Bond Valuation

Definition of a bond: A bond is a form of debt financing used by governments or the

corporate sector or municipalities that is used to raise finance. When governments, public
companies (SOEs) and corporates are in need of funds, they can borrow money on a long-
term basis from the public. The public, mostly the pension fund companies, insurance
companies and investment companies buy the bond from the borrower (issuer) (i.e)
government, municipality or corporates who are in need of funds. The buyer of the bond
becomes the bondholder or the lender who will receive the interest (coupon) at fixed
intervals say quarterly, half-yearly or yearly. At the end of the life of the bond (maturity)
the issuer of the bond will repay the principal amount together with the coupon to redeem
the bond. The issuer of the bond (borrower) uses the funds obtained from the floatation of
bonds to finance long-term investments in the case of companies or to finance re-current
expenditure in the case of governments. The characteristics of the bond include the
coupon, coupon rate, maturity, par (nominal) value and yield -to -maturity
Value of the bond: There are five (5) basic variables that are used when calculating the
value of the bond. One can use formulas but it is much easier to use a financial calculator.
Firstly, there is the nominal value of the bond, secondly is the coupon rate which is the
fixed percentage or interest payment, thirdly, there is the time to maturity. Fourthly, there
is yield to maturity (YTM) or current interest rate on the market (which is not fixed). Lastly,
is the PV of the bond that will be paying for the investment (market value)
N.B. Using a financial calculator on is able to calculate the variables that needs to
be found.
Different types of bonds
1.Government bonds: these are securities issued by governments also known as
treasuries. The debt security with maturity of less than one year are known as Treasury
bills, with maturity of more than one year, but less than ten years are known as Treasury
notes, and those maturing in more than ten years are known as Treasury bonds.
2.Municipal bonds: Cities, towns and regional municipalities issue bonds in order to
support their local long-term projects. Cities like Joburg issue bonds to help finance capital

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expenditure on infrastructure like 2010 Soccer World Cup and Gautrain and roads or to
refinance some of their debt. Advantage of municipal bonds is that the interest received is
tax-exempt and this makes them yield lower interest although they are very attractive form
of investment.
3. Corporate bonds: these are issued by companies that want to raise large sums of
funds for expansion purposes or to service large debts. These bonds are characterised by
higher yields/returns because of the higher risk associated with these type of business.
There is a higher chance that a company may default on payment as compared with stable
(risk-free) government bonds. The corporate bonds are classified as follows: short-term
bonds for those with maturity of less than five years; Intermediate corporate bonds for
those with maturity of between 5 and 12 years; and long-term corporate bonds with
maturity of more than 12 years. Companies are classified according to the industry in
which they operate (real estate or retail bonds) and according to their credit rating which
is tied to the business prospects and financial capacity.
4. Convertible bonds: these bonds give the owner the right to convert the par (nominal)
value of the bond to ordinary shares of the issuing company at a certain fixed ratio
(conversion ratio). These bonds have coupon payments and they rank above any equity
in a default situation as they fall under debt securities.
5. Junk bonds: also referred to as high-yield bonds are issued by companies considered
to be highly risky and speculative. The junk bond is considered to be speculative grade
or below investment grade because they developed negative connotations and are not
widely held in investment portfolios. Mainstream investors and institutions do not deal with
the junk bonds because of the risk imposed on them.
6. Zero-coupon bonds: these have no coupon payments and are offered at a discount.
The owner of the bond will pay taxes on the coupon, although no coupon (interest) is
received. These are more attractive than coupon paying bonds because the investor
eliminates reinvestment risk, and they yield better yields than coupon-paying bonds.
7. Extendable and retractable bonds: these pay a lower interest rate (coupon rate) to
investors because they have more than one maturity date. The extendable bonds give the

