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Conejo Co Q1 Sep/Dec 2017 – Part b ii

Forums › Ask ACCA Tutor Forums › Ask the Tutor ACCA AFM Exams › Conejo Co Q1 Sep/Dec 2017 – Part b ii

  • This topic has 3 replies, 2 voices, and was last updated 5 years ago by John Moffat.
Viewing 4 posts - 1 through 4 (of 4 total)
  • Author
    Posts
  • September 23, 2019 at 12:58 pm #547129
    Giuseppe
    Participant
    • Topics: 1
    • Replies: 5
    • ☆

    Good afternoon,

    It’s not clear to me what they did in the part:
    “Macaulay duration based on fixed annual repayments of interest and capital”

    Why and how did they get $22.17 per year?

    If one bond value is 100$ and pays 3.57$ interest per year, if I need to repay capital and interest in 5 years, I would split the capital through the 5-year period and adding interest.
    Therefore I would use 23.57 every year.

    Clearly I am wrong, but no idea the rational behind their calculation as per below:

    “Annuity factor: (3·57%, 5 years) = (1 – 1·0357–5)/0·0357 = 4·51 approximately
    Annual payments of capital and interest required to pay back new bond issue = $100/4·51 = $22·17 per $100 bond approximately”

    Any help?

    Thanks

    Giuseppe

    September 23, 2019 at 3:12 pm #547143
    John Moffat
    Keymaster
    • Topics: 57
    • Replies: 54679
    • ☆☆☆☆☆

    The reason that you are wrong is that as the capital is repaid, the interest each year will reduce. The interest each year is not $3.57, but is 3.57% of the amount owing at the start of each year.

    It is a fact that however a loan is repaid, the present value of the interest and repayments when discounted at the cost of borrowing will always equal the amount of the loan. (Try it yourself if you want with made up figures, and however the loan is repaid the PV will always be the amount borrowed.)

    Here, the repayment and interest are of equal amounts each year.
    Therefore is the repayment is X per year, then the PV of X per year for 5 years when discounted at 3.57% will be equal to $100.

    Therefore X x 5 year annuity factor at 3.57% = 100
    Therefore X = 100 / (the 5 year annuity factor at 3.57%).

    You can easily prove that it ‘works’. The interest in the first year will be 3.57 and after a repayment of 22.17 they will be owing 81.40 at the end of the first year.
    So the interest in the second year will be 2.91 (3.57% x 81.40) and so they will be owing 81.40 + 2.91 – 22.17 = 62.14 at the end of the second year.

    If you carry on each year in the same way, you will find that at the end of the 5th year the amount owing will be zero (not exactly zero but that is simply because of roundings).

    September 24, 2019 at 11:52 am #547191
    Giuseppe
    Participant
    • Topics: 1
    • Replies: 5
    • ☆

    Good morning,

    thanks for your quick and helpful answer.
    It makes sense to me.

    Thanks again and thank you for the great job done with your lectures.

    Giuseppe

    September 24, 2019 at 3:50 pm #547204
    John Moffat
    Keymaster
    • Topics: 57
    • Replies: 54679
    • ☆☆☆☆☆

    You are welcome, and thank you for your comment 🙂

  • Author
    Posts
Viewing 4 posts - 1 through 4 (of 4 total)
  • The topic ‘Conejo Co Q1 Sep/Dec 2017 – Part b ii’ is closed to new replies.

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