FIN Quiz 4 Unit 6
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
Treasury Securities
-Federal government debt -T-notes - coupon debt with original maturity between one and ten years -T-bonds coupon debt with original maturity greater than ten years
Current Yield
= annual coupon/bond price = $60/$864.10 = 6.94%
Coupon rate
= coupon / face value E.g. $60/$1,000 = 6.00% if coupon rate = 8.25%, then coupon = 8.25%*$1000 = $82.50
Callable provision
An agreement giving the bond issuer the option to repurchase the bond at a specified price prior to maturity
A Japanese firm has a bond outstanding that sells for 91.53% of its ¥100,000 par value. The bond has a coupon rate of 3.40% paid annually and matures in 16 years. What is the yield to maturity of this bond?
Annual coupon = ¥100,000*3.4%= ¥3,400 Current bond price = 91.53%*¥100,000 = ¥91,530 Yield to maturity (YTM) = period rate *1 =4.13410%*1 = 4.13% Bond Value = PV of coupons + PV of par = C[1 - 1/(1 + r)t ]/ r + F / (1 + r)t Here we need to find the YTM of a bond. The equation for the bond price is: P = ¥91,530 = ¥3,400[1 - 1/(1 + r)16 ]/ r + ¥100,000 / (1 + r)16 Notice that the equation cannot be solved directly for r here. Although there is only one unknown variable (r) in this equation, we cannot solve it directly. This is called implicit function of r. You can use an iterative process to find the YTM of the bond through thousands of rounds of calculations. This is exactly what the financial calculator did for us. You may
Bond Pricing Theorem
Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate •If you know the price of one bond, you can estimate its YTM and use that to find the price of the second bond •This is a useful concept that can be transferred to valuing assets other than bonds
Government Bonds
Certificates sold by the government to raise money with the guarantee that the purchaser will be paid back later (with interest)
Example 4: A firm issued a 20-year bond one year ago at a coupon rate of 5.80%. The YTM on the bond is 8.00% now and the bond makes semiannual payments. What is the current bond price?
Is this a premium, discount or par bond? Number of periods = ? = 19*2 = 38 Period rate = ? = 8.00%/2 = 4.00% Payment per period = = 5.80%*$1000/2 = $29.00 The current bond price is $786.95.
Example 6: A firm has a 11.00% coupon bond on the market with 23 years to maturity. The bond makes semiannual payments and currently sell for 97.50% of par. What is the YTM?
Is this a premium, discount or par bond? Price=? YTM vs. Coupon Rate? Number of periods = ? = 23*2 = 46 Period rate = ? = YTM/2 Payment per period = = 11.00%*$1000/2 = $55.00 The yield to maturity (YTM) = 2*5.65358% = 11.31%
Example 5: A firm has a 14% coupon bond on the market with 9 years to maturity. The bond makes semiannual payments and currently sell for 110% of par. What is the YTM?
Is this a premium, discount or par bond? Price=? YTM vs. Coupon Rate? Number of periods = ? = 9*2 = 18 Period rate = ? = YTM/2 Payment per period = = 14.00%*$1000/2 = $70.00 The yield to maturity (YTM) = 2*6.07147% = 12.14%
One More Time Software has 6.40% coupon bonds on the market with 18 years to maturity. The bonds make semiannual payments and currently sell for 106.8 percent of par. What is the current yield on the bonds? The YTM? The effective annual yield?
Number of period = 18*2 = 36; Period rate = YTM/2; Annual coupon = $1000*0.064 = $64; PMT = $64/2 = $32; current bond price = $1,000*106.8% = $1,068. Since the coupon payments are semiannual, this is the semiannual interest rate. The YTM is the APR of the bond, so: Yield to maturity (YTM) = period rate *2 =2.89347%*2 = 5.78693% or 5.79% The current yield is: Current yield = Annual coupon payment / Price = $64 / $1,068 = 0.05993 or 5.99% The effective annual yield is the same as the EAR, so using the EAR equation from the previous chapter: Effective annual yield ( EAR) = [1 + (APR / m)]m - 1 = [1 + 0.0578693/2]2 - 1 = 1.05871 - 1 = 0.05871 or 5.87%
Ngata Corp. issued 20-year bonds 2 years ago at a coupon rate of 5.30%. The bonds make semiannual payments. If these bonds currently sell for 105 percent of par value, what is the YTM?
Number of periods = 18*2 = 36; Period rate = YTM/2; Annual coupon = $1000*0.053 = $53; PMT = $53/2 = $26.5; current bond price = $1,000*105% = $1,050. Since the coupon payments are semiannual, this is the semiannual interest rate. The YTM is the APR of the bond, so: Yield to maturity (YTM) = period rate *2 =2.43972%*2 = 4.87944% or 4.88%.
