Managerial Finance
Jdr
PPT_Chapter_06.pptx
Copyright © 2015 by The McGraw-Hill Companies, Inc. All rights reserved
Chapter 6
Valuing Bonds
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Topics Covered
6.1 The Bond Market
6.2 Interest Rates and Bond Prices
6.3 Yield to Maturity
6.4 Bond Rates of Returns
6.5 The Yield Curve
6.6 Corporate Bonds and the Risk of Default
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3
2
2
2
2
2
Bonds
Terminology
Bond - Security that obligates the issuer to make specified payments to the bondholder
Face Value (Par Value or Principal Value) - Payment at the maturity of the bond
Coupon - The interest payments made to the bondholder
Coupon Rate - Annual interest payment, as a percentage of face value
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3
Bonds
WARNING
The coupon rate IS NOT the discount rate used in the Present Value calculations
The coupon rate merely tells us what cash flow the bond will produce
Since the coupon rate is listed as a %, this misconception is quite common
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5
Bond Pricing
The price of a bond is the present value of all cash flows generated by the bond (i.e. coupons and face value) discounted at the required rate of return
cpn is commonly used as an abbreviation for coupon
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7
Bond Cash Flows
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Bond Pricing
Example
What is the price of a 7.25 % annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume a required return of 0.35%.
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9
Bond Pricing
Example (continued)
What is the price of a 7.25 % annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume a required return of 0.35%.
Bond prices are quoted as a percentage of par
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9
Financial Calculators
Notice how the keys map with the bond terminology
* These keys MUST reference the same time period (i.e. annual, semi-annual, quarterly, monthly, etc. )
The financial calculator functions used for the time value of money can be used for bond calculations as well
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51
n
PMT
FV
i
PV
Maturity
*
$cpn
*
$Par
YTM
*
$Price
Financial Calculators
To get the final answer, push PV and you will get -$1,205.56
Ignore the minus sign and that is the answer
Example (same as before)
What is the price of a 7.25 % annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume a required return of 0.35%.
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51
3
72.50
1,000
.35
PV
n
PMT
FV
i
PV
Bond Pricing
Example (continued)
Q: How did the calculation change, given semi-annual coupons versus annual coupon payments?
Twice as many payments, cut in half, over the same time period.
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14
$$$$
$$$$
$$$$
$$$$
$$
$$
$$
$$
$$
$$
$$
$$
Bond Cash Flows
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Bond Pricing
Example (continued)
What is the price of the bond if the required rate of return is 0.175% AND the coupons are paid semi-annually?
Price % = 120.57%
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13
Financial Calculators
To get the final answer, push PV and you will get -$1,205.74 Ignore the minus sign and that is the answer
Example (same as before)
What is the price of the bond if the required rate of return is 0.175% AND the coupons are paid semi-annually?
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51
6
36.25
1,000
.175
PV
n
PMT
FV
i
PV
Treasury Yields
The interest rate on 10-year U.S. Treasury bonds, 1900-2012
2012
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1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Source: http://www.econ.yale.edu/~shiller/data.htm 3.15 3.1 3.18 3.3 3.4 3.48 3.43 3.67 3.87 3.76 3.91 3.98 4.01 4.45 4.16 4.24 4.05 4.2300000000000004 4.57 4.5 4.97 5.09 4.3 4.3600000000000003 4.0599999999999996 3.86 3.68 3.34 3.33 3.6 3.29 3.34 3.68 3.31 3.12 2.79 2.65 2.68 2.56 2.36 2.21 1.95 2.46 2.4700000000000002 2.48 2.37 2.19 2.25 2.44 2.31 2.3199999999999998 2.57 2.68 2.83 2.48 2.61 2.9 3.46 3.09 4.0199999999999996 4.72 3.84 4.08 3.83 4.17 4.1900000000000004 4.6100000000000003 4.58 5.53 6.04 7.79 6.24 5.95 6.46 6.99 7.5 7.74 7.21 7.96 9.1 10.8 12.57 14.59 10.46 11.67 11.38 9.19 7.08 8.67 9.09 8.2100000000000009 8.09 7.03 6.6 5.75 7.78 5.65 6.58 5.54 4.72 6.66 5.16 5.04 4.05 4.1500000000000004 4.22 4.42 4.76 3.74 2.52 3.73 3.39 1.97
Yield (%)
Bond Pricing
Example (continued)
What is the price of the bond if the required rate of return is 7.25%?
Price % = 100%
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11
Bond Pricing
Example (continued)
What is the price of the bond if the required rate of return is 10%?
Price % = 93.16%
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11
Bond Pricing
Example (continued)
Q: How did the calculation change, given semi-annual coupons versus annual coupon payments?
Time Periods
Paying coupons twice a year, instead of once doubles the total number of cash flows to be discounted in the PV formula.
