Bond Interest Question

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Amtrak

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Hey Everyone,

I'm using Stalla and am reading over the FI section and came across something, probably simple, but just a little confused.

If an issuer sells $1,000,000 par value of 5-year, 8% accrual bond at a price of 100-3/4 the value at issuance = 100.75/100 * $1,000,000 = $1,007,500 and the value at maturity = ($1,000,000)(1+.08/2)^10 = $1,480,244...now here's my question:
I know a million of that value at maturity is the principal being paid back and $400,000 is the scheduled coupon payments ($1,000,000*.04*10) so that leave's the interest earned on the deferred coupon payments to be $80,244. Is there a way to calc the $80,244 or is the only way to back into it by subtracting the principal and coupon payments from the value at maturity? Again, i'm sure its probably something easy i'm missing but I'd appreciate any help! Thanks in advance.
 
Reading your post, the value at maturity is just the future value of 1 million given the 8% annual discount rate, compounded semiannually. The value of the coupon payments is not included.



Edited 1 time(s). Last edit at Thursday, August 2, 2007 at 12:00AM by FourCastles.
 
Amtrak, I believe that the figure of $1,480,244 that you calculated is not the value at of the bond at maturity, but is the total dollar amount you would have at maturity for a bond purchased at par, assuming you could reinvest all coupon interest at the same 8% interest rate.
 
I was confused by this Stalla question as well. The text states that the $1,480,244
represents:

$1,000,000 of principal repayment, $400,000 of scheduled coupon payments, and $80,244 of interest earned on the deferred coupon payments

FourCastles and annasmom, if this figure does not include deferred interest on the coupon payments, how would you calculate it?
 
I agree with annasmom and FourCastles about your calculation. Accrual bonds do not have scheduled coupon payments, though, so I'm a little confused by this question.

Edit: The $40,000 semi-annual payments that are deferred grow at a rate of .08/2. This is how you get the $480,244. Why do you need to strip out the $80,244? Regardless, you should be able to do it intuitively by calulating the FV of the deferred coupon payments, and subtracting out what you know to be the payments.



Edited 1 time(s). Last edit at Thursday, August 2, 2007 at 01:36PM by alphabound.
 
The key idea here is that accrual bonds do capture the reinvested rate that coupon bonds are at risk of missing (due to changes in interest rates while the bonds are outstanding)... I believe Amtrak's question is simply answered as the
Income earned from "deferred interest" is
n=10
i=4
PMT=40,000
FV=480,244

"Coupon payments" received = 400,000 (i.e. 40,000 x 10 pmts)

Therefore the compounded interest on the coupons reinvested at the coupon rate is the difference i.e. 80,244... this is the differentiator between accrual bonds and coupon bonds as it is guaranteed income for accrual bonds and subject to rate changes for coupon bonds.

The above steps are really the only what to calculated the interest earned on reinvestments.
 
I agree. Finding the FV of the deferred payments and subtracting out the original payment amounts is the easiest. Out of curiosity I worked it out on a spreadsheet and came up with a formula that will calculate the 80,244, but it would be insane to try and use it for anything like this problem.
 
Zero coupou bond are pretty straightforward with no reinvestment risk. It needs to be sold at large discount.
I do not know why we need to understand it like this and make life harder.
 
Thanks everyone for your posts! I do understand that finding the FV and subtracting out the original payment amounts would be the easiest, just wondering if there would be another way to arrive at the 80,244...but I see that would most likely be more complicated and not relevant for the exam. Thanks again!
 
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