1. Bonds, Bond Valuation, and Interest Rates
Chapter 5
Bonds, Bond Valuation, and Interest Rates

2. Copyright © 2014 by Nelson Education Ltd.

3. Basic Valuation
The (market) value of any investment asset is simply the present value of expected cash flows.
The interest rate that these cash flows are discounted at is called the asset’s required return.
The higher expected cash flows, the greater the asset’s value.
It makes sense that an investor is willing to pay (invest) some amount today to receive future benefits (cash flows).

4. Basic Valuation Model V0 = CF1 + CF2 + … + CFn
(1 + k) (1 + k) (1 + k)n
Where:
V0 = value of the asset at time zero
CFt = cash flow expected at the end of year t
k = appropriate required return (discount rate)
n = relevant time period

5. Raise funds with debt: Bonds
A bond is a long-term debt where the amount borrowed is repaid at maturity—that is, the end of the bond’s life
principal amount, face value, maturity value, and par value (all the above terminology refers to the amount that must be repaid by the borrower)
coupon interest rate - coupon payment divided to the par value
maturity date - date in which the par value must be repaid
call provision - the issuer can pay them prior to maturity
new issues - the coupon rate on a bond is approximately equal to the rate at which similar risk bonds are trading in the financial markets when the bond is issued

6. Retractable Bonds
Allow investors to sell the bonds back before maturity to the issuer at a pre-set price
Protect investors from the rising interest rates or the event risk
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7. Sinking Fund Provision
Provision to pay off a loan over its life rather than all at maturity
Similar to amortization on a term loan
Reduces risk to investor, shortens average maturity
But not good for investors if rates decline after issuance
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8. Two Ways to Handle Sinking Fund
1. Call x% at par per year for sinking fund purposes. 2. Buy bonds on the open market.
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9. Other Bond Features
Convertible bonds: Bondholders have a right to convert the bond into shares of common stock, at a fixed price.
Income bonds: Pay interest only when the issuer can afford to do so.
Real return bonds: Principal and interests are indexed and protected against inflation.
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10. Zero Coupon Bond Prices
With no interest payments, the price of a zero is the present value of the principal payment at maturity. N 1 2
rd% M
Value
...
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11. The basic bond valuation model
B0 = I I … (In + Mn)
(1+k) (1+k) (1+k)n
Using the above model, find the (market) price of a 10% coupon bond, 3 years to maturity if market interest rates are currently 10%(par value= 100).
B0 = € € (€10 + €100)
(1+.10) (1+.10) (1+.10)3
It can also be calculated by finding the present value of the annuity
B0 = 10 * (1 - [1/(1+.10)3]) * [1/(1+.10)3] =
.10

12. Valuation of a bond using Excel
For example, find the price of a 10% coupon bond with three years to maturity if market interest rates are currently 10%.
Note: the equation
for calculating
price is
=PV(rate,nper,pmt,fv)

13. Changes in bond values over time
In the previous example, what would happen to the bond’s price if interest rates drop from 10% to 8%?
When interest rate falls below the coupon rate, then the bond would sell at a premium
When the interest
rate goes down, the
bond price will
always go up

14. Changes in bond values over time
In the previous example, what would happen to the bond’s price if interest rates increase from 10% to 12%?
When interest rate increases above the coupon rate, then the bond would sell at a discount
When the interest
rate goes up, the
bond price will
always go down

15. Bond value–interest rate relationship

16. Bond Return Vd INT Vd1 – Vd0 Vd0 kd = + Rate of return Current yield
Capital
gains yield = +

17. Bond Valuation – Change in value over time
Bond Characteristics: M = €1,000.00, INT = €60.00, kd = 8%
Years to Maturity
End of Year Value, Vd
Capital Gain = (Vd1-Vd0)/Vd0
Current Yield = INT/Vd0
Total Return 5
€920.15 4
933.76
1.48%
6.52%
8.00% 3
948.46
1.57
6.43
8.00 2
964.33
1.67
6.33 1
981.48
1.78
6.22
1,000.00
1.89
6.11

18. Market value converges at par value to maturity

19. Finding the Yield to Maturity on a Bond
The yield to maturity measures the compound annual return to an investor and considers all bond cash flows.
PV = I I … (In + Mn)
(1+k) (1+k) (1+k)n
Note that this is the same equation of the Basic Valuation Model. The only difference now is that we know the market price but are solving for return.

