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Purchase US Savings Bonds and Treasury Bonds at TreasuryDirect.gov
Bond Features, Types, and Yield Curves Chapter 6 Continued Purchase US Savings Bonds and Treasury Bonds at TreasuryDirect.gov EE Savings Bonds rate is .10% I Savings Bonds (inflation protected) no paper savings bonds as since 2012. Composite rate is = 2.58%. thru April 30, 2018 The History of Savings Bonds Buy T-bill, notes, and bonds on-line
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If you have a TreasuryDirect. gov account and use it to buy and hold U
If you have a TreasuryDirect.gov account and use it to buy and hold U.S. Treasury securities, the coupon interest payments will be made directly into your bank account. Or if you own these securities in a brokerage account, the coupon interest payments are made into your brokerage account. The U.S. Treasury no longer issues checks for interest payments.
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Bond Registration Registered The owner's name and contact information is recorded and kept on file with the company, allowing it to pay the bond's coupon payment to the appropriate person. Registered bonds are now tracked electronically, using computers to record owners' information. vs. Bearer Forms is unregistered, so no records are kept of the owner, or the transactions involving ownership.
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US Government Bonds Treasury Securities Municipal 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 Revenue Bonds for city pools, toll bridges, parking lots, etc. have greater risk than general obligation bonds as they are backed by revenues generated Varying degrees of default risk, rated similar to corporate debt Interest received is tax-exempt at the federal level
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Problem A taxable bond has a yield of 6% and a municipal bond has a yield of 4% If you are in a 40% tax bracket, which bond do you prefer? 6%(1 - .4) = 3.6% The after-tax return on the corporate bond is 3.6%, compared to a 4% return on the municipal At what tax rate would you be indifferent between the two bonds? 6%(1 – T) = 4% T = 33.33%
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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 Sometimes called zeroes, deep discount bonds, or original issue discount bonds (OIDs) Treasury Bills and principal-only Treasury strips are good examples of zeroes
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Floating-Rate Bonds Coupon rate floats depending on some index value
Examples: LIBOR + .5% or PRIME RATE + 1% Example – adjustable rate mortgages (ARMs) and inflation-linked Treasuries There is less price risk with floating rate bonds The coupon floats, so it is less likely to differ substantially from the yield-to-maturity Coupons may have a collar – the rate cannot go above a specified “ceiling” or below a specified “floor”
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Other Bond Types Income bonds – coupon payments depend on level of corporate income Convertible bonds – bonds can be converted into shares of common stock at the bondholders discretion Put bonds – bondholder can force the company to buy the bond back prior to maturity There are many other types of provisions that can be added to a bond and many bonds have several provisions These various provisions affect required returns
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Bond Markets Treasury securities are an exception
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
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Bond Data from FINRA Bond information is available online.
FINRA is the Financial Industry Regulatory Authority: Click the Finra site above. Use “Quick Bond Search” to observe the yields for various bond types, and the shape of the yield curve. Click Corporate, Click Symbol HOG or Issuer Name Harley. Click Issuer Name Abbvie
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Harley Davidson Bonds A3 A- 3.605 4.504 Symbol Name Coupon Maturity
Callable Moody's S&P Price Yield HOG163709 HARLEY DAVIDSON INC - 9/15/ 2017 no 99.564 HOG 3.50 7/28/ 2025 YES A3 A- 99.318 3.605 HOG 2.40 6/15/ 2020 98.875 HOG 4.625 2045 4.504
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Abbvie Corp Bonds Symbol Name Coupon Maturity Callable Moody's S&P
Fitch Price Yield ABBV403937 Abbie Inc 4.4 11/06/ 2042 yes Baa2 A- 4.385 ABBV 2.9 11/06/ 2022 97.958 3.372 ABBV 2.0 11/14/ 2018 99.850 2.214 ABBV 1.80 5/14/ 2018 99.990 1.835 ABBV 2.5 5/14/ 2020 99.215 2.865
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Treasury Quotes Fig 6.3 1. Look at the May 15, 2030 bond.
2. Notice that its price is well above par of 100. Why? 3. Notice the Asked Yield is 2.353%. 4. Why is 2.353% below the coupon rate of 6.25%?
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Clean versus Dirty Prices
Buying a bond after a payment date will cost MORE than the quoted price as it includes the accumulated interest. The quoted price is the Clean Price without accrued interest. The actual price is the Dirty Price with accrued interest. If 10 days since last payment, for a 1,000 bond, then the interest would be (10/184)*([.0625/2]*1,000) = $1.70 more than the clean price.
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Inflation and Interest Rates
Real rate of interest – change in purchasing power Nominal rate of interest – quoted rate of interest, change in purchasing power, and inflation The ex ante nominal rate of interest includes our desired real rate of return plus an adjustment for expected inflation
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The Fisher Effect The Fisher Effect defines the relationship between real rates, nominal rates, and inflation (1 + R) = (1 + r)(1 + h), where R = nominal rate r = real rate h = expected inflation rate Approximation R = r + h
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Example If we require a 10% real return and we expect inflation to be 8%, what is the nominal rate? R = (1.1)(1.08) – 1 = .188 = 18.8% Approximation: R = 10% + 8% = 18% Because the real return and expected inflation are relatively high, there is significant difference between the actual Fisher Effect and the approximation.
