Premium and Discount (section 6.3)
(I) Bonds purchased at a premium
If P > C, then a bond is said to be purchase at a premium
(premium = P C).
· this occurs when Fr > Ci
This says that each bond coupon payment (Fr) exceeds the bond coupon that the investor actually would be happy with (Ci).
A bond coupon is considered taxable income
· this means the investor is paying more tax each period that he/she would like
(pay tax on Fr, when they feel they should pay tax on Ci).
However, when the bond is redeemed on the redemption date, the investor suffers a LOSS equal to P C.
· bond holder paid $P for the bond, but only gets back $C (and P > C).
· This loss can be used to lower your income (in the year that you redeem the bond); this reduces your taxable income and you pay less in taxes
So, it would be better (from a tax point of view) if the investor could “spread” the LOSS that occurs at redemption over the lifetime of the bond
· best if the investor could take the loss and allocate a tiny bit of it to each and every coupon
· investor pays less tax every period (pay tax on Ci, not Fr)
To do this, we use part of each coupon, Fr, to amortize the premium over the lifetime of the bond
· the value of the bond will be reduced from P down to C by the redemption date
This process is called the amortization of a premium or the process of writing down a bond
We will use a bond amortization schedule to show:
· the amortization of the premium at each coupon date
· the book value of the bond after each coupon payment
Example 6.3.1
A $10,000 bond is redeemable at par in 3 years at j2 = 6%. It is bought to yield j2 = 5%. Set up a bond amortization schedule.
Solution to 6.3.1
Notes
1. The book value at any time can be calculated using either purchase price formula, with n = # of payments remaining
2. Sum of book value adjustment column = premium
3. Entries in the book value adjustment column are in the ratio of (1+i )
(II) Bond purchased at a discount
If P < C, then a bond is said to be purchase at a discount (discount = C P).
· this occurs when Fr < Ci
· each bond coupon payment (Fr) is less the bond coupon that the investor actually would be happy with (Ci)
Since a bond coupon is considered taxable income, this means that the investor is paying less income tax each period that he/she would be willing to pay
(pay tax on Fr, when they would be will...