20. Valuation with semi-annual compounding
Example: M = €1,000, C = 5%, Yrs to maturity = 8, kd = 6%
16 3 ?
-931,23  N  I
 PV
PMT FV
Adjustments to computations
N = # years x m; m = # of interest payments per year
i = kd/m
INT = interest payment per period = Annual INT/m

21. Callable Bonds and Yield to Call
Expected rate of return earned on a callable bond assuming it is to be called at the first call date
The company must pay a price (call price) higher than the par value to call the bond.
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22. Yield To Call (YTC): An Example
A 10-year, 10% annual coupon, $1,000 par value bond is selling for $1, with an 5% yield to maturity.
It can be called after 1 year at $1,100.
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23. Yield To Call (YTC) if the Bond is Called 9 Years After Purchase
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24. If You Bought Bonds, Would You Be More Likely to Earn YTM or YTC?
Coupon rate = 10% vs. YTC = rd = 4.21%. Firm could raise money by selling new bonds that pay 4.21%.
Could thus replace bonds that pay $100/year with bonds that pay only $42.1/year.
Investors should expect a call, hence YTC = 4.21%, not YTM = 5%.
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25. If You Bought Bonds, Would You Be More Likely to Earn YTM or YTC
If You Bought Bonds, Would You Be More Likely to Earn YTM or YTC? (cont'd)
In general, if a bond sells at a premium, then (1) coupon > rd, so (2) a call is likely.
So, expect to earn:
YTC on premium bonds
YTM on par & discount bonds
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26. Current Yield Annual coupon pmt Current price
A measure of the amount of cash income to be generated in a given year.
Not an accurate measure of the bond's total expected return (consider a zero coupon bond with a current yield of zero).
Annual coupon pmt
Current price
Current yield =
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27. Current Yield: An Example
10% coupon, 14-year bond,
P = $1,494.93, and YTM = 5.0%
Current yield =
= = 6.69%
$100
$1,494.93
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28. Determinants of Market Interest Rates
Rate of return (interest) = k = Risk-free rate + Premium for risk = kRF + RP
Risk
Return
Risk Premium = RP
k = kRF + RP
kRF
Risk-Free Return = kRF

29. Determinants of Market Interest Rates
Quoted rate = k = kRF + RP = [k* + IP] [DRP + LP + MRP]
k* = real risk-free rate
IP = inflation premium
k* = real risk-free rate
IP = inflation premium
= kRF
DRP = default risk premium
LP = liquidity (marketability) premium
MRP = maturity risk premium
DRP = default risk premium
LP = liquidity (marketability) premium
MRP = maturity risk premium
= RP

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31. The Term Structure of Interest Rates
Relationship between yields and bond maturities
Yield
(%)
Term to Maturity
(years)
Upward sloping (normal)
Flat
Downward sloping (inverted)

32. The term structure of interest rates
Explanations for the shape of the yield curve
Expectations theory
The shape of the yield curve is based on expectations about inflation in the future, i.e. inflation increases => yield curve upward sloping
Liquidity preference theory
Long-term bonds are considered less liquid than short-term bonds, i.e. long-term bonds must have higher yields to attract investors
Market segmentation theory
Borrowers and lenders prefer bonds with particular maturities.

