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Equivalent annual cost

Forums › Ask ACCA Tutor Forums › Ask the Tutor ACCA FM Exams › Equivalent annual cost

  • This topic has 3 replies, 2 voices, and was last updated 9 years ago by John Moffat.
Viewing 4 posts - 1 through 4 (of 4 total)
  • Author
    Posts
  • March 10, 2016 at 10:41 am #305181
    Johann
    Member
    • Topics: 12
    • Replies: 16
    • ☆

    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.

    March 10, 2016 at 11:11 am #305201
    John Moffat
    Keymaster
    • Topics: 57
    • Replies: 54829
    • ☆☆☆☆☆

    There is no reason on earth that it should come to 14,000! (Although the total spend is 14,000 over the 2 years, it is spread over the 2 years and therefore there is interest to take into account).

    The terminal value of the original flows (the value at the end of time 2) is:
    (10,000 x (1.1^2) + (2,000 x 1.1) + 2,000 = 16,300

    The EAC is equivalent to paying 7763.69 at time 1 and at time 2.
    The terminal value of these is:
    (7763.69 x 1.1) + 7763.69 = 16,304 (the difference is solely rounding).

    However I have no idea why you should want to do this – it is irrelevant for the exam 🙂

    March 10, 2016 at 11:18 am #305207
    Johann
    Member
    • Topics: 12
    • Replies: 16
    • ☆

    Dear John

    Thanks for the reply.

    I just hate learning rules and was trying to figure the logic out of it. Now it is clear

    Thanks for your usual assistance much appreciated 🙂

    March 10, 2016 at 12:00 pm #305231
    John Moffat
    Keymaster
    • Topics: 57
    • Replies: 54829
    • ☆☆☆☆☆

    You are welcome 🙂

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