Equivalent annual cost

Good morning professor

Would like to ask a question on asset replacement using Annuity factor in order to calculate the EAC.

Let’s say we buy a machine for $10,000 and this will entail Eur 2000.00 maintenance costs each year.

Now let’s consider the optimum replacement cost happens every two years so

pv = 10,000 * discount factor for yr 0 = 10,000
2000 * discount factor for yr 1 = 2000 * .909 = 1818
2000 * discount factor for yr 2 = 2000 * .826 = 1652

So npv = 10,000+1818+1652 = (13470)

Eac = 13470 / 1.735 = 7763.69

Now my question is if the equivalent annual cost is 7763.69 p.a in present value terms if we multiply 7763.69*1.1 + 7763.69 * 1.1 shouldn’t this come equal to 14,000.00. What am I missing?

On the other hand considering the initial cash flow of 10,000 is occurring in year 0 and therefore discount factor is 1, if we take the annuity by adding 1 to the year 1 discount factor gives

14000 * .826 = 11564 (present value)

11564 / 1.909 = 6057

6057 * 1.1 + 6057 * 1.1= 13991 which is equal to 14000

Don’t know if I have made my point but appreciate if you can explain the logic behind the above.