# They Are More Complex Than You Think

1. How should Jill go about explaining the relationship between coupon rates and bond prices? Why do the coupon rates for the various bonds vary so much? Jill should explain the relationship between coupon rates and bond prices by calculating the price of the bonds, which have similar features except for the coupon rate. Let’s compare ABC Energy issuer with the coupon rate 5% and 0% (the same with a rating and YTM)

Issuer
Maturity
Face Value
Coupon Rate
Rating
Yield
Price
% Change

ABC Energy
20
1000
5%
AAA
2%
\$1,490. 54
49. 05%

ABC Energy
20
1000
5%
AAA
3%
\$1,297. 55
29. 5%

ABC Energy
20
1000
5%
AAA
5%
\$1,000. 00
0. 00%

ABC Energy
20
1000
5%
AAA
6%
\$885. 30
-11. 47%

ABC Energy
20
1000
0%
AAA
2%
\$672. 97
-32. 70%

ABC Energy
20
1000
0%
AAA
3%
\$553. 68
-44. 63%

ABC Energy
20
1000
0%
AAA
5%
\$376. 89
-62. 31%

ABC Energy
20
1000
0%
AAA
6%
\$311. 80
-68. 82%

The table shows that the 5% coupon bond has a wider fluctuation in price than the zero-coupon bond for equivalent changes in yield.
2. How are the ratings of these bonds determined? What happens when the bond ratings get adjusted downwards? The ratings of these bonds are determined by two professional bond-rating firms: Moody’s and Standard & Poor’s (S&P).
Each of these bond-rating firms has a committee that evaluates the risk level of the company’s bond issue. It assigns a rating ranging from AAA or Aaa (best rating) down to D (default). The ratings are periodically re-evaluated whenever there is a significant development in a company’s structure or earning performance. When the ratings get adjusted downward, the bond becomes less attractive. Hence, the rate of return goes up to reduce its price.
3. During the presentation, one of the clients is puzzled why some bonds sell for less than their face value while others sell for a premium.
She asks whether the discount bonds are a bargain. How should Jill respond? Bonds can be issued at a discount, at par, or even at a premium from face value. The majority of bonds are sold at par (\$1,000) with the coupon rate being set equal to the yield that proportional to its rating and maturity. After it is being issued, the yields demanded by investors will change, but the coupon rate still stays the same. If the yield exceeds the coupon rate, investors are demanding a higher rate of return than what the company is currently paying via the coupon payment, which leads the price drops and vice versa.
As long as the yields are a true reflection of the risk level of the bond, there would not be any bargain for the bond price, whether at a discount or premium from face value.
4. What does the term “yield to maturity” mean and how is it to be calculated? The “yield to maturity” (YTM) of a bond is the rate of return that an investor expects to earn when he or she buys the bond at its current price, receive the face value when it matures. The YTM is considered a long-term bond yield expressed as an annual rate. The YTM of a bond is also known as its promised yield.
To calculate a bond’s YTM, we must use the following inputs:
For example: ABC Energy, 5%, 20 years, face value \$1,000, price \$703. 1 (semi-annual coupons) PV= -703. 1, N=40, PMT = 25, FV = 1000 => I = 4 (semi-annual) Interest annual = 4%*2 = 8 %
5. What is the difference between the “nominal” and effective yields to maturity for each bond listed in Table 1? Which one should the investor use when deciding between corporate bonds and other securities of similar risk? Please explain.

Issuer
Face Value
Coupon Rate
Rating Quote
Price
YTM Sinking
Fund Call Period
YTM (semi-annual)
Nominal YTM
Effective YTM