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US Interest Rates 216 year peak of 14.59% in January 1982.
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The Term Structure of Interest Rates
Term structure is the relationship between time to maturity and yields, all else equal It is important to recognize that we pull out the effect of default risk, different coupons, etc. Yield curve – graphical representation of the term structure Normal – upward-sloping, long-term yields are higher than short-term yields Inverted – downward-sloping, long-term yields are lower than short-term yields
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Figure 6.5 A – Upward-Sloping Yield Curve
REPLACE with FIGURE 6.5 A
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Figure 6.5 B – Downward-Sloping Yield Curve
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FIGURE 6.6 page 195 Dated March 13, 2015 Click United States
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Recessions and Inverted Yield Curves
From 1960 to the present, we’ve had 8 inverted yield curves, and 7 recessions following them. Animated yield curves over time 1982 to False signal was in
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3 Factors Affecting Bond Yields
Default risk premium – remember bond ratings Higher rated bonds have lower rates Taxability premium – remember municipal versus taxable Tax-free rates are lower Liquidity premium – bonds that have more frequent trading will generally have lower required returns Anything else that affects the risk of the cash flows to the bondholders will affect the required returns
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Last Problem What is the price of a $1,000 par value bond with a 6% coupon rate paid semiannually, if the bond is priced to yield 5% YTM, and it has 9 years to maturity? 5% YTM: 18 N; 2.5 I/Y; 30 PMT; 1,000 FV; CPT PV = ? What would be the price of the bond if the yield rose to 7%. 7% YTM: 18 N; 3.5 I/Y; 30 PMT; 1,000 FV; CPT PV = ? What is the current yield on the bond if the YTM is 7%? Current Yield = $60 / answer to #2 above PV = $1, Skip the negative sign, as that is just the “Sign Convention.” Also Note: Premium Bond since it pays 6% and other bonds pay just 5% YTM. PV = $ The bond is now a Discount Bond. A 7% YTM is higher than the mere 6% paid by this bond. 60 / = It pays 6.4% current yield.
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Equity Markets and Stock Valuation Chapter 7
Understand stock prices depend on future dividends and dividend growth Compute stock prices using the dividend growth model Understand election of corporate directors Understand how stock markets work Understand stock prices quotations
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Cash Flows for Stockholders
Purchasing stock gives you cash in two ways: The company pays dividends You eventually sell your shares, either to another investor in the market or back to the company. This involves receiving capital gains or losses. As with bonds, the price of the stock is the present value of these expected cash flows
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One-Period Example Suppose you are thinking of purchasing the stock of Moore Oil, Inc. and you expect it to pay a $2 dividend in one year and you believe that you can sell the stock for $14 at that time. If you require a return of 20% on investments of this risk, what is the maximum you would be willing to pay? Compute the PV of the expected cash flows FV = 16; I/Y = 20; N = 1; CPT PV = 2 + 14 {
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Two-Period Example Now what if you decide to hold the stock for two years? In addition to the dividend in one year, you expect a dividend of $2.10 in two years and a stock price of $14.70 at the end of year 2. Now how much would you be willing to pay? PV = 2 / (1.2) + ( ) / (1.2)2 = 13.33 If you have taught students how to use uneven cash flow keys, then you can show them how to do this on the calculator. The notation below is for the TI-BA-II+ Or CF0 = 0; C01 = 2; F01 = 1; C02 = 16.80; F02 = 1; NPV; I = 20; CPT NPV = 13.33
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Three-Period Example Finally, what if you decide to hold the stock for three years? In addition to the dividends at the end of years 1 and 2, you expect to receive a dividend of $2.205 at the end of year 3 and the stock price is expected to be $ Now how much would you be willing to pay? PV = 2 / / (1.2)2 + ( ) / (1.2)3 = 13.33 Notice: the price in each example stayed the same. Or CF0 = 0; C01 = 2; F01 = 1; C02 = 2.10; F02 = 1; C03 = 17.64; F03 = 1; NPV; I = 20; CPT NPV = 13.33
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Stock Value = PV of Dividends
^ (1+R) (1+R) (1+R) (1+R)∞ D D D D∞ + +…+ But how can we estimate all future dividend payments?
