Math 420 Bonds Problem Set 5b
Premium and Discount
1. A 10,000 par value 10-year bond with 7% annual coupons is bought at a premium to yield an annual
effective rate of 5%. Calculate the interest portion of the 8 th coupon.
2. A 1000 par value 5-year bond with 8% semiannual coupons was bought to yield 7.5% convertible
semiannually. Determine the amount of premium amortized in the 6 th coupon payment.
3. A 10-year bond with par value of 1000 is purchased to yield 8% convertible semiannually. The bond
is redeemable at par. The interest paid portion of the first semiannual coupon is 44.50. At what
nominal rate of interest convertible semiannually are the coupons paid?
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Math 420 Bonds Problem Set 5b
4. Tim buys an n – year 1,000 par value bond with 6.5% annual coupons at a price of 825.44.
the price assumes an annual effective yield rate of i. The total write-up in book value of a bond
during the first 2 years after purchase is 23.76. Calculate i.
5. A 30-year 10,000 bond that pays 3% annual coupons matures at par. It is purchased to yield 5% for
the first 15 years and 4% thereafter. Calculate the amount for accumulation of discount for year 8.
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Math 420
Price of Bond between Coupon Dates
Bonds Problem Set 5b
6. A 1000 par value 5-year bond with semiannual coupons of 60 is purchased to yield 8% convertible
semiannually. Two years and two months after purchase, the bond is sold at a price which maintains
the same yield for the buyer. Calculate this price.
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Math 420 Bonds Problem Set 5b
7. Find the flat price, Market price, and Accrued coupon for the following bond on Aug 1, 2002
Face value = 100
Coupon rate = 10% convertible semiannually
Yield rate = 15%, convertible semiannually
Purchase date : June 18, 1990
Redemption date : June 18, 2010
1 st Coupon : Dec 18, 1990
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Math 420
Callable Bonds
Bonds Problem Set 5b
• Callable Bond: a bond that may be redeemed early on a “call date” (i.e. before the maturity date) at the discretion of the borrower (the bond issuer).
• Putable Bond: a bond that may be redeemed early on a “put date” (i.e. before the maturity date) at the discretion of the lender (the bond buyer). They are less common.
- Most bonds issued corporations and by state and local governmental entities are callable.
- Bonds issued by US Treasury are generally not callable.
- A callable bond will sell at a higher yield rate (lower price) than an otherwise identical non-callable
bond because of the uncertainty attached to the ultimate term of the bond.
- A putable bond will sell at a lower yield rate (higher price) than an otherwise identical non-putable
bond.
How do we calculate the price of a callable bond if the term of bond is uncertain?
1. If the redemption values on all redemption dates are equal, a) assume that the redemption date will be the earliest date possible when the bond sells at a
premium. (premium => “loss” to holder upon redemption, and issuer wants this loss to
happen asap) b) assume that the redemption date will be the latest date possible when the bond sells at a
discount. (discount => “profit” to holder upon redemption, and issuer wants this profit to
happen as late as possible)
2. If redemption values on all redemption dates are not equal, then the bond holder should compute the purchase price for all possible call dates at a desired yield rate and then pay no more than the lowest of these prices to guarantee the minimum desired yield rate.
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Math 420 Bonds Problem Set 5b
8. Consider a $100 par value 4% bond with semiannual coupons callable at $109 on any coupon date starting 5 years after issue for the next 5 years, at $104.50 starting 10 years after issue for the next 5 years, and maturing at $100 at the end of 15 years. Find the highest price which an investor can pay and still be certain of a yield of a) 5% convertible semiannually b) 3% convertible semiannually
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