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...

...
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...

...Assignment no. 1
Fixed Income Securities and Markets
Question A.1
Given the following bond:
|starting date |30/09/2011 |
|maturity date |30/09/2014 |
|coupon rate |4.00% |
|coupon frequency |annual |
|day count |act/act |
|nominal value |100 |
a) Calculate the price of the security on the 30/09/2011, if the yield to maturity is 5% (NB: Price=PV of future cash flows).
b) Given the price and the yield to maturity of the bond, calculate the three components of the (expected) total return of this investment (if you invest 100 Euro).
c) What will be the price of this bond after one year (on 30/09/2012) if its yield to maturity is 3%?
d) If on 30/09/2012 you decide to sell the bond at the price calculated in the previous question, what will be the return of your investment? How this differs from the expected return calculated in (b)? Comment.
Solution
a) Using the pricing formula for bonds:
[pic]
b) The three different components are:
a. Coupon: holding the bond until maturity, the investor will receive three coupons of size 4 Euro, therefore the coupon component will be nC=12
b. Capital gain: it is the difference between the price at...

...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...

...Chapter 6
BondValuation
6.5 Duration and Convexity
Problem
Given a 4-yr treasury bond with a face value of $1,000, an annual coupon rate of 3.20%, which had a yield to maturity of 2.53%, this bond makes 2 semi-annual coupon payments. Thus has 8 periods until maturity and we are required to determine what the duration, modified duration, and convexity of this bond is, based on the Annual Percentage Rate (APR) and the Effective Annual Rate (EAR). Also, we are asked to explain an intuitive interpretation of duration.
Methodology
First, I entered the coupon rate for all bonds 1 through 8 and calculated the discount rate/period(r). Then, I used the present value formula (yr-8 cash flow/(1+discount rate/period)^8) to find the bond price. I copied the formulas for present value and duration from the duration and convexity spreadsheet into the corresponding cells. Next, to find the duration I was able to calculate the weight and convexity of liabilities by taking (sum of weight * (time ^2 + time)) / ((1+yield to maturity / # of payments)^2). Finally, I was able to calculate the total assets minus liabilities, the present value of assets minus present value of liabilities, the duration of assets minus duration of liabilities and the convexity of assets minus the convexity of liabilities.
Assumptions
I assumed that this 4-yr Treasury bond had a face value of...

...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;...

...CHAPTER 7
BondsValuation
CHAPTER ORIENTATION
This chapter introduces the concepts that underlie asset valuation. We are specifically concerned with bonds. We also look at the concept of the bondholder's expected rate of return on an investment.
CHAPTER OUTLINE
I. Types of bonds
A. Debentures: unsecured long-term debt.
B. Subordinated debentures: bonds that have a lower claim on assets in the event of liquidation than do other senior debtholders.
C. Mortgage bonds: bonds secured by a lien on specific assets of the firm, such as real estate.
D. Eurobonds: bonds issued in a country different from the one in whose currency the bond is denominated; for instance, a bond issued in Europe or Asia that pays interest and principal in U.S. dollars.
E. Zero and low coupon bonds allow the issuing firm to issue bonds at a substantial discount from their $1,000 face value with a zero or very low coupon.
1. The disadvantages are, when the bond matures, the issuing firm will face an extremely large nondeductible cash outflow much greater than the cash inflow they experienced when the bonds were first issued.
2. Zero and low coupon bonds are not callable and can be retired only at maturity.
3. On the other hand, annual cash outflows...

...Asset Valuation
0 r 1 2 n
...
CF1 CF2 CFn
Value
PV =
CF1
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1
+
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2
+ ... +
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.
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...

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