1. BOND VALUATION AND INTEREST RATES
CHAPTER 8
BOND VALUATION AND INTEREST RATES

2. Chapter outline Introduction What is a bond? Characteristics of bonds
How to value a bond
The different types of bonds
Bond markets and bond ratings
What determines bond yields?
The influence of interest and inflation rates on bonds
Conclusions

3. Learning outcomes By the end of this chapter, you should be able to:
Explain what a bond is and the main characteristics of a bond
Calculate the value of a bond
Describe the various types of bonds, bond markets and bond ratings
Examine what determines bond yields
Explain the relationship between bonds, interest rates and the inflation rate.

4. Introduction A form of debt financing
Used by governments and the corporate sector, usually to finance expansion
Determine a bond’s current value by calculating the present value of all the future cash flows

5. What is a bond?
Companies or governments in need of bonds can borrow money from the public on a long-term basis
The public buys the bond from the borrower (bond issuer) and becomes the lender (bond holder)
The bond issuer is obliged to pay interest (coupons) to the lender at fixed intervals
At the end of the life of the bond (maturity), the bond issuer has to repay the principal amount (par/nominal amount) to the bond holder
Bond issuer generally uses to funds from the bond issue to finance long-term investments/current expenditure

6. Characteristics of a bond
Nominal amount
Amount borrowed and repaid at the end of the life of the bond
Coupon rate
Fixed interest rate that the issuer pays the bond holder every period
Coupon
Amount that the issuer pays the bond holder every period
Maturity
Time left until the bond reaches the end of its term and the nominal value has to be repaid
Yield-to-maturity (YTM)
Interest rate required on bonds. Not fixed rate, but fluctuates

7. Characteristics of a bond
Bonds = interest-only loans
Annuity = makes fixed payments for a specific period of time
Therefore, bond = annuity
If YTM > coupon rate
Investors in the market receive a higher interest rate than bond investors
To attract investors they should be compensated by selling the bond at a cheaper price (trading at a discount)
If coupon rate > YTM
Bond investors will receive a higher interest rate than investors in the market
They will have to pay for the privilege by selling the bond at a more expensive price (trading at a premium)

8. Bond values and interest rates

9. How to value a bond Calculating the value of a bond = 5 variables
With any 4 variables, the 5th can be calculated
Bond = annuity
PV of an annuity: Calculating all the future cash flows and adding them together
Bond = 2 parts
Annuity part (coupon payments)
Nominal value (paid at maturity)
Calculated separately and added together
Bond PV = PV of annuity + PV of nominal value

10. Financial calculator

11. Formulas C = Annuity payment N = Nominal value i = Interest rate
t = Time to maturity

12. Calculating the PV of the bond
Ladybird Ltd. wants to sell bonds with a nominal value of R1 000 that pay annual coupons at a rate of 12% for a period of 7 years. The interest rate in the market is 13%. What is the current value of the Ladybird bond?
Formula
1-[1/(1+i)t]
Annuity = C x i
1-[1/(1.13)7]
= 120 x
= 120 x = N
Nominal = (1+i)t
1000
= (1.13)7 =
R R = R955.77
Financial Calculator
1000 FV
120 PMT
13 I/YR
7 N
PV =

13. Timeline of cash inflows and outflows

14. Semi-annual payments South African bonds are mostly semi-annual
Make 2 payments a year (every 6 months)
Therefore, 3 things needs to happen:
The maturity has to double (maturity x 2)
The coupon rate has to be halved (coupon rate ÷ 2)
The yield-to-maturity has to be halved (YTM ÷ 2)

15. Semi-annual payments
The reason for this is that instead of receiving for instance 10% per year in coupons for a 10 year period, the company:
Makes 2 payments a year of 5% each
There are 2 payments a year for 10 years, therefore 20 periods
The YTM also has to be halved

16. Calculating the PV of the bond
Ladybird Ltd. wants to sell bonds with a nominal value of R1 000 that pay semi-annual coupons at a rate of 12% for a period of 7 years. The interest rate in the market is 13%. What is the current value of the Ladybird bond?
Formula
1-[1/(1+i)t]
Annuity = C x i
1-[1/(1.065)14]
= 60 x
= 60 x = N
Nominal = (1+i) t
1000
= (1.065)14 =
R R = R954.93
Financial Calculator
1000 FV
60 PMT
6.5 I/YR
14 N
PV =

17. Calculate the time to maturity
A company wants to sell bonds with a nominal value of R1 000 that pays annual coupons of 13%. The yield-to- maturity is 15% and the bond are currently selling for R How much time is left to maturity?
Financial Calculator FV
130 PMT
15 I/YR PV
N = 7 years

18. Calculate the coupon rate
A company wants to sell bonds with a nominal value of R that pays annual coupons for 6 years. The yield-to-maturity is 15% and the bond are currently selling for R921. What is the coupon rate of the bond?
Formula
1-[1/(1+i)t]
Annuity = C x i
1-[1/(1.15)6]
= C x
= C x N
Nominal = (1+i)t
1000
= (1.15)6 =
R R = R488.67
= C x
C =
Coupon rate = /1 000
= 12.91%
Financial Calculator FV
6 N
15 I/YR PV
PMT =
Coupon rate = /1 000
= %

19. Calculate the yield to maturity
A company wants to sell bonds with a nominal value of R1 000 that pays annual coupons of 17%. The bond are currently selling for R904. The time to maturity is 19 years. What is the yield to maturity?
Financial Calculator FV
170 PMT
19 N PV
I/YR = 18.88%