Suppose you buy a 7 percent coupon, 20-year bond today when it's first issued. If interest rates suddenly rise to 15 percent, what happens to the value of your bond? Why?
Price and yield move in opposite directions; if interest rates rise, the price of the bond will fall. This is because the fixed coupon payments determined by the fixed coupon rate are not as valuable when interest rates rise—hence, the price of the bond decreases. When a bond is first issued its coupon rate is usually set equal to its required rate of return or YTM on the issuing date. Apparently, the required rate of return increases from 7% to 15% which causes the bond price drop dramatically.
Bond Classifications
Registered vs. Bearer Forms Security -Collateral - secured by financial securities -Mortgage - secured by real property, normally land or buildings -Debentures - unsecured, backed by reputation only Notes - unsecured debt with original maturity less than 10 years Seniority
Sinkable bond
Sinkable provision -- an advantage to investors
maturity date
The date on which an investment becomes due for payment. Yield to Maturity (YTM) is the rate of return earned on a bond if it is held to maturity. E.g. 8.00% YTM is usually different from coupon rate
Suppose that a French company issues a bond with a par value of €1,000, 23 years to maturity, and a coupon rate of 5.80% paid annually. If the yield to maturity is 4.70%, what it the current price of the bond?
The price of any bond is the PV of the interest payments (coupons), plus the PV of the par value. Notice this problem assumes an annual coupon. Annual coupon = €1000*5.8% = €58 Bond Value = PV of coupons + PV of par = C[1 - 1/(1 + r)t ]/ r + F / (1 + r)t P = €58({1 - 1/(1 + 0.0470)23} /0.0470) + €1,000[1 / (1 + .0470)23] = €804.94459 + €347.71732 = €1,152.66190 The current bond price is €1,152.66.
Is the yield to maturity on a bond the same thing as the required return? Is YTM the same thing as the coupon rate? Suppose today a 10 percent coupon bond sells at par. Two years from now, the required return on the same bond is 8 percent. What is the coupon rate on the bond then? The YTM?
The yield to maturity is the required rate of return on a bond expressed as a nominal annual interest rate. For noncallable bonds, the yield to maturity and required rate of return are interchangeable terms. Unlike YTM and required return, the coupon rate is not a return used as the interest rate in bond cash flow valuation, but is a fixed percentage of par over the life of the bond used to set the coupon payment amount. For the example given, the coupon rate on the bond is still 10 percent, and the YTM is 8 percent.
Grohl Co. issued 15-year bonds a year ago at a coupon rate of 4.10%. The bonds make semiannual payments and has a par value of $1,000. If the YTM on these bonds is 4.50%, what is the current bond price?
To find the price of this bond, we need to realize that the maturity of the bond is 14 years. The bond was issued one year ago, with 15 years to maturity, so there are 14 years left on the bond. Also, the coupons are semiannual, so we need to use the semiannual interest rate and the number of semiannual periods. Number of period = 14*2 = 28; Period rate = 4.50%/2 = 2.25%; annual coupon = $1000*0.041 = $41; PMT = $41/2= $20.50 P = C[1 - 1/(1 + r)t ]/ r + F / (1 + r)t = $20.50([1 - 1/(1 + 0.0225)28]/ 0.0225) + $1,000/(1+0.0225)28 = $422.46047 + $536.32388 = $958.78434 The current bond price is $958.78.
Example 1: What is the price of a bond with a face value of $1,000, a $100 coupon, 20 years to maturity and a 10.00% rate of return? Assume that this bond makes annual payments.
What is coupon rate? = $100/$1000 = 10.00% bond price ($1,000) = face value ($1,000) The bond is sold at par -- par bond r = kd (YTM,10%) = coupon rate (10%=$100/$1000)
Call provision
a provision in a bond contract that gives the issuer the right to redeem the bonds under specified terms prior to the normal maturity date a disadvantage to investors
Example 3: What is the price of a bond with a face value of $1,000, a $100 coupon, 20 years to maturity and 8.00% rate of return?
bond price ($1,196.36) > face value ($1,000) The bond is sold at premium -- premium bond r = kd (YTM, 8%) < coupon rate (10%) Interest rate ¯ Þ Bond price Why?
Example 2: What is the price of a bond with a face value of $1,000, a $100 coupon, 20 years to maturity and a 12.00% rate of return?
bond price ($850.61) < face value ($1,000) The bond is sold at discount -- discount bond r = kd (YTM,12%) > coupon rate (10%) Interest rate Þ Bond price ¯ Why?