ABC Energy
1000
5%
AAA
703. 20
yes
3
4. 0001%
8. 0001%
8. 1601%

ABC Energy
1000
0%
AAA
208. 320
yes
n/a
3. 9999%
7. 9997%
8. 1597%

TransPower
1000
10%
AA
1,092.00
yes
5
4. 5000%
9. 0001%
9. 2026%

Telco Utilities
1000
11%
AA
1206. 430
no
5
4. 4999%
8. 9998%
9. 2023%

The nominal yield to maturity on the bond is calculated by multiplying the semi-annual yield by two. The effective YTM is calculated by compounding the semi-annual yield for two periods. For example, on the ABC Energy 5%, 20 year bond, the semi-annual YTM is 4%. The effective annual YTM would be calculated [(1+0. 4)^2]-1 = 0. 0816 or 8. 16%.
Since the YTM is a promising yield with the actual yield being dependent on the reinvestment rate that each investor is able to earn, it is best to compare similar risk bonds on the basis of their nominal YTMs.
6. Jill knows that the call period and its implications will be of particular concern to the audience. How should she go about explaining the effects of the call provision on bond risk and return potential? Call provisions are attached to bonds so that it allows companies to refinance their debt at lower rates when interest rates drop.
The existence of a call provision presents a risk to the bond investor that their investment horizon on that bond may be prematurely ended. Moreover, there is reinvestment risk associated with callable bonds, since the bonds are called when rates are low. The company does pay a premium when the bond is called. Furthermore, there is a deferred call period for five years, which the bond can’t be called. In the case of callable bonds, investors should calculate the yield to the first call of the bonds to decide.
For this calculate, the future value is set to equal to \$1,000 + 1-year coupon, the maturity is assumed to be the number of years until the bond becomes callable.
7. How should Jill go about explaining the riskiness of each bond? Rank the bonds in terms of their relative riskiness.

Issuer
Face Value
Coupon Rate
Rating Quote
Price
YTM Sinking Fund
Call Period
YTM (semi-annual)
Nominal YTM
Effective YTM
Risk Rank (1=low)

ABC Energy
1000
5%
AAA
703. 120
yes
3
4. 0001%
8. 0001%
8. 1601%
1

ABC Energy
1000
0%
AAA
208. 320
yes
n/a
3. 9999%
7. 9997%
8. 1597%
2

TransPower
10001
0%
AA
109220
yes
5
4. 5000%
9. 001%
9. 2026%
3

Telco Utilities
1000
11%
AA
120630
no
5
4. 4999%
8. 9998%
9. 2023%
4

The bond ratings provide a general guide as to the credit risk associated with each bond. Within its ratings, investors need to be aware of call risk, reinvestment risk, maturity, and the sinking fund provision’s effect on risk. Callability makes a bond have a higher reinvestment risk. Among the AAA bonds, the zero-coupon bond has no call risk, no reinvestment risk, but a higher price risk. Among the AA bonds, Telco Utilities has a longer maturity and no sinking fund making it the riskiest. One of Jill’s best clients poses the following questions, “If I buy 10 of each of these bonds, reinvest any coupons received at the rate of these bonds, reinvest any coupons received at the rate of 5% per year and hold them until they mature, what will my realized return be on each bond investment? ” How should Jill respond?

Issuer
Face Value
Coupon Rate
Price
Years Until
YTM Sinking Fund
Call Period
YTM (semi-annual)
Nominal YTM
Effective YTM
FV of coupon
FV of coupon + FV
Realized Return (Semi-Annual)
Realized Return

ABC Energy
1000
5%
703. 1
20
yes
3
4. 0001%
8. 001%
8. 1601%
\$1,685. 06
\$2,685. 06
3. 41%
6. 81%

ABC Energy
1000
0%
208. 3
20
yes
n/a
3. 9999%
7. 9997%
8. 1597%
\$0. 00
\$1,000. 00
4. 00%
8. 00%

TransPower
1000
10%
1092
20
yes
5
4. 5000%
9. 0001%
9. 2026%
\$3,370. 13
\$4,370. 13
3. 53%
7. 06%

Telco Utilities
1000
11%
1206
30
no
5
4. 4999%
8. 9998%
9. 2023%
\$7,479. 54
\$8,479. 54
5. 00%
9. 99%

In the case of the ABC Energy, 5% coupon bond, the realized return is calculated as follows: Future value of reinvested coupon N=40, I = 2. 5, PV=0, PMT=25 => FV= 1685. 06 Realized return = [(1685. 06+1000)/703. 1]^(1/40) -1 = 3. 41% *2 = 6. 82%

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