20. The different types of bonds
Government bonds
Treasury bills: maturity of less than 1 year
Treasury notes: maturity between 1 and 10 years
Treasury bonds: maturity longer than 10 years
Municipal bonds
Municipalities support debt with property taxes
Corporate bonds
Higher yields – higher risk (lower than governments)
Companies are classified according to:
Specific industry
Credit rating

21. The different types of bonds
Convertible bonds
Gives the owner the right to convert the nominal amount to ordinary shares
Junk bonds
High-yield bonds
Highly risky and speculative
Higher return
You own a R1000 bond and you can convert your bond into ordinary
shares at a ratio of 4:1.
Therefore, with R1000, you can get R250 worth of shares (R1000/4)

22. The different types of bonds
Zero-coupon bonds
No coupon payments
Offered at a considerable discount to par
Extendable and retractable bonds
Pays a lower coupon rate to investors
Have more than 1 maturity date
Extendable: gives holder right to extend maturity
Retractable: gives holder right to shorten maturity
Electronix Ltd. is selling 10-year
bonds with a nominal value of
R1000 at a YTM of 7%.
1000 FV,
10 N,
7 I/YR
PV =

23. The different types of bonds
Foreign-currency bonds
Issued in a currency other than the issuer’s own currency
USA = Yankee bonds
Japanese Yen bonds = Samurai bonds
British Pound bonds = Bulldog bonds
New Zealand dollar bonds = Kiwi bonds
Inflation-linked bonds
Provides protection against inflation
Increasing the nominal value by the change in inflation

24. Bond markets and reporting
Most markets are OTC markets (over-the- counter)
Collection of dealers around the world who buy and sell bonds (via electronic networks)
Bond markets = debt, credit or fixed-income markets
NYSE: both a stock and a bond exchange
JSE: Bought BESA (Bond Exchange of South Africa), therefore the JSE trade in both shares and bonds

25. Bond ratings
Bonds are rated according to the creditworthiness of the issuing entity
World’s leading rating agencies:
Moody’s
Standard & Poor’s (S&P)
Fitch
All bonds with a rating of BB and less can be rated as junk bonds
South Africa: BBB+ = Strong capacity to pay interest and repay principal, but susceptible to adverse effects and economic conditions

26. Credit ratings by Moody’s, S&P and Fitch

27. What determines bond returns?
Real interest rate & expected inflation rate
Increase in these rates increases the return
Interest rate risk and time to maturity
The longer the time to maturity, the higher the return
Risk of interest rate changes (interest rate premium)
Default risk
The risk of default (non-payment)
Credit risk premium
Lack of liquidity
The ease with which assets are converted into cash
Liquidity premium

28. The influence of interest and inflation rates
Major influence on bond yield is the inflation and market interest rate
Nominal interest rate: has not been adjusted for inflation (inflation is still included)
Real interest rate: has been adjusted for inflation (inflation not included)
Inflation: the sustained, rapid increase in the general price level (decreasing purchasing power of the currency)
FV of the investment
1 – inflation rate = real amount
Real amount – original amount
original amount x 100
= real interest rate

29. The Fisher Effect
The relationship between the nominal interest rate, real interest rate and inflation rate is important to ultimately know what you can buy with your money (purchasing power)
Necessary to receive compensation for the effect that inflation has on purchasing power
Fisher effect: 1 + n = (1 + r) x (1 + i)
Where
n = nominal rate
r = real rate
i = inflation rate

30. Conclusion
A bond is a debt instrument issued either by a government or a corporation in need of funds. The bond pays interest on the nominal amount (coupon payments). The loan has a fixed maturity and when it reaches maturity, the nominal amount is repaid.
A bond consists of the following variables:
Nominal value
Coupon rate
Coupon
YTM
Maturity
Price of the bond

31. Conclusion (cont.)
When the YTM (the interest rate in the market) and the coupon rate differ, the price of the bond will also differ from the nominal value of the bond. When the interest rate in the market goes up, the price of the bond goes down to compensate the investor for earning a lower coupon rate (trading at a discount).
When the YTM is lower then the coupon rate, the price of the bond will increase relative to the nominal value. The price of the bond will be more because the bond will pay a higher coupon rate than in the market and, therefore, the investor has to pay more for that privilege.

32. Conclusion (cont.)
If the YTM and the coupon rate are equal, then the price of the bond will equal the nominal value.
When calculating the price of a bond, the PV of the lump sum paid out at maturity (the nominal value) will have to be calculated and added to the PV of all the future cash flows (the coupon payments).
A bond that makes semi-annual payments makes two payments a year – once ever six months. This means that the coupon rate has to be divided by two, and the coupon payment and maturity will have to be multiplied by two.

33. Conclusion (cont.)
There are various types of bonds, namely government, municipal, corporate, convertible, zero-coupon, extendable, retractable, foreign currency, junk and inflation-linked bonds.
The New York Stock Exchange is the biggest bond exchange in the world; South Africa’s BESA is a leader in emerging economies. Mostly, the bond market is an OTC market.
Moody’s, Standard & Poor’s and Fitch are the three main credit-rating agencies.

34. Conclusion (cont.)
Bonds are rated in order to indicate to investors the level of risk of payment default.
The bond coupon rate is dependent on the real interest rate implicit in the coupon, the expected inflation rate, the time left to maturity, and the interest rate risk, default risk and liquidity risk.
The difference between real and nominal interest rates is that the real interest rate has been adjusted for inflation, where the nominal rate has not been adjusted for inflation.
The Fisher Effect illustrates the relationship between the nominal rate, real rate and inflation rate.