Bond Valuation

Question 1

How to start a business? (picture)

Answer 1

Question 2

An interest rate is…? (picture)

Answer 2

Question 3

What is a bond?
Example?

Answer 3

• A bond is a security sold by governments or corporations to raise money from investors today in exchange for promised future payments.

For example, on 01/10/2023, the UK government issued 100,000 five-year, £100 bonds with a 10% coupon rate and annual payment.

Question 4

What are the key terms associated with bonds? (4)

Answer 4

Maturity:

• The length of time remaining until the repayment date.

In reality, no all bonds have a final maturity date. For example, English consols are the bonds that guaranteed by the Bank of England to pay the holder cash flows forever.

Face value:

• The amount of money that must be repaid at the end of the bond’s life.

Coupon rate:

• The interest rate set by the bond issuer as the promised interest payments.

In practice, the coupon rate can be set as zero. A bond that does not make coupon payments is called a zero-coupon bond, such as American treasury bills.

Coupon payment interval:

• The number of interest payments during a year.

Question 5

What is a zero-coupon bond?

Answer 5

A bond that does not make coupon payments and is sold at a discount to its face value.

Question 6

Where are bonds issued?

Answer 6

Bonds are issued in the Primary market but are (generally) transferable and are therefore capable of being traded on the secondary markets also.

Question 7

Why are bonds considered less risky than equity? (3)

Answer 7

1. The coupon payable is a legally defined obligation.
2. The nominal value of the bond may be secured against assets (collateralized).
3. Equity holders are subordinate to bondholders in terms of creditor position if a business goes bankrupt.

Question 8

Ensuring the debt is repaid

How (2)?

Answer 8

• Collateral–specific company assets that are linked to the debt. The lender can claim these assets if the company reneges on the debt repayments.
• Covenants (positive, negative and financial) can be written in to the contracts

Question 9

What is a debt covenant?

Why are they put in place?
What happens if one or more are breached

Answer 9

Provisions in a bond contract designed to protect lenders by restricting the actions of the borrower.

• Covenants are inserted into contracts to prevent the company taking actions that will increase the risk of default on the debt
• If one or more covenants are breached, the debt may become repayable immediately.

Question 10

An Introduction to Bonds

Bonds are generally rated (in terms of their _________ ______).
The ratings given follow the same naming conventions as for other instruments (although default rates are likely to __________).

Answer 10

Bonds are generally rated (in terms of their credit risk).
The ratings given follow the same naming conventions as for other instruments (although default rates are likely to differ).

Question 11

What is the difference between equity and debt finance?

Answer 11

• Equity finance involves raising capital by selling shares,
• while debt finance involves borrowing money through issuing bonds

Question 12

Different time length bonds (3)

Answer 12

Short-term bonds:

• These have a maturity of less than 5 years.

Medium-dated bonds:

• These mature in 5 to 15 years.

Long-term bonds:

• These have a maturity of over 15 years.

These boundaries aren’t rigid. They are often flexible depending on the context.

Question 13

An Introduction to Bonds II
Examples of long-dated bonds include:

Answer 13

IBM and Reliance of India have issued 100- year bonds, as have Coca-Cola and Walt Disney (Disney’s was known as the ‘Sleeping Beauty bond’).
Canadian Pacific Corporation is paying a dividend of 4 per cent on a 1,000-year bond issued in 1883.

Question 14

Types of bond

The types of bond available are, arguably, only constrained by the market’s ability to invent them! Examples include: (7)

Answer 14

• Corporate bonds (higher risk than government bond)
• Government issued bonds
• Municipal bonds
• Debentures
• Convertible bonds (right to convert them into shares)
• Zero-coupon bonds
• Eurobonds (Not Euros but bonds issued in a currency other than that of the country of issue)! May be dominated in Euro-Yen, Euro-dollars or any other currency.

Question 15

How do you value a bond?

Answer 15

The value of a bond is the present value of its future coupon payments and face value, discounted at the bond’s yield to maturity (YTM).

Question 16

Present Value of a Bond example

Consider a 30-year, £100 coupon bond with 10% annual coupons with 6% YTM

Formula

Answer 16

Question 17

Example:
Assume that a bond with a par value of $1000 and will be mature within 3 years
The coupon rate is 11.25% per annum and the coupon is paid semi-annually
Assume the YTM quote is 0.17% , what is the price of this Bond?

