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Hello Sir, can you please answer the following questions regarding this question Levante 12/11 part b?
1- How is the value for 6% calculated as $95.78? Is it via yield to maturity, the way we did for 5% coupon rate?I tried doing that and I got almost $99 as value.
2- How did we end up concluding if 5% should be on discount?
2- The value of discount to be offered is 4.28%. Is it IRR using values from 5% coupon and 6%?
I have tried going through the related technical article as well but I am yet slightly confused.
Please help. Thanks.
1. With a coupon rate of 5% then the interest is $5 per year for 5 years, and then there is the repayment of $100 after 5 years. The present value of these is $95.78. (If you use annuity factors as I would, it comes to $95.76, but that is just the rounding in the tables and is irrelevant)
2. Since in (1) a bond with a nominal value of $100 and a coupon rate would have a value of $95.78, they would only be able to issue it at $95.78, which would be a discount of 100 – 95.78 = 4.22% on nominal value.
3. See my answer to (2) 🙂
Hi John,
Can u explain a bit about part (b)
If only a 5% coupon is offered, the bonds will have to be issued at just under a 4·3% discount. To raise the full $150 million, if the bonds are issued at a 4·3% discount, then 1,567,398 $100 bond units need to be issued, as opposed
to 1,500,000. This is an extra 67,398 bond units for which Levante Co will need to pay an extra $6,739,800 when the
bonds are redeemed in five years.
On the other hand, paying a higher coupon every year of 6% instead of 5% will mean that an extra $1,500,000 is needed
for each of the next five years.
If the directors feel that the drain in resources of $1,500,000 every year is substantial and that the project’s profits will cover
the extra $6,739,800 in five years’ time, then they should issue the bond at a discount and at a lower coupon rate. On the
other hand, if the directors feel that they would like to spread the amount payable then they should opt for the higher coupon
alternative.The company wishes to raise $150M.
If the bonds were issued at nominal value, then they would have to issue 150M / 100 = 1.5M units.
However, since they will have to issue at $95.72, the number of units they will have to issue to raise $150M is 150M/95.7 = 1,567,398 units (the examiner has rounded – he should really have divided by 95.72 which gives a slightly different answer).Since the bonds will be redeemed at par, it means they will have to pay out 67398 x $100 more that if they had issued the bonds at par, because there are 67398 more units.
A 6% coupon means paying 1% more interest a year than a 5% coupon.
1% x $150M = $1.5M
Thank you John.
Can I say 6 % bond is 1.5m per year and in five years is $7.5m.
And for 5%, is $6.7398m to pay more.Hence, can say 6% bond is slightly more expensive?
You could say that by all means (although it should be written as $7.5M over 5 years 🙂 )
Part b) Option ii) Coupon Rate – I used the IRR approach as follows:
Yr. C/F DF (5%) PV DF (10%) PV
0 (95.71) 1 (95.71) 1 (95.71)
1–5 5.00 4.329 21.65 3.791 18.96
5 100 0.784 78.40 0.621 62.10
4.34 (17.65)IRR formula 5 + 4.34/21.99 x 5 = 5.99% = rd = coupon rate when nominal value = market value
Would this have been acceptable?
The choice is between issuing bonds at the nominal value and paying high interest each year, and alternatively issuing bonds at a discount and therefore paying lower interest each year but then having to repay a higher amount on redemption when the bonds mature.
So the big difference is one of cash flows – either pay out more each year, or pay out less each year but then more at the end.
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