# calculation of average book value

I recall AAR = Average income/average book value the book value of the years: 300,200,100,0 and average book value = (300+0)/2 is this a short for (300+200+100+0)/4 (which makes more sense to me) or there is other explanation?

Don’t think so… these could be different… If you are given beginning and ending values, Avg = (BV+EV)/2 Ex: if book values are 300, 150, 50,0 per your method: avg = (300+150+50+0)/4 = 125. But correct value is (300+0)/2 = 150.

thank you sumit. is there such a formula ---- average book value = (beginning + ending )/2 ?

simple arithmetic mean

I don’t understand this either. This is from reading 35 btw section 4.5.

The net incomes in the book are 6 24 48 18 -6

Simple arithmetic mean is what is used in the book for this one to get 90/5 = 18.

The value of the project is 200 with 40 depreciation per year. So it should be 160 120 80 40 0 i.e. 400/5 = 80 going by the same logic as net income, yet they take an arithmetic average over just two years???

The way I thought of calculating it gives the same average book value provided in the reading. Net income only occurs at the end of each year, but you still start with book value at t=0, so that value needs to be included in calculation. Average book value then becomes (200 + 160 + 120 + 80 + 40 + 0)/6 = 600/6 = 100

Same answer as the beginning minus final over two

But I am curious as if average of the beginning and end balance is always to be used or only in level depreciation, as it only makes sense to me to be used when level…