# How to calculate the age of assets from NBV

I am looking to calculate the age of my assets from the NBV, under the reducing balance method.

• ### 23 month basis period

Here's a maths question for you:

NBV = X

Cost =A

Rate of depreciation (reducing balance)=B

Years = C

So, I calculate X = A x (1-B)^C

I am struggling to reverse the formula to give me a value for the number of years, where I know the original cost, the rate, and the current NBV.

This is a real life problem - rather than some homework!

Thanks,

### Replies (11) 17th Nov 2016 13:07

NBV / (1 - B)^c = Cost

Thanks (0) By NomDePlume
17th Nov 2016 13:39

Well if you wanted the mathematical solution:

C=[log(X)-log(A)]/log(1-B)

Thanks (0) By Abacus Finch
17th Nov 2016 13:45

I think the question was to solve for the number of years

C = log(X/A) / log(1 – B)

Thanks (0) By NomDePlume
17th Nov 2016 13:50

Which is, of course, the same equation

Thanks (0) By Abacus Finch
17th Nov 2016 14:00

Thanks (0) By NomDePlume
17th Nov 2016 14:10

But yours was more elegant :)

Thanks (0) By tom123
17th Nov 2016 13:53

Great, thanks I will give this a try (and report back)!

Thanks (0) By tom123
17th Nov 2016 14:13

Thanks again, this does exactly what I need.

I can honestly say this is the first time I have used 'log' in a work environment!

Cheers.

Thanks (1) By Scriptic
17th Nov 2016 15:17

Using Excel
In A1 turn Depreciation into a markup - B/(1-B)
in B1 enter NBV (including decimals)
in B2 enter B1+(B1*\$A\$1)
Drag and drop for no. of years

Thanks (1) By Simon Hurst
18th Nov 2016 12:42

In this case using the right formula solves the problem but, in general, if you can't work out what the formula should be, it might also be worth having a look at Excel's Goal Seek feature (Data ribbon tab, What If? Analysis drop down). This can help you work 'backwards' from a known answer to the required input for a formula.

Thanks (0) 