33. Interest rate Levels and Stock Prices
Effects on corporate profits
Interest is a cost to business, so interest rate changes have a direct impact on business profits
Interest rates affect investment behavior, so when rates on bonds increase, money is taken out of the stock markets to invest in the bond markets => general prices of stocks are pushed down and the prices of bonds are pushed up

34. Interest rates and business decisions
A firm’s decision concerning what types of financing should be used for investments in assets is based on forecasts of future interest rates
Suppose that interest rates are expected to fall over the next period, then the firm would borrow short-term and “lock” into lower long-term rates when the rates fall

35. Term structure of interest rates
Self – test problems
Term structure of interest rates
If you have information that a recession is ending, and the economy is about to enter a boom, and your firm needs to borrow money, it should probably issue long-term rather than short-term debt
(a) TRUE
(b) FALSE

36. Term structure of interest rates
Self – test problems
Term structure of interest rates
And the right answer is…..
(a)

37. Self – test problems Risk and return
Your uncle would like to restrict his interest rate risk and his default risk, but he still would like to invest in corporate bonds. Which of the possible bonds listed below best satisfies your uncle’s criteria?
(a) AAA bond with 10 years to maturity
(b) BBB bond with 10 years to maturity
(c) AAA bond with 5 years to maturity
(d) BBB bond with 5 years to maturity

38. Self – test problems
Risk and Return
And the right answer is…..
(c)

39. Exam – type problems Problem 1
Suppose the annual yield on a two-year Treasury bond is 11.5 percent, while that on a one-year bond is 10 percent; k* is 3 percent, and the maturity risk premium is zero.
Using the expectations theory, forecast the interest rate on a one-year bond during the second year
What is the expected inflation rate in Year 1? Year 2?

40. Problem 1 Solution Given: One-year bond yield 10.0%
Two-year bond yield 11.5%
k* 3.0%
MRP 0.0%
One-year rate
In Year 2

41. Exam – type problems Problem 2
Today is January 1, 2005, and according to the results of a recent survey, investors expect the annual interest rates for the years 2008 – 2010 to be:
Year One-Year Rate % % %
The rates given here include the risk-free rate, kRF , and appropriate risk premiums. Today a three – year bond – that is, a bond that matures on December 31, 2007, has an interest rate equal to 6%. What is the yield to maturity for bonds that mature at the end of 2008, 2009 and 2010?

42. Problem 2 – Solution Year One-Year Rate 2008 5% 2009 4% Today = 1/1/05% % %
Today = 1/1/05
3-yr yield = 6%

43. Bankruptcy and Reorganization
A business is declared insolvent when it cannot meet its financial obligations.
Two options to deal with insolvency:
dissolve through liquidation (bankruptcy)
reorganize and stay alive
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44. Bankruptcy and Reorganization (cont'd)
Two main chapters of the federal Bankruptcy Act:
Bankruptcy and Insolvency Act (BIA), bankruptcy
Companies' Creditors Arrangement Act (CCAA), reorganization
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45. Reorganization
If a company can't meet its obligations, it files under CRA, which stops creditors from foreclosing, taking assets, and shutting down the business.
Company has 120 days to file a reorganization plan.
Court appoints a "trustee" to supervise reorganization.
Management usually stays in control.
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46. Reorganization (cont'd)
Company must demonstrate in its reorganization plan that it is "worth more alive than dead."
Otherwise, judge will order liquidation under the Bankruptcy and Insolvency Act.
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47. Priority of Claims in Case of Liquidation
Suppliers can repossess goods delivered within 30 days prior to bankruptcy
Costs for environmental damage
Trustee expenses
Unremitted payroll taxes and deductions
Unpaid wages, up to $2,000 per worker.
Secured creditors from sales of secured assets
Expenses incurred after bankruptcy filing
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48. Priority of Claims in Case of Liquidation (cont'd)
Municipal taxes
Claims for rent, up to 3 months prior to bankruptcy
Creditor costs who first filed a claim
Injury claim costs to employees not covered under Workers' Compensation
Other unsecured creditors
Preferred stockholders
Common stockholders
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49. Bankruptcy and Reorganization
In a liquidation, unsecured creditors generally get zero. This makes them more willing to participate in reorganization even though their claims are greatly scaled back.
Various groups of creditors vote on the reorganization plan. If both the majority of the creditors and the judge approve, the company "emerges" from bankruptcy with lower debts, reduced interest charges, and a chance for success.
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