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holder the right to extend the initial maturity to a later maturity date. The investor would be
attracted to an extendable bond to take advantages of potentially falling interest rates (as
interest fall, bond prices increase), without assuming the risk of a longer bond.
Retractable bonds give the holder the right to retract the maturity (make the maturity
shorter). This bond attracts investors who believe interest rates will rise and bond prices
will fall. Bond issuers find the extendable and retractable bonds desirable because of lower
interest rate, and the options given to buyers to make the issues easier to sell.
8. Foreign- currency bonds: this bond is issued in a currency other than the issuer`s own
currency (e.g. Telkom issuing US Dollar Bonds) to take advantage of international interest-
rate variations and diversification purposes.
9. Inflation-Linked bonds: these provide protection/hedged against inflation and is done
by increasing the nominal value by the change in inflation measured by the CPI. As the
principal increases, the coupon rate is applied to this increased amount, so the coupon
also increases. This ensures that the investor is protected against inflation risk.
Bond markets and bond ratings:
A bond market is a financial market where participants buy and sell debt securities (bonds)
Bond markets are also known as debt, credit or fixed-income markets. The New York
Stock Exchange (NYSE) is the world`s largest centralised bond market and represents
mostly corporate bonds. The Bond Exchange of South Africa (BESA) is the largest bond
exchange in Africa. In June 2009, BESA became a wholly owned subsidiary of the JSE
where the shares, bonds and derivatives are traded in one market. In South Africa all long-
term government bonds are regarded as risk-free.
Bond ratings: a bond is rated according to the creditworthiness of the issuing entity. If the
company`s credit rating is AAA it implies that there is almost no risk in defaulting, while
the one with BBB, means there is greater risk of defaulting on payments. Remember, the
greater the risk the greater the return (interest) to compensate for the increased risk
carried by the investor. The world`s leading rating agencies are Moody`s, Standard &
Poor`s (S&P) and Fitch. The bonds are rated in order to indicate to investors the level of
risk of payment default.

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What determines bond returns:
Investors put their money into bonds and other debt securities for the purpose of receiving
compensation for the risk they are prepared to take. The return, or coupon an investor
receives consists of compensation for the following variables: - real interest rate, expected
inflation rate, interest rate risk, default risk, and lack of liquidity. The inflation rate and the
market interest rate have major influence on bond yields. The relationship between the
nominal interest rate, real interest rate and inflation rate is best explained by the Fisher
Effect. The difference between real and nominal interest rates is that the real interest rate
has been adjusted for inflation, whereas the nominal rate has not been adjusted for
inflation.
Formulas
1.Bond Value = C x (1 – [1÷(1+i)t] ÷ i) + N÷(1+i)t
C= coupon (PMT)
i= interest in the market or YTM (1/Y)
N = nominal value amount or Par/ Future value of the bond
Number of years to maturity = N
2. PV of annuity = C x (1 – [1÷(1+i)t] ÷ i)
3. PV of the nominal amount = N÷(1+i)t
Example 1.
Starbucks bonds are sold at par value of R1000. The coupon rate is 6.25% and
the bond matures after 10 years, the current interest rate on the market is
(YTM) is 6.276%.
Calculate the present value of bond. (i) using the formula (ii) using the
calculator.
PV of annuity = C x 1 – [1÷(1+i)t] ÷ i
(a) PV of annuity = R62.50 x (1 – [1÷ (1+ 0.06276)10] ÷ 0.06276)
= R62.50 x (1- [1÷ 1.83803] ÷ 0.06276)
= R62.50 x (0.45594 ÷ 0.06276)

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 = R62.50 x 7.265
= R454.063
(b) PV of nominal amount = N÷(1+i)t
= R1000 ÷ (1.06276)10 = R1000 ÷ 1.83803 = R544.061
(c) Add two values to obtain the Bond Value = R454.063 + R544.061
PV of the bond = R998.12
Using the Financial Calculator:
Key in Press Display
1000 FV 1000
62.50 PMT (Coupon) 62.50
10 N 10
6.276 I/YR (YTM) 6.276
Comp PV -998.12

Example 2
SAB Miller has issued debentures at R1 000 each. These debentures are
currently trading at R840 each, and the debentures have 10 years to maturity.
The coupon rate on the debenture is 15% per annum. Calculate the YTM.
𝑴−𝑫𝑩𝟎
𝑰+
𝒏
4. YTM = ⌈ 𝑴+𝑫𝑩𝟎 ⌉
𝟐

