CHAPTER 4 BONDS ANND THEIR VALUATION
Bond value--semiannual payment 1. You intend to purchase a 10-year, $1,000 face value bond that pays interest of $60 every 6 months. If your nominal annual required rate of return is 10 percent with semiannual compounding, how much should you be willing to pay for this bond?

N = 20 I/Y = 5 PV = -1124.62 PMT = 60 FV = 1000 Bond value--semiannual payment 2. Assume that you wish to purchase a 20-year bond that has a maturity value of $1,000 and makes semiannual interest payments of $40. If you require a 10 percent nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond?

N = 40 I/Y = 5 PV = -828.41 PMT = 40 FV = 1000

Bond value--semiannual payment 3. A bond that matures in 12 years has a 9 percent semiannual coupon (i.e., the bond pays a $45 coupon every six months) and a face value of $1,000. The bond has a nominal yield to maturity of 8 percent. What is the price of the bond today?

N = 24 I/Y = 4 PV = -1076.23 PMT = 45 FV = 1000

Bond value--semiannual payment 4. A corporate bond with a $1,000 face value pays a $50 coupon every six months. The bond will mature in 10 years, and has a nominal yield to maturity of 9 percent. What is the price of the bond?

N = 20 I/Y = 4.5 PV = -1065.04 PMT = 50 FV = 1000

Yield to maturity--semiannual bond 5. A corporate bond has a face value of $1,000, and pays a $50 coupon every six months (that is, the bond has a 10 percent semiannual coupon). The bond matures in 12 years and sells at a price of $1,080. What is the bond’s nominal yield to maturity?

Yield to maturity--semiannual bond 6. You just purchased a $1,000 par value, 9-year, 7 percent annual coupon bond that pays interest on a semiannual basis. The bond sells for $920. What is the bond’s nominal yield to maturity? N = 18 I/Y = 4.14*2 = 8.28 PV = -920 PMT = 35 FV = 1000 Current...

...Asset Valuation
0 r 1 2 n
...
CF1 CF2 CFn
Value
PV =
CF1
(1+ r )
1
+
CF2
(1 + r )
2
+ ... +
CFn
(1+ r )
n
.
Prof. P. Yourougou
MBC 633 – Managerial Finance
Lect. 03 - 2
Various Interest Rate Measures
Coupon rate Coupon rate
periodic cash flow a bond issuer contractually periodic cash flow a bond issuer contractually promises to pay a bond holder promises to pay abond holder rates used by individual market participants to rates used by individual market participants to calculate fair present values (PV) calculate fair present values (PV) rates participants would earn by buying securities at rates participants would earn by buying securities at current market prices (P) current market prices (P) rates actually earned on investments rates actually earned on investments
Required rate of return (rrr) Required rate of return (rrr)
Expected rate of return (Err) Expected rate of return (Err) Realized rate of return (rr) Realized rate of return (rr)
Prof. P. Yourougou
MBC 633 – Managerial Finance
Lect. 03 - 3
BondValuation
Premium bond has Premium bond has
A coupon rate (INT) greater than the required A coupon rate (INT) greater than the required rate of return (rrr) and rate of return (rrr) and the fair present value of the bond (Vbb) is the fair present value...

...Lecture 03: Applying the Time Value of Money to Security Valuation – Valuation of Bonds and Debt Securities
A bond or a debenture is a long term debt instrument carrying a fixed rate of interest which is known to investors. A bond is redeemable after a specified period.
Bonds are also called gilt edged securities or gilt when issued by the government since it is free of default risk.
Features of aBond or Debenture
• Face Value – Face value is called par value. A bond / debenture is generally issued at a par value and interest is paid on the par value.
• Interest Rate – Interest rate is fixed and known to the bondholders / debenture holders. Interest paid on a bond is tax deductible. The interest rate is also called the coupon rate.
• Maturity – A bond is issued for a specified period of time. It is repaid on maturity.
• Redemption Value – The value which a bondholder will get on maturity is called redemption value.
• Market Value – A bond / debenture may be traded on the stock exchange. The price at which it is currently sold or bought is called the market value of the bond / debenture.
A bond is a long-term promissory note that promises to pay the bondholder a predetermined, fixed amount of interest each year until maturity. At maturity, the principal will...

