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- November 22, 2019 at 5:56 pm
It seems this examiner likes testing annuity-type bonds and, judging by examiner reports , students struggle with them.
One that has me stumped is Bento June 2015.
” i. $30 million loan in the form of an 8% bond on which interest is payable annually, based on the loan amount outstanding at the start of each year. The bond will be repaid on the basis of fixed equal annual payments (constituting of interest and principal) over the next four years;”
Solution suggest annuity of $9.057m each year, which is an annuity based on the 4yr 8% coupon. Which seems fine. But how does this meet the requirement of the annual interest being “based on the loan amount outstanding at the start of each year”. As principal is being repaid each year, the amount of the loan outstanding at the start of each year is decreasing, which would lead me to think the interest charged (8%) would decrease each year, so how would the annual cashflows stay constant… or is it that the $9.507m per annum payment contains differing amounts of principal and interest each year, so that this requirement holds? I’m probably getting bogged on small detail but i’ve messed up annuity bonds a couple of times now.
ThanksNovember 22, 2019 at 7:22 pm
Too late for me to edit my comment, but rooting around I think my confusion was between the Interest cost to hit our p&L account as finance cost (8% of o/s loan each year) vs. the actual cashflows (principal & interest) being paid to bondholders. Similar to accounting for leases, where the finance cost to hit our P&L is different to the actual cashflows paid for rental of asset..?November 23, 2019 at 11:14 am
Let me give you an example:
If money is borrowed at (say) 10% a year, then however it is repaid the PV of the repayments (interest and principal) when discounted at 10% will always be equal to the amount borrowed.
If they borrow $100, they might pay interest of $10 a year for 5 years and then repay the $100 in 5 years time. Alternatively they might pay no interest at all during the period but then have to pay $100 x 1.1^5 in 5 years time. It doesn’t matter how it is all paid – the PV would always be $100. Try it yourself and see 🙂
(It is because the whole point of the discounting is to ‘remove’ the interest at 10%).
So, for the same example, if they are repaying interest and principal by paying a fixed amount of X per year, then the PV of X per year at 10% must equal the amount borrowed.
The PV of X per year for 5 years is X x the 5 year annuity factor.
Therefore X must be equal to the amount borrowed divided by the 5 year annuity factor.
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