Where:
I is the annual interest, entered as an amount not a rate
M is the par value
DB0 is the current value of the debenture
n is the years to maturity.
If we substitute, our equation will now look as follows:
𝟏𝟎𝟎𝟎 −𝟖𝟒𝟎
𝟏𝟓𝟎+
𝟏𝟎
YTM = 𝟏 𝟎𝟎𝟎 + 𝟖𝟒𝟎
𝟐

YTM = 18.04%

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Using the Financial Calculator:
Key in Press Display
1000 FV 1000
150 PMT (Coupon) 150
10 N 10
PV -840 840
CompI/YR 18.64%
(YTM)
Kd =K(1-t) = 18.64(1-0.28) = 13.42%
Assignment use your financial calculator: 18.64% = kd= 13.42%
Example 3
Thompson Limited can raise long-term capital by issuing 10-year debentures
to the value of R500 000 at a discount of R50 each, on the capital market. The
par value of each debenture is R1 000 each. Market value is R950 each. They
have a coupon interest rate of 12% per annum. Calculate the yield to maturity
of the debenture.
We can calculate the YTM using a financial calculator:
Key in Press Display
950+/- PV -950.00
120 PMT (Coupon) 120
1000 FV 1000.00
10 N 10.00
I/YR (YTM) 12.92%

Example 4
You want to own an asset with a real return of 10%. Currently, the inflation rate is
3.6%. What nominal interest rate would you have to earn. Page 278
Formula: r = [(1+n) ÷ (1+i) – 1]
1+n = (1+r) x (1+i)
= 1.10 x 1.036
= 1.1396
N = 1.1396 – 1
= 13.96%

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Self-Test Questions:
1.Define the term bond, and explain the five characteristics of bonds.
2. If the coupon rate is less than the YTM, what happens to the price of the bond?
3. Explain the steps used to calculate the value of the bond, and draw-up the formula used to calculate the bond
value.
4. What are the two payments whose PV has to be calculated to determine the price of a bond?
5. What is the major differences between corporate bonds and government bonds?
6. Identify the major attributes of extendable and retractable bonds.
7. What are the determinants of bond coupon rates?
8. What is the difference between the nominal and real interest rate?
9. Why is the inflation rate important in bond valuation?
10. Why is a lack of liquidity a risk for a bond investor?

8.1 The amount of interest that has to be paid to the bondholder is called the:

a) interest rate
b) coupon rate
c) yield-to-maturity
d) coupon

8.2 A bond that makes no coupon payments during the life of the bond, but is sold at a
considerable discount, is known as:

a) an inflation-linked bond
b) a zero-coupon bond
c) a discount bond
d) a premium bond

8.3 The coupon divided by the nominal value represents the:

a) nominal value
b) par value
c) yield-to-maturity
d) coupon
e) coupon rate

8.4 Which of the following bonds have the lowest return?

a) a bond with a B3 rating

b) a bond with a Baa1 rating
c) a bond with a BB rating
d) a bond with a BBB rating

8.5 If a bond is R1 000 at maturity and the bond currently sells for R990, then:

a) the YTM is more than the coupon rate

b) the coupon rate is more than the YTM
c) The YTM and the coupon rate are the same
d) The bond is selling at above par

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8.6 If a bond has a nominal value of R1 000, but sells for R900, the bond is trading at
___________________, which indicates that:

a) a discount; yield-to-maturity is higher than the coupon rate

b) a discount; coupon rate is higher than the yield-to-maturity
c) a premium; coupon rate is higher than the yield-to-maturity
d) a premium; yield-to-maturity is higher than the coupon rate

8.7 A bond that makes semi-annual payments and has a maturity of 30 years with a
coupon rate of 10% and a yield-to-maturity of 11% will make a total of:

a) 30 coupon payments
b) 15 coupon payments
c) 60 coupon payments
d) 45 coupon payments

8.8 A bond makes semi-annual payments and has a maturity of 30 years with a coupon
rate of 10% and a yield-to-maturity of 11%. What is the coupon payment of this specific
bond with a nominal value of R1 000?

a) R100
b) R50
c) R200
d) R150

8.9 Bond A is a 6% coupon bond, and Bond B a 6,5% coupon bond. The market interest
rate is 5,5% and both bonds have a maturity of 10 years. If the interest rate increases
by 2%, what will the price change of both bonds be?