Discount Rate
Since the time periods are now half years, the discount rate is also changed from the annual rate to the half year rate.
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Interest Rate Risk
The value of the 7.25% bond falls as interest rates rise
Bond price ($)
Interest rate (%)
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0 0.5 1 1.5 2 2.5 3.0000000000000004 3.5000000000000004 4 4.5 5 5.4999999999999991 5.9999999999999991 6.4999999999999991 6.9999999999999991 7.5 8 8.5 9.0000000000000018 9.5000000000000018 10.000000000000002 10.500000000000002 11.000000000000004 11.500000000000004 12.000000000000004 12.500000000000004 13.000000000000004 13.500000000000004 14.000000000000004 1217.5 1200.4917493175694 1183.8115754522223 1167.4515239927387 1151.4038718140082 1135.6611192524776 1120.215982583024 1105.0613867842621 1090.1904585798816 1075.5965197442224 1061.2730806608356 1047.2138341233294 1033.4126493682702 1019.8635663304256 1006.5607901110409 993.49868565032023 980.67177259564073 968.07472035746014 955.70234334520683 943.54959637582249 931.61157024793363 919.88348747496389 908.36069817077828 897.03867608176222 885.913014759475 874.97942386831278 864.23372562282657 853.67185134960573 843.28983816882908
Interest Rate Risk
Bond price ($)
Interest rate (%) = YTM
30-year bond
3-year bond
Different maturity bonds have different interest rate risk
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0 0.5 1 1.5 2 2.5 3.0000000000000004 3.5000000000000004 4 4.5 5 5.4999999999999991 5.9999999999999991 6.4999999999999991 6.9999999999999991 7.5 8 8.5 9.0000000000000018 9.5000000000000018 10.000000000000002 10.500000000000002 11.000000000000004 11.500000000000004 12.000000000000004 12.500000000000004 13.000000000000004 13.500000000000004 14.000000000000004 1217.5 1200.4917493175694 1183.8115754522223 1167.4515239927387 1151.4038718140082 1135.6611192524776 1120.215982583024 1105.0613867842621 1090.1904585798816 1075.5965197442224 1061.2730806608356 1047.2138341233294 1033.4126493682702 1019.8635663304256 1006.5607901110409 993.49868565032023 980.67177259564073 968.07472035746014 955.70234334520683 943.54959637582249 931.61157024793363 919.88348747496389 908.36069817077828 897.03867608176222 885.913014759475 874.97942386831278 864.23372562282657 853.67185134960573 843.28983816882908 3175 2876.0986426444479 2612.9817638304758 2380.9106853584499 2175.8139164277309 1994.1888981561556 1833.0187573524652 1689.7017029261044 1561.991082271596 1447.9444349679425 1345.8801481048638 1254.3405404946361 1172.0603893936179 1097.9400692950217 1031.0226029587648 970.47403433604472 915.56662492654391 865.66445228107716 820.21105424711948 778.71881715768041 740.75985215782111 705.95814264131673 673.98277849502017 644.54212049083094 617.37876153580009 592.26517126812814 568.99992723845867 547.40445011780196 527.32017242464553
Bond Yields
Current Yield - Annual coupon payments divided by bond price
Yield To Maturity - Interest rate for which the present value of the bond’s payments equals the price
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Bond Yields
Calculating Yield to Maturity (YTM = r)
If you are given the price of a bond (PV) and the coupon rate, the yield to maturity can be found by solving for r
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19
Bond Yields
Example
What is the YTM of a 10.0% annual coupon bond, with a $1,000 face value, which matures in 3 years? The market price of the bond is $1,136.16.
r = YTM = 8.80%
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21
Financial Calculators
To get the final answer, push i and you will get 5.00%
NOTE: You must enter the price as a negative or your calculator when generate an error
Example (same as before)
What is the YTM of a 10.0 % annual coupon bond, with a $1,000 face value, which matures in 3 years? The market price of the bond is $1,136.16.
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51
3
100
1,000
i
-1,136.16
n
PMT
FV
i
PV
Bond Yields
Example (continued)
What is the current yield of a 10.0 % annual coupon bond, with a $1,000 face value, which matures in 3 years? The market price of the bond is $1,136.16.
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21
Bond Yields
WARNING
Calculating YTM by hand can be very tedious
It is highly recommended that you learn to use the “IRR,” “YTM,” or “i” functions on a financial calculator
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22
Bond Rates of Return
Rate of Return – Total income per period per dollar invested
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Bond Rates of Return
Example
A bond increases in price from $963.80 to $1,380.50 and pays a coupon of $21.875 during the same period. What is the rate of return?