...
HW BondValuation and Bond Yields
Clifford Clark is a recent retiree who is interested in investing some of his savings in corporate bonds. His financial planner has suggested the following bonds:
• Bond A has a 7% annual coupon, matures in 12 years, and has a $1000 face value.
• Bond B has a 9% annual coupon, matures in 12 years, and has a $1000 face value.
• Bond C has an 11% annual coupon, matures in 12 years, and has a $1000 face value.
Each bond has a yield to maturity (YTM) of 9%.
1) Without calculation, indicate whether each bond is trading at a premium, discount, or at par.
In order to indicate whether each bond is trading at a premium, discount, or at par, you need to compare the yield to maturity (YTM). If the YTM is greater than the bond coupon rate, then the bond is considered to be trading at a premium. If the YTM is lesser than the bond coupon rate, then the bond is considered to be trading at a discount, and if the YTM is equal to the bond coupon rate, then the bond is considered to be trading at par.
Bond A: YTM = 9%, 9% > the coupon rate of 7%, therefore the bond is traded at a discount.
Bond B: YTM = 9%, 9% = the coupon rate of 9%, therefore the...

...dollar
delivered in half-year n, i.e., of a zero coupon bond which pays $1 in half-year n. In the next
two columns there are the cash flows of two bonds, A and B. Essentially, bond A pays a 20%
semi-annual coupon and bond B pays a 10% semi-annual coupon. Both bonds mature in 2.5
years, when each also pays its principal of 100. Assume semi-annual compounding.
Half
Year
1
2
3
4
5
n
Bond ABond B
.95
.91
.87
.80
.70
10
10
10
10
110
5
5
5
5
105
A. Calculate the price of each bond assuming there are no arbitrage opportunities in the
market. (That is, calculate the present value of each of the bonds.)
B. Now suppose that in fact bond A is traded at $111.97 while bond B is traded at
$91.41. Are there arbitrage opportunities in the market? If yes, how would you take
advantage of them? [Assume that zero coupon bonds are traded.]
C. Calculate the yields to maturity (or the interest/discount rates rn) from the discount
factors n given above (i.e., from the prices of the above zero coupon bonds). Plot
these against the time to maturity t of the bonds. This is the term structure of interest
rates or the yield curve based on zero coupon bonds.
D. Calculate the yield to maturity (i.e., the IRR) of bonds A and B...

...MBA 8135
Practice BondValuation Problems
SOLUTIONS
1. Calculate the current price of a $1,000 par value bond that has a coupon rate of 6% p.a., pays coupon interest annually, has 14 years remaining to maturity, and has a yield to maturity of 8 percent.
PMT = 60; FV = 1000; N = 14; I = 8; CPT PV = 835.12
2. You intend to purchase a 10-year, $1,000 par value bond that pays interest of $60 every six months. If the yield to maturity is 10% with semiannual compounding, how much should you be willing to pay for this bond?
FV = 1000; PMT = 60; N = 20; I = 10/2=; CPT PV = 1124.62
3. What is the price of a $5000 par value bond, with a coupon rate of 7.5% (coupon interest paid quarterly), 15 years remaining to maturity and a yield to maturity of 8.25%?
FV = 5000; PMT = 93.75; N = 60; I = 8.25/4=; CPT PV = 4678.99
4. Dak, Inc. has a bond outstanding with a par value of $10,000 that makes monthly coupon payments. The coupon rate is 9 percent and the bond has 24 years remaining to maturity. If the yield to maturity of similar bonds is 9.35 percent, what is the current price of the bond?
FV = 10000; PMT = 75; N = 288; I = 9.35/12=; CPT PV = 9665.71
5. A ten year bond with a coupon rate of 12% (payable annually) and a par value of $1,000 is selling for $1,192.50 today. What is the bond’s yield to maturity?
PV = -1192.50;...