a) Bond A = 17,21; Bond B = 15,18%

b) Bond A = -15,97; Bond B = -18,63%
c) Bond A = -13,55%; Bond B = -13,40%
d) Bond A = 15,68%; Bond B = 20,04%

8.10 An investment claims to give you a return of 15% per year, but in reality you receive
only 12,4%. What is the inflation rate?

a) 3,50%
b) 2,45%
c) 2,61%
d) 2,31%

8.11 The interest rate which has not been adjusted for inflation is known as the:

a) real rate
b) inflation rate
c) nominal rate
d) par rate
e) coupon rate

8.12 When the market price of a bond increases, it is an indication that the yield-to-maturity:

a) has increased
b) has decreased

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c) has remained the same
d) is higher than the coupon rate

8.13 You want to invest in an asset that claims to give you a return of 14,2%. The inflation
rate is currently 6,29%. What are you really earning?

a) 7,44%
b) 7,91%
c) 8,01%
d) 7,23%

8.14 Zuma Ltd needs to raise R40 000 000 in order to expand the business. The company
plans to sell 20-year zero-coupon bonds at a nominal value of R10 000. The bonds are
priced at 8% yield. How many bonds will Zuma Ltd have to sell to reach R40 000 000?

a) 20 000
b) 18 644
c) 19 548
d) 17 630

8.15 Samson Corp decides to introduce a new bond issue that is currently selling at par and
has a 30-year maturity. This semi-annual bond makes coupon payments of R45 per
period. The yield-to-maturity will be:

a) 4,5%
b) 4,0%
c) 9,0%
d) 8,5%

8.16 A bond that makes semi-annual payments has a maturity of 30 years, with a coupon
rate of 10% and a yield-to-maturity of 11%. What is the current value of this specific
bond with a nominal value of R1 000?

a) R923,87
b) R909,63
c) R913,06
d) R912,75

8.17 What is the difference between a normal loan (which makes principal and interest
payments) and a bond?

8.18 You have a choice between two bonds. Bond A makes yearly payments and has a
maturity of 20 years and a coupon rate of 10%. Bond B has a maturity of 15 years and
makes semi-annual payments at a coupon rate of 11,3%. The nominal value of both
bonds is R10 000 and the yield-to-maturity is 11,2%.

a) What is the value of Bond A?

b) What is the value of Bond B?
c) Which bond is selling at a premium and which is selling at a discount?

8.19 Willow Ltd Bonds pays a 9% coupon, and makes payments semi-annually. The market
price currently is R1 108 and the bond matures in 15 years. What is the yield-to-
maturity?

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8.20 Ipeleheng wants to invest in a R2 000 bond that is currently selling for R1 900. The
bond matures in 6 years and the yield-to-maturity is 10%.

a) What is the coupon payment?

b) What is the coupon rate?
c) What is the coupon rate if the bond makes semi-annual payments?

8.21 Thumelo Corporation offers a 6% bond that is currently selling for R860. The yield-to-
maturity is 9%. How many years until the bond matures?

LQ 8.1

Lucky Luke Bonds are currently selling for 95% of the par value. The nominal value of the
bond in 6 years’ time is R10 000. The coupon rate paid semi-annually is 15%.

You are required to:

Answer the following question:

What is the yield to maturity?

LQ 8.2

Bond Risky is a 5% coupon bond that makes semi-annual payments, while Bond Not-so-risky
is a 7% coupon bond that makes annual payments. Both bonds have 5 years left until they
mature and the bond are currently selling at par.

You are required to:

Answer the following question:

What would the price change of each bond be if the interest rates in the market went up by
2%?

LQ 8.3
You are required to:
Answer the following questions:
Which bond in LQ 8.2 has the bigger interest rate risk? Why?

LQ 8.4

You are required to:

Read the following and answer the question:

Bond 007 and Bond 030 both have coupon payments of 15% of par, make semi-annual
payments, and have nominal values of R1 000. Bond 007 has seven years left until maturity,
while Bond 030 has 30 years left to maturity. Currently both bonds are sold at par, but what
would the price change be for both if the interest rate decreased by 3%?

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LQ 8.5

You are required to:

Answer the following question:

Which bond in LQ 8.4 has the bigger interest rate risk? Why?

