decreases by an equal amount each year. For example, let us say the limited useful life of a car is 5 years, and the cost of the car today is R60 000. What we are saying is that after 5 years you will have to buy a new car, which means that the old one will be valueless at that point in time. Therefore, the amount of depreciation is calculated:

$\frac{\mathrm{R}60\phantom{\rule{3.33333pt}{0ex}}000}{5\phantom{\rule{3.33333pt}{0ex}}\mathrm{years}}=\mathrm{R}12\phantom{\rule{3.33333pt}{0ex}}000\phantom{\rule{1.em}{0ex}}\mathrm{per year}.$

The value of the car is then:

 End of Year 1 R60 000 - 1 $×$ (R12 000) = R48 000 End of Year 2 R60 000 - 2 $×$ (R12 000) = R36 000 End of Year 3 R60 000 - 3 $×$ (R12 000) = R24 000 End of Year 4 R60 000 - 4 $×$ (R12 000) = R12 000 End of Year 5 R60 000 - 5 $×$ (R12 000) = R0

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