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Dear Sir,
In the approach for question b(ii), I am confusing about the way to determine the amount of repayment each year.
– Suggested answer from ACCA stated that:
“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”– However, on my own thinking, it should be calculated as follows
“Repayment each year = $100/total discount factor (using yield rate based on BBB rating)
=$100/4.57 = $21.89”
In my approach, I already know:
1/ The present value of the bond: $100
2/ The effective interest each year to determine the discount factor.I also know that with the approach of ACCA, the PV of all of the repayments when discounted at the coupon rate will always be equal to the amount originally borrowed. So, should I ignore the coupon rate of 3.57% in my calculation to determine repayment each year?
Thanks in advance.
In other words, my approach would bee similar to the approach to determine coupon rate in section b(i).
For all 2 sections, we have to determine the amount received each year.
– In section b(i), new bond with “unknown coupon rate”, as well as “unknown repayment”
– In section b(ii), new bond with “unknown repayment each year”So, please help me clarify the difference.
Always, the PV of the repayments (interest and capital) discounted at the coupon rate will equal the amount borrowed (in this case the nominal value). This is the case however repayments are made. Usually interest is paid at the coupon rate each year and then there is the repayment of the full amount at maturity.
However in this case (and something the examiner does reasonably often) there are repayments each year of an equal amount consisting partly of interest (at the coupon rate) and partly of capital. Because it is an equal amount each year, the total repayment each year is the nominal amount divided by the annuity factor at the coupon rate of 3.57%. This total repayment is the interest (at 3.57%) plus part repayment of the capital.
So in the answer to part (iv) of the question, the interest paid in the first year is 3.57% x 1320 = 47.124 (on which there is a tax saving, leaving a net 40.06 reduction in the profit). The remainder of the repayment would reduce the borrowing remaining and therefore reduce the interest element in the following year. (This last sentence is irrelevant for this particular question but there have been several past equations where you have been required to produce a forecast SOPL and a forecast SOFP for several future years. in which case the amount remaining owing would reduce each year and the interest would therefore also reduce each year – the total of the two remaining at the same equal amount each year).
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