1. Valuing Bonds and Corporate Debt
Chapters 5 and 13.3&13.4
Valuing Bonds and Corporate Debt
Lecture Outline
Bond Characteristics
Bond Prices and Yields
Interest Rate Risk
Default Risk
Corporate Debt
Convertible Securities
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2. Bond Characteristics Definitions
Governments and corporations borrow money for the long term by issuing securities which are called bonds:
They collect the money when they issue the bond, or sell it to the public.
The money they collect is the amount of the loan.
The amount of the loan may be known as the par value, face value, maturity value, or the principal.
The date on which the loan will be paid off is the maturity date.
The buyers of the bond are known as the bondholders.
The bondholders are actually lending money when they purchase the bond.
The seller of the bond is called the issuer.
The issuer is actually borrowing money when it issues the bond.
At maturity, the issuer repays the face value of the loan to the bondholders.
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3. Bond Characteristics Coupon Rate vs Discount Rate WARNING!
The issuer promises to make specified fixed income payments (interest) each year to the bondholders.
These payments are known as the coupon.
In Canada, the coupons are paid semi-annually
The coupon rate is the annual interest payment divided by the face value of the bond.
The interest rate (or discount rate) is the rate at which the cash flows from the bond are discounted to determine its present value.
WARNING!
The coupon rate, though a percent, is not the interest rate (or discount rate).
The coupon rate tells us what cash flows a bond will produce.
The coupon rate does not tell us the value of those cash flows.
To determine the value of a cash flow, you must calculate its present value
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4. Bond Prices What is a Bond Worth?
What would you be willing to pay right now for a bond which:
Pays a coupon of $65 per year for 3 years.
Has a face value of $1,000.
The cash flows on this bond would be: 1 2 3
-Price ?
$65 $
To determine the price, you must calculate the present value of these cash flows.
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5. Bond Prices What is a Bond Worth?
The coupon rate on this bond is 6.5%:
That is, you would receive $65 per year on a $1000 face value ($65/$1,000 = 6.5%).
But, to determine the PV of the bond, you need to know the discount rate for the bond.
The discount rate is the interest rate which investors are earning on a similar security.
Assume that similar 3 year bonds offer a return of 5.1%.
That is, 5.1% is the discount rate for this bond.
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6. Bond Prices What is a Bond Worth?
To determine the price of the bond, you would calculate the PV of the cash flows using a 5.1% discount rate: 1 2 3
-Price ?
$65
$65 +
1000
BOND PRICE = PV today:
$65/ (1.051) = $61.85
$65 / (1.051)2 = $58.84
$1065 / (1.051)3 = $917.36
$1,038.05
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7. Can you see the problem with using this method?
Bond Prices
What is a Bond Worth?
Thus, if discount rates are 5.1%, you would be willing to pay $1, for a bond with a coupon rate of 6.5% and a remaining life of three years.
But, suppose this were a 20 year bond … what would it be worth?
You could use the same procedure as you used for the first bond:
Calculate the PV of each cash flow.
Add up these present values.
Can you see the problem with using this method?
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8. Bond Prices What is a Bond Worth?
The coupon payments on a bond are an annuity.
In the last year of the bond’s life the holder receives a payment equal to the face value of the bond.
Thus you can calculate the PV of the bond:
PV = PV (coupons) + PV (face value)
= (coupon x annuity factor) + (face value x discount factor)
= $65x[1/0.051–1/(0.051( )3)]+1000x[1/( )3]
= $ = $1,038.05
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9. Bond Prices
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10. Bond Prices How Bond Prices Vary with Interest Rates
When interest rates are 5.1%, a 3 year bond with a 6.5% coupon rate is worth $1,
Critical question:
What would happen to the value of this bond if interest rates were to change?
You would have to recalculate the PV of the cash flows to determine its worth.
Say interest rates rise to 6.5% and then to 15%.
What is the value of this bond under each of these scenarios?
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11. Bond Prices How Bond Prices Vary with Interest Rates
If the discount rate is 6.5% then the PV is:
PV = PV (coupons) + PV (face value)
= $65x[1/0.065–1/(0.065( )3)]+1000x[1/( )3]
= $
= $1,000.00
If the discount rate is 15% then the PV is:
PV = PV (coupons) + PV (face value)
= $65x[1/0.15–1/(0.15(1+0.15)3)]+1000x[1/(1+0.15)3]
= $
= $805.93
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12. Check the next slide for a graph!
Bond Prices
How Bond Prices Vary with Interest Rates
Can you see the relationship between the coupon rate, the interest (discount) rate and the price of a bond?
