CHAPTER 10 / Bonds

Solutions

Concept Review Questions

1. Match the following bond type to the description that fits best:

Bond Type Description

(a) Stripped bond iii. The bond has had its coupon removed; the coupon is an
asset that can be owned separately from the bond.
(b) Agency bond v. The bond is issued by a Crown corporation.
(c) Convertible bond i. The bond can be converted into shares of the issuing
corporation.
(d) Bearer bond ii. The bond owner’s name is not recorded on the bond.
(e) Registered bond iv. The bond owner’s name is recorded on the bond; coupon
payments are made directly to the owner.

3. Describe what a “debenture” is and how it differs from a regular bond.

A debenture is an unsecured loan certificate issued by a company, backed up general
credit rather than by specific assets.

5. Explain the relationship between market rates and bond prices.

There is an inverse relationship between secondary market bond prices and market rates.
When market rates are higher than the coupon rate on an existing bond it will sell at a
discount, that is, at less than par (remember par value is $1,000). Conversely, when
market rates are lower than the coupon rate on an existing bond, it will sell at a premium.

7. Which of the following covenants is not typically applicable to a bond issue?

(a) Ensuring that a current ratio is maintained and a debt-to-equity position is not
exceeded
(b) Limitations on mergers and acquisitions
(c) Limitations on dividend payments to shareholders
(d) Limitations on when coupon payments can be made
Answer: (d) Limitations on when coupon payments can be made

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9. Which of the following statements accurately defines yield to maturity (YTM)?

(a) The YTM is the total anticipated return on a bond if it is held until maturity.
(b) The YTM is the yield at which the bond was originally sold.
(c) The YTM describes the proportion of coupon payments remaining until
maturity.
(d) The YTM is the current percentage above or below face value that a bond is
worth.
Answer: (a) The YTM is the total anticipated return on a bond if it is held until maturity.

11. If equities typically outperform bonds relative to returns, then what is the appeal of
investing in bonds?
Investing in bonds allows an investor to diversify among asset classes and thereby
minimize risk. Further, bonds are typically considered lower risk investments when
compared to equities. They also have a steady fixed income stream via coupon payments,
unlike dividends, which are paid at the discretion of the board of directors.

13. Although bonds are considered lower risk than equities, they do present some risks.
Which of the following accurately describes a major risk that is associated with bonds?
(a) The potential that the bond could be stolen if your house is broken into
(b) The potential that the issuer could default on coupon payments and/or
repayment at maturity, resulting in a capital loss
(c) The potential that the issuer decides to end all bond coupon payments due to a
slumping economy
(d) The potential that interest rates go down, causing the investor’s bond to be
worth less than par
Answer: (b) The potential that the issuer could default on coupon payments and/or
repayment at maturity, resulting in a capital loss.

15. Which of the following statements regarding bond investing is most reasonable?
(a) The percentage of an investment portfolio’s allocation to bonds that may be
most reasonable is driven by the life-cycle stage of the investor, the time
horizon of the investments, the risk tolerance applicable to the investor, and
other factors.
(b) The life-cycle stage is the only driver that is relevant in determining how much
of an investment portfolio should be invested in bonds.
(c) The time horizon of investments should normally override risk tolerance when
making sound bond investment decisions.
(d) Bond investing should only be considered during the wealth accumulation life-
cycle stage.
Answer: (a) The percentage of an investment portfolio’s allocation to bonds that may be
most reasonable is driven by the life cycle stage of the investor, time horizon of the
investments, the risk tolerance applicable to the investor, and other factors.

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The following bond prices are posted for LLC CO corporate bonds:
Description Term Bid Yield Ask Yield Change Bid Price Ask Price Change
LLC CO 1.750 5 YR 1.52 1.51 –0.06 100.88 100.92 0.253
LLC CO 3.250 20 YR 2.65 2.62 –0.03 109.98 110.01 1.101

17. Your parents own an LLC CO 20-year bond; they have asked you to find out what they
could sell it for. What price could they sell it for today?
(a) $999.99
(b) $1,429.54
(c) $1,152.88
(d) $1,099.80
Answer: (d) $1,099.80

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Problems
1. Calculate the conversion ratio where a convertible bond can be exercised with a
conversion price of $33.33.
Conversion ratio = $1,000 bond’s par value ÷ $33.33 conversion price = 30.00
30 common shares can be purchased with a $1,000 bond.

3. Heavy Duty Mechanics Inc. issued bonds with a conversion price of $35.71 while its
shares were trading at $20.00. Subsequently, the stock price soared to $78.25. Is the
bond now in the money, out of the money, or at the money? How much (rounded to
nearest dollar) is the investor’s profit with the new stock price?
The bond is in the money because a profit situation exists, with the profit calculated as
follows:
Conversion ratio = $1,000 par value ÷ $35.71 conversion price = 28.00
28 shares can be purchased.
($78.25 – $35.71 = $42.54 profit per share) × 28 shares = $1,191, or
(28 shares × $78.25 new stock price = $2,191) – $1,000 bond par value = $1,191.

5. In the problem above, how much unpaid interest will have accrued on March 1 and on
December 1 of any particular year? How much is the dirty price on these dates? (Assume
that each month has the same number of days in it.)
Accrued interest on March 1st is: ($15.00 ÷ 6 months) × 1 month = $2.50.
Accordingly, the dirty price (which is the clean price in Q4 above plus accrued interest) is
$935.75 + $2.50 = $938.25
Accrued interest on December 1st is: ($15.00 ÷ 6 months) × 4 months = $10.00.
Accordingly, the dirty price (which is the clean price in Q4 above plus accrued interest) is
$935.75 + $10.00 = $945.75.

7. Calculate the clean price of a 4.0% semi-annual payment, 10-year bond that was issued
2 years ago given a market rate on similar bonds of 5.0%. Would the bond sell for a
premium or at a discount? Explain why.
The present value of the bond can be calculated as follows:
1 1
1− 1−
(1+𝑖𝑖)𝑛𝑛 (1.025)16
Step 1: PVAn = PMT × � � = $20.00 × � � = $261.10
𝑖𝑖 .025
𝐹𝐹𝐹𝐹 $1,000
Step 2: PV = 𝑛𝑛 = = $673.62
(1+𝑖𝑖) (1.025) 16

Step 3: Sum the PVA and PV = $261.10 + $673.62 = $934.72

The (clean) price is easily calculated on the TI-BAII Plus with the following keying
sequence: 2 P/Y, 2 C/Y, 16 N, 20 PMT, 1000 FV, 5 I/Y, PV = 934.72

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 CHAPTER 10 / Bonds

The bond would sell at a discount that is, less than the par value of $1,000 because the
coupon rate of 4% is lower (less attractive to an investor) than the 5% coupon rate that
would be paid on a similar (new) bond just being issued at market rate.

9. Calculate the price of a 4% perpetual bond for an investor who requires a rate of return
of 7%.
Annual coupon payment = $1,000 × 4% = $40.
𝑃𝑃𝑃𝑃 40
PV = = = $571.43
𝐼𝐼 .07