Solution to Case 8

Bond Analysis and Valuation

Corporate Bonds −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 could explain the relationship between coupon rates and bond prices by calculating the prices of bonds, which have similar features except for their coupon rates, under different assumptions regarding the yield to maturity. [For example, the 0%, AAA-rated, 20-year ABC Energy bond and the 5%, AAA-rated. 20-year ABC Energy bond.]

Bond Coupon Rate Maturity Face Value Rating Yield Price % Change

ABC Energy 5% 20 $1,000 AAA 2% $1,490.54 49.05% ABC Energy 5% 20 $1,000 AAA 5% $1,000.00 0.00% ABC Energy 5% 20 $1,000 AAA 8% $705.46 -29.45%

ABC Energy 0% 20 $1,000 AAA 2% $672.97 78.56% ABC Energy 0% 20 $1,000 AAA 5% $376.89 0.00%

ABC Energy 0% 20 $1,000 AAA 8% $214.55 -43.07%

The table shows that the 5% coupon bond has a wider fluctuation in price than the zero-coupon bond for equivalent changes in yields.

1

2. How are the ratings of these bonds determined? What happens when the bond ratings get adjusted downwards?

The ratings are determined by professional rating agencies such as Standard & Poor’s and Moody’s. Each of these rating agencies has a committee that evaluates the risk level of a company’s bond issue and accordingly assigns a rating ranging from AAA or Aaa (best rating) down to D (default). The ratings are periodically re-evaluated whenever there is any significant development in a company’s capital structure or earnings performance. When ratings get adjusted downward, the bond becomes less attractive and therefore its required rate of return goes up, reducing 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?

Jill should explain that bonds can be issued at a discount, at par, or even at a premium from face value, depending on the firm’s preference for the coupon rate that will be paid. The vast majority of bonds are sold at par ($1000) with the coupon rate being set equal to the yield that is commensurate with its rating and maturity. After being issued, however, the yields demanded by investors will change based on economic and company-specific factors, but the coupon rate is fixed. Thus, the price has to vary in line with the consensus yield demanded by investors. 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, leading to a drop in price and vice-versa. Thus, as long as the yields are a true reflection of the risk level of the bond (which would happen in efficient markets), bond prices, whether at a discount or a premium from face value, would be “just right” and not really a bargain or overpriced.

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, reinvests the coupons, and receives the face value when it matures. 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 year, Face Value = $1000, Price = $703.1 (semi-annual coupons)

PV = -$703.1; FV = $1000; N = 40; PMT = $25; CPT I = 8.03%

2

Issuer Face Value Coupon Rate Rating Quoted Price

Years until maturity

Sinking Fund

Yield to maturity

ABC Energy $1,000 5% AAA $703.10 20 Yes 8.0310% ABC Energy $1,000 0% AAA $208.30 20 Yes 8.1597% TransPower $1,000 10% AA $1,092.00 20 Yes 8.9927%

Telco Utilities $1,000 11% AA $1,206.40 30 No 8.9923%

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 Quoted PriceYears until

maturity Sinking

Fund Call

Period

Nominal Yield to maturity

Effective YTM

ABC Energy $1,000 5% AAA $703.10 20 Yes 3 Years 8.0001% 8.1601%ABC

Energy $1,000 0% AAA $208.30 20 Yes NA 7.9997% 8.1597%TransPo

wer $1,000 10% AA $1,092.00 20 Yes 5 Years 9.0001% 9.2026%Telco

Utilities $1,000 11% AA $1,206.40 30 No 5 Years 8.9998% 9.2023%

The nominal yield to maturity on the bonds is calculated by multiplying the semi-annual yield by 2. 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 4.00%. The effective annual YTM would be calculated as ((1+.04)2)-1 = .0816 or 8.16%. Since the YTM is merely a promised 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. Jill should explain to the audience that call provisions are attached to bonds so as to allow companies to refinance their debt at lower rates when interest rates drop. Thus, 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 (typically equal to one extra coupon) when the bond is called. Furthermore, there is generally a deferred call period of about 5 years, during which the bond cannot be called. In the case of callable bonds, investors should calculate the yield to first call of the bonds and decide accordingly. For this calculation, the future

3

value is set equal to $1000 + 1 year’s coupon, and the maturity is assumed to be the number of years until the bond becomes freely callable.

7. How should Jill go about explaining the riskiness of each bond? Rank order the

bonds in terms of their relative riskiness.

Issuer Face Value

Coupon Rate Rating

Quoted Price

Years until maturity

Sinking Fund

Call Period

Nominal Yield to maturity

Effective YTM

Risk Rank (1=low)

ABC Energy 1000 5% AAA 703.1 20 Yes 3 Years 8.0001% 8.1601% 1 ABC Energy 1000 0% AAA 208.3 20 Yes NA 7.9997% 8.1597% 2 TransPower 1000 10% AA 1092 20 Yes 5 Years 9.0001% 9.2026% 3

Telco Utilities 1000 11% AA 1206.4 30 No 5 Years 8.9998% 9.2023% 4

The bond ratings provide a general guide as to the credit risk associated with each bond. Within each rating though, investors need to be aware of call risk, reinvestment risk, maturity risk, and the sinking fund provision’s effect on risk. Callability makes a bond have higher reinvestment risk. Among the AAA bonds, the zero coupon bond has no call risk, no reinvestment risk, but the highest price risk. Among the AA bonds, Telco Utilities’ bond has a longer maturity and no sinking fund making it the riskiest of the lot.

8. One of Jill’s best clients poses the following question, “ If I buy 10 of each 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 she proceed?

Realized Return = [{Future Value of reinvested coupons + Face Value}/Price of Bond ]1/n - 1

Issuer Face Value Coupon Rate

Quoted Price

Years until maturity

Call Period

Nominal Yield to maturity

FV of Coupon

FV of Coupon+Face Vaue

Realized Return

ABC Energy 1000 5% 703.1 20 3 Years 8.0001% $1,685.06 $2,685.06 6.82%

ABC Energy 1000 0% 208.3 20 NA 7.9997% $0.00 $1,000.00 8.00%

TransPower 1000 10% 1092 20 5 Years 9.0001% $3,370.13 $4,370.13 7.06%

Telco Utilities 1000 11% 1206.4 30 5 Years 8.9998% $7,479.54 $8,479.54 6.61% In the case of the ABC Energy, 5% coupon bond the realized return is calculated as follows: Future Value of Reinvested Coupons: PMT = -$25 (semiannual); n = 40; i/y = 2.5%; (reinvestment rate); PV = 0; CPT FV = $1,685.06 Realized Return = [{(1685.06+1000)/703.1}]1/40 – 1 = 3.41%*2= 6.82% Note: The number of bonds purchased does not affect the realized return

4