Coupon Rate Interest Rate Price of Bond
6.5% % $1,038.05
6.5% % $1,000.00
6.5% % $
Check the next slide for a graph!
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13. Bond Prices How Bond Prices Vary with Interest Rates
Can you see the relationship between the coupon rate, the interest (discount) rate and the price of a bond?
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14. How Bond Prices Vary with Int. Rates
There is an inverse relationship between bond prices and the interest rate:
If interest rates go up, bond prices go down
If interest rates go down, bond prices go up
More Precisely:
When the market interest rate exceeds the coupon rate, bonds sell for less than face value. (sells at discount)
When the market interest rate equals the coupon rate, bonds sell for their face value. (sells at par)
When the market interest rate is below the coupon rate, bonds sell for more than face value. (sells at premium)
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15. If you pay $1,136.16 for this bond, what is your return?
Bond Yields
Measuring the Returns on Bonds
There are three methods used for measuring the return an investor would receive on an investment in bonds:
Current Yield.
Yield to Maturity.
Rate of Return.
Suppose you could buy a 3 year bond, with a 10% coupon rate.
If you pay $1, for this bond, what is your return?
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16. Bond Yields Current Yield
Current yield is calculated by dividing the coupon payments by the bond’s price:
Current Yield = Coupon Payments Bond Price
You are buying a bond with:
Coupon Payments = $100 per year.
Price of $1,
 Current Yield = $ = = 8.8% $1,136.16
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17. Bond Yields Current Yield The current yield on this bond is 8.8%.
But, the current yield only takes into account the interest income earned on the bond.
It does not include any capital gains or losses on your investment.
If you pay $1, for this bond, will you have a capital gain, or a loss, when the bond matures?
In three years, when the bond matures, you will receive $1,000 for it.
Thus, you will have a capital loss of $ over the life of the bond.
So, your actual return on this bond must be less than the 8.8% current yield.
Conclusion:
Current yield, because it ignores capital gains and losses, mismeasures the rate of return on a bond.
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18. Bond Yields Yield to Maturity
We need a measure of return which takes account of both
current yield (interest income) and
changes in the bond’s value over its life (capital gains and losses).
This measure is called Yield to Maturity.
Yield to maturity is defined as “the discount rate which makes the PV of the bond’s cash flows equal to its price.”
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19. Bond Yields
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20. YTM Approximation Formula
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21. When Price = $1,136.16 the discount rate = 5% (ytm is 5%)
Bond Yields
When Price = $1, the discount rate = 5% (ytm is 5%)
Paid Price=$1,136.16
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22. Bond Yields Yield to Maturity Note that yield to maturity depends on
the coupon payments and
the current price of the bond and
the final repayment.
Thus, it is a measure of your return if you buy the bond today and hold it until maturity.
But what if you wanted to hold this bond for only one year … now how would you calculate your return?
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23. Bond Yields Rate of Return Let’s continue with our previous example:
You buy a 3 year bond with a 10% coupon for $1,
One year later, you sell it for $1,130.
For this example we need to calculate the bond’s rate of return:
Rate of return = coupon income + price change
investment
= $100 + ($1,130 - $1,136.16)
$1,136.16
= = 8.3%
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24. Bond Prices and Yields Yield to Maturity vs Rate of Return
Note that the rate of return over a particular holding period is not the same as the yield to maturity.
But, is there a relationship between yield to maturity and rate of return?
Yes:
If the bond’s yield to maturity is unchanged over the holding period, then the yield to maturity will equal the rate of return.
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25. Bond Yields = $100x[1/0.05–1/(0.05(1 + 0.05)2)]+1000x[1/(1+ 0.05)2]
Yield to Maturity vs Rate of Return
Continuing with our previous example, suppose the yield to maturity stays at 5% for one year, then at the end of the holding period, its price would be:
PV = PV (coupons) + PV (face value)
= $100x[1/0.05–1/(0.05( )2)]+1000x[1/( )2]
= $
= $1,092.97
 It rate of return = coupon income + price change
investment
= $100 + ($1, $1,136.16)
$1,136.16
= 0.05 = 5%
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26. Yield to Maturity vs Rate of Return
Note that:
The yield to maturity equals 5%.
The rate of return over the one year holding period also equals 5%.
This occurs because the price of the bond changes with time so that:
Total Return on the Bond = Yield to Maturity
The rules with respect to rate of return and yield to maturity are:
If interest rates do not change, the rate of return on the bond is equal to the yield to maturity.
