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could you please explain to me about the balancing adjustment of 500 in the question, and why did the answer deducted 125 for balancing adjustment. How did they get to that figure,
The 500 given in the question is not a balancing adjustment – it is the expected sales value at the end of 5 years.
The tax allowable depreciation is 125 per year, and so in year 5 there is a tax balancing allowance of the different between the tax written down value of 625 (1250 – (5 x 125)) and the sale proceeds of 500.
This is standard tax rules, and I suggest that you watch my free Paper FM (was F9) lectures on investment appraisal with tax, because this is revision of Paper FM.
You can find lectures working through the whole of this question if you follow the link to ‘Revision Kit Live’ from the main Paper AFM page.