LQ 8.6

Leo has some money that he wants to invest. There is currently a bond on the market which
makes semi-annual payments and is selling for R1 698. The nominal value of the bond is
R1 000 and the bond matures in eight years. The yield-to-maturity is 9%.

You are required to:

Answer the following question:

What is the coupon rate per year of this bond?

LQ 8.7

Your company was in need of R5 million for expansion purposes. You decided to issue semi-
annual R1 000 bonds which pay a coupon of 10% for a 15-year period. A year after the bonds
were issued, the interest rate in the market increased by 1,5%.

You are required to:

Answer the following questions:

a) What was one bond worth one year after it was first issued?

b) If your company issued 1 500 bonds at par in the first year, how many would you still
have to sell at the new present value?

8.1 d) coupon

8.2 b) a zero-coupon bond

8.3 e) coupon rate

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8.4 b) a bond with a Baa1 rating

8.5 a) the YTM is more than the coupon rate

8.6 a) a discount; yield-to-maturity is higher than the coupon rate

8.7 c) 60 coupon payments

8.8 b) R50

8.9 c) Bond A = -13,55%; Bond B = -13,40%

8.10 d) 2,31%

8.11 c) nominal rate

8.12 b) decreased

8.13 a) 7,44%

8.14 b) 18 644

8.15 c) 9,0%

8.16 d) R912,75

8.17 In the case of a normal loan, the company would borrow money and make payments
every period which would include a part of both the principal and the interest on that
loan. In the case of a bond, the bondholder receives fixed coupon payments (interest
payments), and when the bond matures, the bondholder will receive the nominal
value. Therefore, in the case of a normal loan, the payment consists of the principal
and interest, and the interest can change according to the prime lending rate. The

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 coupon rate on a bond remains fixed, while the present value of the bond may
change according to changes in the market rate.

8.18

a) R9 056,76 – discount (market value < par value)

Using the equation:

R10 000 = R10 000 = R1 196,46

PV of the lump sum: 1,112^20 8,358

1 – [1 ÷ (1 + 0,112)^20]
PV of the annuity = R1 000 x 0,112

0,88035
= R1 000 x 0,112

= R7 860,27

The total PV of the bond is therefore R1 196,46+ R7 860,27 = R9 056,73

Using the financial calculator:

Enter 20 11.2 1 000 10 000

n i PV PMT FV

Solve for 9 056,76

b) R10 071,87 – premium (market value > par value)

Using the equation:

R10 000 = R10 000 = R1 950,23

PV of the lump sum: 1,056^30 5,1276

1 – [1 ÷ (1 + 0,056)^30]
PV of the annuity = R565 x 0,056

0,805
= R565 x 0,056

= R8 121,66

The total PV of the bond is therefore R8 121,66 + R1 950,23 = R10 071,87

Using the financial calculator:

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 Enter 30 5,6 565 10 000

n i PV PMT FV

c) BondSolve for
A is selling at a discount;10 071,87
Bond B is selling at a premium.

8.19 7,77%

PV = 1 108
FV = –1 000
PMT = –90 / 2 = -45
n = 15 x 2 = 30
i = 3,88 x 2 = 7,77%

When using the equation to calculate the YTM, it is a process of trial and error.

Total bond value = PV of the lump sum + PV of the annuity

R1 108 = R1 000 + 45 x 1 – [1 ÷ (1 + YTM)^30]

(1 + YTM)^30 YTM

We now have to use trial and error and what we know about bond prices and interest
rates to ‘guess’ what the YTM could be. We know that the bond is currently selling for
more than the nominal price (trading at a premium). This indicates that the interest rate
in the market (YTM) is less than the coupon rate, which is 9%.

Let’s try a YTM of 8%:

Total bond value = R1 000 + 45 x 1 – [1 ÷ (1 + 0,04)^30]

(1,04)^30 0,04

Total bond value = R308,32 + R778,14

= R1 086,46

The value of R1 086,46 indicates that the YTM is not 8% and needs to be a bit smaller.

This process should be repeated until the correct yield is found. The YTM for this bond
is 7,77%. Calculating the YTM using an equation can become a lengthy process.

Using the financial calculator:

Enter 30 −1 108 45 1 000

n i PV PMT FV

Solve for 3,88%

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 i Is the bond selling at a discount or a premium?