If interest rates increase, then the rate of return will be less than the yield to maturity.
If interest rates decrease, then the rate of return will be more than the yield to maturity.
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27. Multiple Period Rate of Return
How do you calculate the rate of return if the investment lasts for longer than 1 year? For example:
You buy a 3 year bond with a 6.5% coupon for $1,
Two years later, you sell it for $1,
You will receive two coupon payments on this bond:
$65 at the end of the first year and $65 at the end of the second year. Assume that you reinvest the first coupon payment at 4% for one year.
Your coupon income for this investment will be:
Coupon Income = ($65 x 1.04) + $65 = $132.60
Rate of return = coupon income + price change
investment
= $ ($1, $1,038.05) = =10.58%
$1,038.05
However, this is a two year rate of return. You must annualize it:
Annual Rate of return = (1.1058)1/2 – 1 = = 5.2%
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28. Interest Rate Risk We have seen that:
bond prices fall when interest rates rise and
bond prices rise when interest rates fall.
You have also seen that the rate of return on your bond investments will vary as interest rates change.
This is why we say that bonds are subject to interest rate risk.
It is the risk in bond prices due to fluctuations in interest rates.
Bond investors worry that if interest rates go up, they will have losses on their bonds.
But bonds are not equally affected by changes in interest rates:
Some bonds have big price changes in response to int. rate changes.
Some bond prices react very little to a change in interest rates.
Bonds with larger maturity are more affected by int. rate changes than bonds with shorter maturity.
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29. Interest Rate Risk Compare the two curves on the next slide.
The blue curve shows how the price of a 30 year bond varies according to interest rates.
Notice how steep the curve is.
Notice that a change in rates results in a large change in price.
The red curve shows how the price of a 3 year bond varies according to interest rates.
Notice how flat the curve is.
Notice that a change in rates results in a small change in price.
Which bond would you rather own, the 30 year or the 3 year, if you expected interest rates to go up? Why?
Which bond would you rather own, the 30 year or the 3 year, if you expected interest rates to go down? Why?
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30. Price change in response to interest rate changes (30 year bond vs 3 year bond):
$4,500
$4,000
Bond Price
$3,500
$3,000
30 year bond
 Price
$2,500
$2,000
 Rates
$1,500
 Price
$1,000
Rates
3 year bond
$500 $0
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
7.00%
8.00%
9.00%
10.00%
11.00%
12.00%
13.00%
14.00%
Interest Rates
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31. Default Risk
Both corporations and the Government of Canada borrow money by issuing bonds.
There is an important difference between corporate borrowers and government borrowers:
Corporate borrowers can run out of cash and default on their borrowings.
The Government of Canada cannot default – it just prints more money to cover its debts.
Default risk (or credit risk) is the risk that a bond issuer may default on its bonds.
To compensate investors for this additional risk, corporate borrowers must promise them a higher rate of interest than the Canadian government would pay.
The default premium or credit spread is the difference between the promised yield on a corporate bond and the yield on a Canada bond with the same coupon and maturity.
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32. Default Risk You are thinking of investing in one of these bonds:
Government of Canada 10 years, 6% coupon, 6% yield.
Safe Corp 10 years, 6% coupon, 6.5% yield.
Risky Corp 10 years, 6% coupon, 10% yield.
The corporate bonds both have a higher yield than the Canada because of default risk. Safe Corp has little risk of default and a small default premium (credit spread) of 0.5%. Risky Corp has high default risk and thus a large default premium of 4%.
The safety of a corporate bond can be judged from its bond ratings, provided by companies such as DBRS, Moody’s, and Standard and Poor’s.
Bond ratings list bonds in order from the lowest risk of default to the highest risk of default.
AAA (triple A) bonds have the least risk of default.
Then comes AA, A, BBB, BB, B, CCC, CC, C
Bonds rated BBB and above are called investment grade bonds.
Bonds rated BB and below are called speculative grade, high yield, or junk bonds. (See table 5.1 in your text for a list of bond ratings and their meanings)
Note that the yield on a bond varies inversely with its rating (See figure 5.9) :
Bonds with a high bond rating have less risk and thus lower yields.
Bonds with a low bond rating have a lot of risk and higher yields.
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33. Corporate Debt Overview of Liabilities Limited Liability
When companies borrow money, they promise to make regular interest payments and to repay the principal (the original amount borrowed).
However, corporations have limited liability.
This means that the shareholders have the right to default on the debt and to hand over the company’s assets to the lenders.
Limited Liability
Clearly a company will choose bankruptcy only if the value of the assets is less the than the amount of the debt.