...This case discusses the valuation of stocks and bonds. It says that in textbooks, the valuation of stocks and bonds is simply stated as the present value of all the future cash flows expected from the security. The concept is logical, straightforward, and simple. The valuation of bonds is usually presented first, since the relatively certain cash flows are broken into an annuity and a payment of the par value at some specific date in the future. Preferred stock valuation follows bondvaluation and the value of preferred stock is shown to be the present value of perpetual annuity. The cash flows from the constant-size dividend are fairly certain, and most preferred stocks do not have a maturity date. Finally, common stock is presented but neither the future cash flows (from dividends) nor the final value is known with any degree of certainty.
The case describes Home Products, Inc, a leading manufacturer of prescription and ethical drugs; specialty foods and candies; and proprietary drugs. Total revenues in the last fiscal year were in excess of $9 billion. Company's capital structure is made up of 34% long-term debt, 3% preferred stock, and 63% common stock. The case describes the two largest domestic long-term debt, and close this issue disclosing that these two bonds are rated A by Moody's. Then, it talks about preferred stocks. 5.5...

...BOND PROBLEM SOLUTIONS
1. Six years ago, The Corzine Company sold a 20-year bond issue with a 14 percent annual coupon rate and a 9 percent call premium. Today, Corzine called the bonds. The bonds originally were sold at their face value of $1,000. Compute the realized rate of return for investors who purchased the bonds when they were issued and who surrender them today in exchange for the call price.
PV = 1000; N = 6; PMT = 140; FV = 1090; CPT I/Y
I/Y = 15.02%
2. You just purchased a bond which matures in 5 years. The bond has a face value of $1,000, and has an 8 percent annual coupon. The bond has a current yield of 8.21 percent. What is the bond’s yield to maturity?
CURRENT YIELD = ANNUAL COUPON ( PV
0.0821 = 80 ( PV
PV = 80 ( 0.0821 = 974.42
N = 5; PMT = 80; FV=1000; PV = 974.42 CPT I/Y
I/Y = 8.65%
3. The Dass Company’s bonds have 4 years remaining to maturity. Interest is paid annually; the bonds have a $1,000 par value; and the coupon interest rate is 9 percent. What is the yield to maturity at a current market price of $829? Would you pay $829 for one of these bonds if you thought that the appropriate rate of return was 12 percent?
PV = 829; N = 4; FV = 1000; PMT =90; CPT I/Y
I/Y = 14.99%
YES, IF YOU THOUGHT THE APPROPRIATE RATE WAS 12%, YOUR PV WOULD...

...Financial Institutions and Markets
Jim Wilcox
Bond Yields, Returns, Risks, and Duration
•
•
•
•
•
Bonds and Loans
Yields and Returns
Price Volatility and Risk in Default-Free Bonds
Measuring Interest Rate Risk
Duration: Types, Calculation, Meaning, Uses
• Next Time: Chapter 11 re: Duration
Week # 2
January 28, 2014
1
Coming Soon!
What We Did
1.
2.
3.
4.
Week # 2
January 28, 2014
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Yield to Maturity (YTM):
A Result, Not a Cause!
• YTM = percentage rate that equates (known) bond
price to PV of all promised (via bond) payments
• If the price of a coupon bond = its principal (or FV),
then YTM = the bond’s coupon rate (C/FV)
– If bond price exceeds its face value, YTM < coupon rate
Week # 2
January 28, 2014
3
Yields on U.S. Treasury Bonds, 2003-2012:
Short-Term Yields (but not Prices) Varied More
Week # 2
January 28, 2014
4
Bond Yields Differ from Returns,
in Concept and in the Data
• Returns (over some time span) = current yield (via coupon)
plus percentage change in the bond’s price (over time span)
• Longer-maturity-bond prices fall more increase in YTM
– A measure called Duration, D, will conveniently show us how much
Week # 2
January 28, 2014
5
in case we want a blank slide…
Week # 2
January 28, 2014
6
Relation of a Bond’s Price to Its...