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Developing an Asset Pricing Model
You could continue to push back the year in which you will sell the stock You would find that the price of the stock is really just the present value of all expected future dividends So, how can we estimate all future dividend payments? (3 special cases)
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#1. Zero Dividend Growth Model
If dividends are expected at regular intervals forever, then this is a perpetuity and the present value of expected future dividends can be found using the perpetuity formula P0 = D / R (we can use either lower or upper case R) Constant dividend model has “g” of zero. The firm will pay a constant dividend forever This is like preferred stock The price is computed using the perpetuity formula
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Example Suppose stock is expected to pay a $0.50 dividend every quarter and the required return is 10% with quarterly compounding. What is the stock price? P0 = .50 / (.1 / 4) = .50 / = $20 If the required return rises , the stock price falls If the constant dividend jumps up , the stock price rises . If dividends are paid quarterly, then the discount rate must be a quarterly rate. Also, if students have been using a financial calculator for most of their calculations, they often forget to convert the interest rate and leave it as a percent, i.e., P = .5 / (10/4) = .2. Ask them if this is a reasonable answer – “Would you only be willing to pay $0.20 for an asset that will pay you $0.50 every quarter forever?”
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#2. The Dividend Growth Model DGM a. k. a
#2. The Dividend Growth Model DGM a.k.a. the Gordon Model or Dividend Discount Model Dividends are expected to grow at a constant percent per period, g. P0 = D1 /(1+R) + D2 /(1+R)2 + D3 /(1+R)3 + … P0 = D0(1+g)/(1+R) + D0(1+g)2/(1+R)2 + D0(1+g)3/(1+R)3 + … With a little algebra and some series work, this reduces to: g is the growth rate in dividends. The subscripts denote the period in which the dividend is paid.
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Example of a DGM the dividend growth model
Suppose The Frozen Penguin, Inc. just paid its annual dividend of $.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk, how much should the stock be selling for? P0 = .50(1+.02) / ( ) = $3.92 Students sometimes take the wrong dividend in the DGM. Use the that will be paid NEXT period, not the one that has already been paid.
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Second Example Suppose the Pirate Hedge Fund, Inc. is expected to pay a $2 dividend in one year. If the dividend is expected to grow at 5% per year and the required return is 20%, what is the price? P0 = 2 / ( ) = $13.33 Why isn’t the $2 in the numerator multiplied by (1.05) in this example? Does this result look familiar? The examples used to develop the model were based on a 5% growth rate in dividends.
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Stock Price Sensitivity to Dividend Growth, g
D1 = $2; R = 20%; so P = $2/(.20 – g) As the growth rate approaches the required return, the stock price increases dramatically.
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Stock Price Sensitivity to Required Return, R
D1 = $2; g = 5%; so P = $2/(R - .05) As the required return approaches the growth rate, the price increases dramatically. Required Return
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Gordon Growth Company Originator of the DGM is Prof. Myron Gordon, U of Toronto 1920 – Sept 2010. Gordon Growth Company is expected to pay a dividend of $4 next period and dividends are expected to grow at 6% per year. The required return is 16%. What is the current price? P0 = $4 / ( ) = $40 Remember that we already have the dividend expected next year, so we don’t multiply the dividend by 1+g
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What is the price expected to be in year 4?
P4 = D4(1 + g) / (R – g) = D5 / (R – g) P4 = 4(1+.06)4 / ( ) = 50.50 What is the implied return given the change in price during the four year period? 50.50 = 40(1+return)4; return = 6% PV = -40; FV = 50.50; N = 4; CPT I/Y = 6% The price grows at the same rate as the dividends ! We know the dividend in one year is expected to be $4 and it will grow at 6% per year for four more years. So, D5 = 4(1.06)(1.06)(1.06)(1.06) = 4(1.06)4
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#3 Stocks with Nonconstant Growth
Also known as a Supernormal growth model. Suppose a firm is expected to increase dividends by 20% in one year and by 15% in the second year. After that dividends will increase at a rate of 5% per year indefinitely. If the last dividend was $1 and the required return is 20%, what is the price of the stock? Remember that we have to find the PV of all expected future dividends.
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Nonconstant Growth – Solution
Compute the dividends until growth levels off D1 = 1(1.2) = $1.20 D2 = 1.20(1.15) = $1.38 D3 = 1.38(1.05) = $1.449 Find the expected future stock price P2 = D3 / (R – g) = / ( ) = 9.66 Find the present value of the expected future cash flows P0 = 1.20 / (1.2) + ( ) / (1.2)2 = 8.67 P2 is the value, at year 2, of all expected dividends year 3 on. The final step is exactly the same as the 2-period example at the beginning of the chapter. We can look at it as if we buy the stock today and receive the $1.20 dividend in 1 year, receive the $1.38 dividend in 2 years and then immediately sell it for $9.66. Calculator: CF0 = 0; C01 = 1.20; F01 = 1; C02 = 11.04; F02 = 1; NPV; I = 20; CPT NPV = 8.67
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Two Quick Quiz Questions
What is the value of a stock that is expected to pay a constant dividend of $2 per year if the required return is 15%? What if the company starts increasing dividends by 3% per year, beginning with the next dividend? The required return stays at 15%. 1. Zero growth is: 2 / .15 = 13.33 2. Constant growth is: 2(1.03) / ( ) = $17.17 1. Zero growth – 2 / .15 = 13.33 2. Constant growth is: 2(1.03) / ( ) = $17.17
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