Good Afternoon.

I am currently an AAT Intermidiate student, and I am compleatly baffled by the equation for working out the percentage of reducing balance depreciation. (i.e r=1- 4(square root) s/c.  I get the first half of the calculations fine its the second half thats got me stuck.  Is there someone who can explain it to me step by step please.  Thank you.

Andy

I’m not sure what your forumula means but here’s the explanation of reducing balance (RB).

Year 1

You buy an asset for £1,000 and depreciate at 25% RB.

Depreciation = £250

NBV (Net Book Value) = £750

Year 3

Depreciation = £750 x 25% = £187.50

NBV = £562.50

Year 3

Depreciation = £562.50 x 25% = £140.63

NBV = £421.87

etc
etc
etc

I believe he’s talking about the formula to calculate what percentage to use for the reducing balance.

It’s actually r = 1 - nth root (s/c)

where
n = number of years the asset is expected to last
s = net residual value (how much the asset will be worth then)
c = original cost
r = rate of depreciation to apply

For example, an asset expected to last four years, with a scrap (residual) vale of £256 and an original cost of £10,000 would be

r = 1 - 4th root (256/10,000)
r = 1 - 0.4
r = 0.6 = £60% reducing balance

Which part are you getting stuck on?  Most calculators have an nth root button, it’s often labelled X[superscript]-Y[/superscript]

It’s much more impotant to have an understanding of the depreciation methods - don’t bothere getting bogged down with formulae, if you take a look at past papers on the AAT site you’ll realise they’re never used. Good luck.