Bond pricing, premium and discount

2 free worked examples

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1. Exam FMBond pricing, premium and discountCore

   A 1,000 par-value 10-year bond with 8% annual coupons is bought to yield 6% effective. Find the price.

   1. A$1,000.00$
   2. B$1,080.00$
   3. C$1,147.20$
   4. D$1,200.00$
   5. E$1,260.00$

   Solution

   1. Use the basic formula $P=Fr{a}_{\overline{n}|i}+C{v}^n$, with the coupon rate applied to FACE and the yield discounting to REDEMPTION.
   2. $Fr=1,000(0.08)=80$, $a_{\overline{10}|0.06}=7.360087$, $v^{10}=0.558395$.
   3. $P=80(7.360087)+1,000(0.558395)=588.81+558.40$.
   4. $=1,147.20$ - a premium bond, because the coupon rate exceeds the yield.

   Trap. Discounting the coupons at the coupon rate rather than the yield.

2. Exam FMBond pricing, premium and discountStretch

   A callable bond trades at a premium. To be safe, an investor should price it to which date?

   1. AThe maturity date
   2. BThe earliest call date
   3. CThe latest call date
   4. DThe midpoint of the call window
   5. EIt makes no difference

   Solution

   1. The ISSUER chooses when to call, and will choose whichever date is worst for the investor.
   2. A premium bond's book value falls towards redemption over time, so the investor loses most if the bond is called EARLY.
   3. Pricing to the earliest call therefore guarantees at least the assumed yield whatever the issuer does.
   4. For a DISCOUNT bond the reasoning reverses: the book value rises, so the worst case is the latest call date.

   Trap. Pricing a callable premium bond to maturity and overpaying for a bond that will be called.