Finance Exam 25 questions and one hour limit !!!
karaomer16
fin201_chapter7_spring2016.pptBond Valuation
Chapter 7
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What is a bond?
- A long-term debt instrument in which a borrower agrees to make payments of principal and interest, on specific dates, to the holders of the bond.
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Key Features of a Bond
- Par value – face amount of the bond, which
is paid at maturity (assume $1,000). - Coupon interest rate – stated interest rate (generally fixed) paid by the issuer. Multiply by par value to get dollar payment of interest.
- Maturity date – years until the bond must be repaid.
- Issue date – when the bond was issued.
- Yield to maturity - rate of return earned on
a bond held until maturity (also called the “promised yield”).
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Determining the Price of a Bond
The Bond Valuation Formula
- The price of a bond is the present value of a stream of interest payments plus the present value of the principal payment.
PB = PV(Interest Payments) + PV(Principal Payment)
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Bond Prices
What is the current price of each bond if the interest rate is 10% ?
What is the current price of each bond if the interest rate is 7% ?
| Bond A | Bond B | Bond C | |
| Maturity | 10 Years | 10 Years | 10 Years |
| Coupon Rate | 13% | 10% | 7% |
| Face Value | $1000 | $1000 | $1000 |
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Bond Price Characteristics
Relationship #1: The value (price) of a bond is inversely related to changes in interest rates (and ytm).
- Rates … Price
- Rates … Price
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Bond Price Characteristics
Relationship #2: Price (Pb) will be < par value (M) if the coupon rate (c) is less than the ytm. Conversely, Pb > M if c >ytm.
A bond where Pb > M is a premium bond.
A bond where Pb < M is a discount bond.
A bond where Pb = M is a par bond
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Bond Price Characteristics
Relationship #3:
As the maturity date approaches, Pb converges to M.
Pb increases with maturity if c < ytm.
Pb decreases with maturity if c > ytm.
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Bond Price Characteristics
Example: Assume that the interest rate is 8%. Calculate the price of the following two bonds assuming 20 years to maturity and 1 year to maturity.
Bond A Bond B
Par Value (M) $1,000 $1,000
Coupon Rate (c) 3% 10%
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Bond Price Characteristics
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20 years |
1 year |
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Bond A |
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Bond B |
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Bond Price Characteristics
Relationship #4:
Long term bond prices are more sensitive to changes in interest rates than are short term bond prices.
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Semi-Annual Bonds
- Multiply years by 2
- Divide interest rate by 2
- Divide annual coupon by 2
Example:
What is the value of a 10-year, 10% semiannual coupon bond, if the interest rate is 13%?
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Computing Yield to Maturity
- Yield to Maturity (YTM) is the rate implied by the current bond price
- Finding the YTM requires trial and error if you do not have a financial calculator and is similar to the process for finding r with an annuity
- If you have a financial calculator, enter N, PV, PMT, and FV, remembering the sign convention (PMT and FV need to have the same sign, PV the opposite sign)
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YTM with Annual Coupons
- Consider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1,000. The current price is $928.09.
- Will the yield be more or less than 10%?
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The students should be able to recognize that the YTM is more than the coupon since the price is less than par.
YTM with Semiannual Coupons
- Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1,000, 20 years to maturity and is selling for $1,197.93.
- Is the YTM more or less than 10%?
- What is the semiannual coupon payment?
- How many periods are there?
- What is the YTM?
N = 40; PV = -1,197.93; PMT = 50; FV = 1,000; CPT I/Y = 4% (Is this the YTM?)
YTM = 4%*2 = 8%
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Current Yield vs. Yield to Maturity
- Current Yield = annual coupon / price
- Yield to maturity = current yield + capital gains yield
- Example: 10% coupon bond, with semiannual coupons, face value of 1,000, 20 years to maturity, $1,197.93 price
- What is the Current yield?
- What is the YTM?
- What is the price of the bond in one year, assuming no change in YTM?
- What is the Capital gains yield?
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Current yield = 100 / 1,197.93 = .0835 = 8.35%
Price in one year, assuming no change in YTM = 1,193.68
Capital gain yield = (1,193.68 – 1,197.93) / 1,197.93 = -.0035 = -.35%
YTM = 8.35 - .35 = 8%, which is the same YTM computed earlier
This is the same information as the YTM calculation on slide 7.15. The YTM computed on that slide was 8%
Lecture Tip: You may wish to discuss the components of required returns for bonds in a fashion analogous to the stock return discussion in the next chapter. As with common stocks, the required return on a bond can be decomposed into current income and capital gains components. The yield-to-maturity (YTM) equals the current yield plus the capital gains yield. A further example is provided in the IM.
The Bond Indenture
- Contract between the company and the bondholders that includes
- The basic terms of the bonds
- The total amount of bonds issued
- A description of property used as security, if applicable
- Sinking fund provisions
- Call provisions
- Details of protective covenants
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Types of Corporate bonds
- Mortgage bonds
- Debentures
- Subordinated debentures
- Investment-grade bonds
- Junk bonds
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Government Bonds
- Treasury Securities
- Federal government debt
- T-bills – pure discount bonds with original maturity of one year or less
- T-notes – coupon debt with original maturity between one and ten years
- T-bonds – coupon debt with original maturity greater than ten years
- Municipal Securities
- Debt of state and local governments
- Varying degrees of default risk, rated similar to corporate debt
- Interest received is tax-exempt at the federal level
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Zero Coupon Bonds
- Make no periodic interest payments (coupon rate = 0%)
- The entire yield-to-maturity comes from the difference between the purchase price and the par value
- Cannot sell for more than par value
- Treasury Bills and principal-only Treasury strips are good examples of zeroes
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Most students are familiar with Series EE savings bonds. Point out that these are actually zero coupon bonds. The investor pays one-half of the face value and must hold the bond for a given number of years before the face value is realized. As with any other zero-coupon bond, reinvestment risk is eliminated, but an additional benefit of EE bonds is that, unlike corporate zeroes, the investor need not pay taxes on the accrued interest until the bond is redeemed. Further, it should be noted that interest on these bonds is exempt from state income taxes. And, savings bonds yields are indexed to Treasury rates.