If bankruptcy does occur, the handover of the assets is rarely straightforward and can lead to creditors jostling each other for a share of the remaining assets.
Corporate Governance
Because lenders do not own the firm, they do not normally have any voting power.
In addition, since interest is an obligation, it is treated as an expense and deducted from taxable income.
This means the government provides a subsidy for debt which it does not provide on stock.
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34. Corporate Debt Types of Debt Long-Term Debt Short-Term Debt
There are many kinds of debt, each with its own characteristics.
Most debt has its rate fixed at the time of issue.
However, some debt carries a floating interest rate. This rate will be tied to some benchmark rate such as the prime rate or LIBOR.
Prime Rate: The rate charged by large banks to customers with good to excellent credit ratings. The prime rate is adjusted up and down with interest rates.
London Interbank Offered Rate (LIBOR): The rate at which international banks lend to each other.
Long-Term Debt
Debt with more than 1 year remaining to maturity. Long-term debt is often called funded debt.
In 1993, Walt Disney and Coca Cola issued 100-year bonds. (Wall Street calls the Disney bond the “Sleeping Beauty” bond.) Such a long maturity is highly unusual, but not unprecedented; the Canadian Pacific Corporation is paying a 4% coupon on a 1000-year bond issued in The Disney bond was sold at par and its yield at the time of issue was 7.55%.
Short-Term Debt
This is debt carried on the balance sheet as a current liability. It is often called unfunded debt.
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36. Corporate Debt Types of Debt Sinking Fund Callable Bond Refunding
A fund established to retire the debt before its maturity date.
Callable Bond
A bond which may be repurchased by the firm before maturity at a specified call price.
Refunding
When an old bond issue is replaced with a new one by the firm.
Usually this is done when interest rates fall, meaning the firm saves on interest costs by issuing new debt.
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37. Corporate Debt Seniority Country and Currency
If a company gets into financial difficulty, its creditors share its assets.
However, subordinated lenders have a junior claim and will get a share of the assets only after the claims of the senior creditors have been paid.
Secured debt is debt which has a first claim on specified collateral in the event of default.
The risk of default is measured by bond ratings, with the lower the rating the greater the risk of default.
Country and Currency
A firm may issue debt in its own country and currency.
It can also issue its debt in a different country and/or a different currency.
A eurobond is a bond that is denominated in the currency of one country but issued to investors in other countries.
Example: A Canadian corporation issues bonds in Yen to investors in France, UK or Australia
A foreign bond is issued in the currency of its country, but the borrower is from another country.
Example: Air Canada has some long-term debt in US$ in the USA, Swiss franc in Switzerland and euro in Germany.
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38. Corporate Debt Public vs Private Placements Protective Covenants
In a public issue, a firm issues its debt to anyone who wishes to buy it.
Such debt can be freely traded in securities markets.
In a private placement, the issue is sold directly to a small number of institutional investors.
Such debt cannot be resold to individual Canadians but only to qualified institutional investors.
Protective Covenants
Lenders usually impose conditions on a borrower to ensure that their money will be well used and that the borrower will not take unreasonable risks.
Restrictions on a firm which are designed to protect the bondholders are known as protective covenants.
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39. Corporate Debt Long Term Leases
Instead of borrowing money to buy equipment, a firm may lease or rent it on a long term basis.
The firm promises to make a series of payments to the lessor (the owner of the equipment).
A lease is just like the obligation to make payments on an outstanding loan.
If the firm can’t make the lease payments, the lessor repossesses the equipment.
The lender would do precisely the same thing, if the equipment were collateral for a defaulted loan.
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40. Convertible Securities
Warrants
Firms have the option to repay an issue of bonds before maturity. However, there are also cases where the investors have an option. For example warrants give the investor the right to buy shares from a company at a set price before a set date.
Warrants are sometimes known as a “sweetener” because they make the bond issue more attractive to potential investors.
They give an investor a chance to lock-in a purchase price for a security.
If that security goes up in value, then the warrant could turn out to be very valuable.
Of course, if the security did not go up in value, the warrants would expire worthless.
Convertible Bonds
Convertible bonds may be exchanged at the option of the holder for a specified amount of another security, usually common shares.
The convertible bondholder hopes that the price of the shares will rise significantly so that s/he can convert at a big profit.
But if the shares don’t go up, there is no obligation to convert, so the investor keeps the bond and collects interest payments.
Convertible Preferreds
Companies can also issue convertible preferred shares.
These shares pay a fixed dividend and they also allow the investor to convert the preferreds for the firm’s common stock.
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