The period rate is 3,88% and the bond makes semi-annual payments, The yield-to-
maturity is therefore 7,77% (3,88% x 2).

8.20

FV = –1 000
PV = 860
PMT = –60
i = 9
n = 6,32

a) The coupon payment is R177,04.

Using the equation:

R2 000 = R2 000 = R1 128,67

PV of the lump sum: 1,10^6 1,772

1 – [1 ÷ (1 + 0,10)^6]
PV of the annuity = (coupon) x 0,10

0,4355
= (coupon) x 0,10

= (coupon) x 4,35526

Total value of the bond: R1 900 = (coupon x 4,35526) + 1 128,67

R771,33 = coupon x 4,35526
Coupon = 771,33 ÷ 4,35526
Coupon = R177,10

Using the financial calculator:

Enter 6 10 –1 900 2 000

n i PV PMT FV

b) Solve÷for
R177,04 R2 000 = 8,85%. We know that 177,04
the coupon rate (8,85%) should be less
than the YTM (10%), because the bond is sold for less than the nominal value. It is
therefore sold at a discount (trading at a discount).

c) The coupon rate is 88,72%

Using the equation:

R2 000 = R2 000 = R1 113,67

PV of the lump sum: 1,05^12 1,79586

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 1 – [1 ÷ (1 + 0,05)^12]
PV of the annuity = (coupon) x 0,05

0,44316
= (coupon) x 0,05

= (coupon) x 8,86325

Total value of the bond: R1 900 = (coupon x 8,86325) + 1 113,67

R786,33 = coupon x 8,86325
Coupon = 786,33 ÷ 8,86325
Coupon = R88,72

Using the financial calculator:

Enter 12 5 –1 900 2 000

n i PV PMT FV

Solve
R88,72 for 000 = 4,436%. The bond makes
÷ R2 88,72 semi-annual payments. The 4,436%
should therefore be multiplied by two to get the yearly coupon rate, which is 8,872%
(4,436% x 2)

8.21 6,32 years

FV = –1 000
PV = 860
PMT = –60
i = 9
n = 6,32

Using the financial calculator:

Enter 9 −860 60 1000

n i PV PMT FV

Solve for 6,32

LQ 8.1

16,34% – When using the equation to calculate the YTM, it is a process of trial and error.

Total bond value = PV of the lump sum + PV of the annuity

R9 500 = R10 000 + 750 x 1 – [1 ÷ (1 + YTM)^12]
(1 + YTM)^12 YTM

We now have to use trial and error and what we know about bond prices and interest rates to
‘guess’ what the YTM could be. We know that the bond is currently selling for less than the

16
nominal price (trading at a discount). This indicates that the interest rate in the market (YTM)
is more than the coupon rate, which is 15%.

Let’s try a YTM of 16%:

Total bond value = R10 000 + 750 x 1 – [1 ÷ (1 + 0,08)^12]

(1,08)^12 0,08

Total bond value = R3971,14 + R5 652,06 = R9 623,20

The value of R9 623,20 indicates that the YTM is not 16% and needs to be a bit bigger.

This process should be repeated until the correct yield is found. The YTM for this bond is
16,34%. Calculating the YTM using an equation can become a lengthy process.

Using the financial calculator:

Enter 12 −9 500 750 10 000

n i PV PMT FV

Solve
i for Is the bond selling
8,17% at a discount or a premium?

The period rate is 8,17%, and the bond makes semi-annual payments. The yield-to-maturity
is therefore 16,34% (8,17% x 2).

LQ 8.2

Bond Risky price change: (R1 000 – R916,84) / R1 000 = 8,32%

Using the equation:

R1 000 = R1 000 = R708,92

PV of the lump sum: 1,035^10 1,4106

1 – [1 ÷ (1 + 0,035)^10]
PV of the annuity = R25 x 0,035

0,2911
= R25 x 0,035

= R207,93

The total PV of the bond is therefore R708,92+ R207,93 = R916,85

Using the financial calculator:

Enter 10 3,5 25 1 000

17

n i PV PMT FV
Bond Not-so-risky price change: (R1 000 – R922,21) / R1 000 = 7,78%

Using the equation:

R1 000 = R1 000 = R649,94

PV of the lump sum: 1,09^5 1,5386

1 – [1 ÷ (1 + 0,09)^5]
PV of the annuity = R70 x 0,09

0,35007
= R70 x 0,09

= R272,28

The total PV of the bond is therefore R649,94 + R272,28 = R922,22

Using the financial calculator:

Enter 5 9 70 1 000

n i PV PMT FV

Solve for 922,21

LQ 8.3

Bond Risky has the higher interest risk, because the price change with an interest rate
increase of 2% is 8,32%, compared to a price change of Bond Not-so-risky of 7,78%. The
reason that Bond Risky has a greater interest rate risk is that the coupon payments are smaller
compared to Bond Not-so-risky, and it has been illustrated in LQ 8.2 that the smaller the
coupon payments, the bigger the interest rate risk implicit in that specific bond.

LQ 8.4

Bond 007 price change: (R1 000 – R1139,42) / R1 000 = 13,94%

Using the equation:

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 R1 000 = R1 000 = R442,28
PV of the lump sum: 1,06^14 2,261

1 – [1 ÷ (1 + 0,06)^14]
PV of the annuity = R75 x 0,06

0,5577
= R75 x 0,06

= R697,13

The total PV of the bond is therefore R442,28 + R697,13 = R1 139,41

Using the financial calculator:

Enter 14 6 75 1 000

n i PV PMT FV

Solve for 1 139,42

Bond 030 price change: (R1 000 – R1 242,42) / R1 000 = 24,24%

Using the equation:

R1 000 = R1 000 = R30,31

PV of the lump sum: 1,06^60 32,99

1 – [1 ÷ (1 + 0,06)^60]
PV of the annuity = R75 x 0,06

0,96969
= R75 x 0,06

= R1 212,11

The total PV of the bond is therefore R30,31 + R1 212,11 = R1242,42

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Using the financial calculator:

Enter 60 6 75 1 000

n i PV PMT FV

Solve for 1 242,42

LQ 8.5

Bond 030 has the higher interest risk, because the price change with an interest rate decrease
of 3% is 24,24%, compared to a price change in Bond 007 of 13,94%. The reason that Bond
030 has a greater interest rate risk is that the time to maturity is longer compared to Bond 007,
and it has been illustrated in LQ 8.4 that the longer the time to maturity, the bigger the interest
rate risk implicit in that specific bond.

LQ 8.6

a) The coupon rate is 21,43%.

Using the equation:

R1 000 = R1 000 = R494,47

PV of the lump sum: 1,045^16 2,02237

1 – [1 ÷ (1 + 0,045)^16]
PV of the annuity = (coupon) x 0,045

0,505531
= (coupon) x 0,045

= (coupon) x 11,23402

Total value of the bond: R1 698 = (coupon x 11,23402) + 494,47

R1 203,53 = coupon x 11,23402
Coupon = 1203,53 ÷ 11,23402
Coupon = R107,13

Coupon payment per period = 107,13

Coupon payment per year = 107,13 x 2 = 214,27
Coupon rate = coupon payment / nominal value = 21,43%

Using the financial calculator:

Enter 16 4.5 –1 698 1 000

n i PV 20 PMT FV

Solve for 107,13

Coupon payment per period = 107,13
Coupon payment per year = 107,13 x 2 = 214,27
Coupon rate = coupon payment / nominal value = 21,43%

LQ 8.7

a) R896,83

Using the equation:

R1 000 = R1 000 = R209,01

PV of the lump sum: 1,0575^28 4,784654

1 – [1 ÷ (1 + 0,0575)^28]
PV of the annuity = R50 x 0,0575

0,7910
= R50 x 0,0575

= R687,82

The total PV of the bond is therefore R209,01+ R687,82 = R896,83

Using the financial calculator:

Enter 28 5,75 50 1000

n i PV PMT FV

b) Solve
If 1500 for were issued in the
bonds –896.83
first year the bond was issued at par, it means that
the company received a total of R1,5 million (R1 000 x 1 500).

The company is therefore still in need of R4,5 million. The new value of the bonds is R896,83.
The company will therefore have to sell a total of 5 018 (R4,5 million / R896,83) to accumulate
the additional R4,5 million.

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