Answer 17

$1,331.40 - Premium

Question 18

What is Yield to Maturity (YTM)?

Answer 18

The discount rate that sets the present value of a bond’s future cash flows equal to its current market price.

Question 19

What are callable and puttable bonds?

Answer 19

Callable bonds:

• Issuers can call back the bonds at pre-specified prices before maturity, usually offering higher yields to compensate lenders

Puttable bonds:

• Bondholders can resell the bond back to the issuer at pre-specified prices before maturity, usually offering lower yields due to having the option to cancel the debt

Question 20

Bond prices and market interest rates move in ___________ _____________.

Different name of bond based on price

Answer 20

Bond prices and market interest rates move in opposite directions.

• When the coupon rate = YTM, the bond’s price is equal to its par value.
• When the coupon rate > YTM, the bond’s price is higher than its par value, making it a premium bond.
• When the coupon rate < YTM, the bond’s price is lower than its par value, making it a discount bond.

Question 21

How does bond value change as interest rate varies YTM)?

Answer 21

Conclusion: As interest rate (YTM) rises, bond value falls and vice versa.

Question 22

What is Macaulay Duration?

Suppose a company has a 3-year UK bond with a par value of £100, paying a coupon of 10% per annum and with a YTM of 12%. What is the bond’s Macaulay duration?

Answer 22

The weighted average maturity of a bond’s cash flows, measuring the bond’s sensitivity to interest rate changes.

aka how long does it take to get back the bond price

Question 23

How to measure the sensitivity of a bond’s price to yield? – Modified Duration

What is it?

Using our 3-year bond from the previous example:
D = 2.73; YTM = 0.12; K = 1

Answer 23

A bond’s duration also tells investors how much a bond’s price might change when interest rates change

i.e. how much risk they face from interest rate changes.

Question 24

The Term Structure of Interest Rates

What is it and aka?

What does the term structure express?

Yield curve a plot of the yields on Treasury notes and coupon bonds relative to maturity.

Answer 24

The relationship between maturity and yield is known as the yield curve, or the term structure of interest rates.

The term structure expresses the relationship between short term and long term rates of interest for investments that are riskless (i.e, t.bills).

Yield curve a plot of the yields on Treasury notes and coupon bonds relative to maturity.

Question 25

**The Yield Curve** 3 types and what they mean

Answer 25

The Yield Curve is not necessarily uniform in shape. _Normal yield curve_ - Upward sloping yield curve - Current long-term rate is greater than current short-term rate - Short term rates expected to rise _Flat yield curve_ - Current long-term rate = current short-term rate - Short term rates expected to remain the same _Inverted/negative yield curve_ - Downward sloping yield curve - Current long-term rate is less than current short-term rate - Short term rates expected to decline

Question 26

What are the three main hypotheses explaining the yield curve shape? (3+1/3,4,2,2)

Answer 26

1. **Expectations Hypothesis:** - This theory is saying that investing in a succession of short term bonds gives exactly the same expected return as investing in a long term bond - In other words, the expected future spot rate is equal to the forward rate for that time period. - The only reason that the term structure is rising is simply that investors expect short term rates to rise. Alternatively, the only reason that the term structure is falling is that investors expect short term rates to fall 2. **Liquidity Preference Hypothesis:** - Short-dated bonds are less sensitive to interest rate changes than long-dated bonds. Based upon the choices investors have regarding Bonds with different maturities: - **Short-dated fixed rate securities** enable investors to **switch/move** their **investments** to **exploit** the **greatest** **yields** and **protect** their **capital**. - **Long-dated fixed rate redeemable Bonds** “lock” investors to a **given rate of interest** over a long period. If yields were to change in that time this **exposes investors to capital risk.** - Investors demand a **liquidity premium** for holding a **long-dated bond** (Hence long-term rates are above short-term rates) upward sloping more often than not. 3. **Inflation Risk Hypothesis:** - Investors are **risk averse** and are uncertain about the **future rate of inflation.** - Investors demand a **premium** for holding **long-term** bond, compared to short-term bonds (inflation premium). 4. **The Risk of Default** - **Credit risk** (possibilities of default) there is a risk that their promised return is not actually delivered - Investors are **risk averse** and therefore **demand a risk premium for undertaking credit risk .**