Par value (face value)
is the amount repaid on the maturity date (usually $1,000)
coupon payment
is the annual interest payment. E.g. $60.00
Bond represents
long-term debt (> 1 year)
YTC (yield to call)
the rate of return earned on a bond when it is called before its maturity date
Interest Rate Risk
the risk of capital losses to which investors are exposed because of changing interest rates •Price Risk -Change in price due to changes in interest rates -Longer-term bonds have more price risk than short-term bonds (or vice versa) -Lower coupon rate bonds have more price risk than higher coupon rate bonds (or vice versa)
Convertible bond
•A bond which, at the election of the holder, can be swapped for a fixed number of shares of common stock at any time prior to the bond's maturity
Present Value of Cash Flows as Rates Change
•Bond Value = PV of coupons + PV of par = PV annuity + PV of lump sum •Remember, as interest rates increase present values decrease •So, as interest rates increase, bond prices decrease and vice versa
Bonds and Stocks: Similarities
•Both provide long-term funding for the organization •Both are future funds that an investor must consider •Both have future periodic payments •Both can be purchased in a marketplace at a price "today"
The Bond Indenture
•Contract (formal and legally binding agreement) between the company and the bondholders and includes -The basic terms of the bonds (coupon rate? Maturity date? YTM?) -The total amount of bonds issued -A description of property used as security, if applicable -Sinking fund provisions -Call provisions -Details of protective covenants
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 1000, 20 years to maturity, $1197.93 price -Current yield = 100 / 1197.93 = .0835 = 8.35% -Price in one year, assuming no change in YTM = 1193.68 -Capital gain yield = (1193.68 - 1197.93) / 1197.93 = -.0035 = -.35% -YTM = 8.35 - .35 = 8%, which the same YTM computed earlier
Differences Between Debt and Equity
•Debt -Not an ownership interest -Creditors do not have voting rights -Interest is considered a cost of doing business and is tax deductible -Creditors have legal recourse if interest or principal payments are missed -Excess debt can lead to financial distress and bankruptcy •Equity -Ownership interest -Common stockholders vote for the board of directors and other issues -Dividends are not considered a cost of doing business and are not tax deductible -Dividends are not a liability of the firm and stockholders have no legal recourse if dividends are not paid -An all equity firm can not go bankrupt
Bonds and Stocks: Differences
•From the firm's perspective: a bond is a long-term debt and stock is equity • •From the firm's perspective: a bond gets paid off on the maturity date; stock continues indefinitely.
Bond Ratings (reflecting default risk) Investment Quality
•High Grade -Moody's Aaa and S&P AAA - capacity to pay is extremely strong -Moody's Aa and S&P AA - capacity to pay is very strong •Medium Grade -Moody's A and S&P A - capacity to pay is strong, but more susceptible to changes in circumstances -Moody's Baa and S&P BBB - capacity to pay is adequate, adverse conditions will have more impact on the firm's ability to pay
Bond Prices: Relationship Between Yield and Coupon
•If YTM = coupon rate, then bond price = par value •If YTM > coupon rate, then bond price < par value -Why? -Selling at a discount, called a discount bond •If YTM < coupon rate, then bond price > par value -Why? -Selling at a premium, called a premium bond
Bond Ratings Speculative (junk bond, high yield, high risk)
•Low Grade -Moody's Ba, B, Caa and Ca -S&P BB, B, CCC, CC -Considered speculative with respect to capacity to pay. The "B" ratings are the lowest degree of speculation. •Very Low Grade -Moody's C and S&P C - income bonds with no interest being paid -Moody's D and S&P D - in default with principal and interest in arrears
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 •Sometimes called zeroes, deep discount bonds, or original issue discount bonds (OIDs) •Treasury Strips are good examples of zero-coupon securities
Bond Markets
•Primarily over-the-counter transactions with dealers connected electronically •Extremely large number of bond issues, but generally low daily volume in single issues •Makes getting up-to-date prices difficult, particularly on small company or municipal issues •Treasury securities are an exception
Treasury Quotations
•Quote -2024 Nov 15 137:29 137:31 -49 3.9133 -What is the coupon rate on the bond? -When does the bond mature? -What is the bid price? What does this mean? -What is the ask price? What does this mean? -How much did the price change from the previous day? -What is the yield based on the ask price?
Bond holder receives:
•Regular coupon payment every period until the bond matures •The face value at maturity.
Bond Characteristics and Required Returns
•The coupon rate depends on the risk characteristics of the bond when issued •Which bonds will have the higher required rate of return (YTM), all else equal? -Secured debt versus a debenture -Subordinated debenture versus senior debt -A bond with a sinking fund versus one without -A callable bond versus a non-callable bond
•When will a firm call its callable bonds?
•When the interest rate drops, the firm will refinance and issue new bonds at a lower interest rate.
Computing Yield-to-maturity
•Yield-to-maturity 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)