ROR = 45.5%
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Bond Valuation Spreadsheet
Esc and Double click on spreadsheet to access
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Interest Rate Risk
Price path for Premium Bond
Price path for Discount Bond
Today
Maturity
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Bond Yield Spreadsheet
Esc and Double click on spreadsheet to access
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The Yield Curve
Term Structure of Interest Rates - A listing of bond maturity dates and the interest rates that correspond with each date
Yield Curve - Plot of relationship between bond yields to maturity and time to maturity
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The Yield Curve
Treasury strips are bonds that make a single payment. The yields on Treasury strips in May 2013 show that investors received a higher yield on longer term bonds.
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1st Qtr 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 0.14000000000000001 0.22 0.56000000000000005 0.76 0.98 1.23 1.49 1.72 1.91 2.1 2.2599999999999998 2.42 2.54 2.65 2.73 2.8 2.87 2.93 2.97 3.01 3.05 3.09 3.12 3.15 3.17 3.2 3.22 3.24Maturity (years)
Yield %
Interest Rates & Inflation
In the presence of inflation, an investor’s real interest rate is always less than the nominal interest rate
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Interest Rates & Inflation
If you invest in a security that pays 8% interest annually and inflation is 4%, what is your real interest rate?
Real interest rate = .0385 or 3.85%
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Interest Rates & Inflation
Treasury Inflation Protected Securities (TIPS)
Example:
If you invest in 5% coupon, 3 year TIPS and inflation is 3% each year, what are your real annual cash flows?
| Year | 1 | 2 | 3 |
| Real cash flows | $50 | $50 | $1,050 |
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TIPS: U.S. Treasury issued debt with fixed real flows, but with nominal cash flows (interest and principal) that are increased as the consumer price index increases.
Note: What are the nominal cash flows for the example above?
36
Nominal and Real rates
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30712 30741 30772 30802 30833 30863 30894 30925 30955 30986 31016 31047 31078 31106 31137 31167 31198 31228 31259 31290 31320 31351 31381 31412 31443 31471 31502 31532 31563 31593 31624 31655 31685 31716 31746 31777 31808 31836 31867 31897 31928 31958 31989 32020 32050 32081 32111 32142 32173 32202 32233 32263 32294 32324 32355 32386 32416 32447 32477 32508 32539 32567 32598 32628 32659 32689 32720 32751 32781 32812 32842 32873 32904 32932 32963 32993 33024 33054 33085 33116 33146 33177 33207 33238 33269 33297 33328 33358 33389 33419 33450 33481 33511 33542 33572 33603 33634 33663 33694 33724 33755 33785 33816 33847 33877 33908 33938 33969 34000 34028 34059 34089 34120 34150 34181 34212 34242 34273 34303 34334 34365 34393 34424 34454 34485 34515 34546 34577 34607 34638 34668 34699 34730 34758 34789 34819 34850 34880 34911 34942 34972 35003 35033 35064 35095 35124 35155 35185 35216 35246 35277 35308 35338 35369 35399 35430 35461 35489 35520 35550 35581 35611 35642 35673 35703 35734 35764 35795 35826 35854 35885 35915 35946 35976 36007 36038 36068 36099 36129 36160 36191 36219 36250 36280 36311 36341 36372 36403 36433 36464 36494 36525 36556 36585 36616 36646 36677 36707 36738 36769 36799 36830 36860 36891 36922 36950 36981 37011 37042 37072 37103 37134 37164 37195 37225 37256 37287 37315 37346 37376 37407 37437 37468 37499 37529 37560 37590 37621 37652 37680 37711 37741 37772 37802 37833 37864 37894 37925 37955 37986 38017 38046 38077 38107 38138 38168 38199 38230 38260 38291 38321 38352 38383 38411 38442 38472 38503 38533 38564 38595 38625 38656 38686 38717 38748 38776 38807 38837 38868 38898 38929 38960 38990 39021 39051 39082 39113 39141 39172 39202 39233 39263 39294 39325 39355 39386 39416 39447 39478 39507 39538 39568 39599 39629 39660 39691 39721 39752 39782 39813 39844 39872 39903 39933 39964 39994 40025 40056 40086 40117 40147 40178 40209 40237 40268 40298 40329 40359 40390 40421 40451 40482 40512 40543 40574 40602 40633 40663 40694 40724 40755 40786 40816 40847 40877 40908 40939 40968 40999 41029 41060 41090 41121 41152 41182 41213 41243 41274 41305 41333 41364 41394 3.05 3.16 3.14 3.17 3.4 3.46 3.69 3.48 3.43 3.09 3.13 3.13 3.17 3 3.19 3.28 3.39 3.42 3.37 3.33 3.37 3.48 3.52 3.65 3.71 3.57 3.64 3.17 3.22 3.34 3.41 3.32 3.59 3.66 3.64 3.71 3.58 3.3 3.29 3.45 3.51 3.7 3.69 3.84 4 4.2300000000000004 3.75 3.9 3.91 3.79 3.77 3.76 3.84 3.9 3.84 3.89 3.89 3.57 3.68 3.76 3.61 3.5 3.5 3.58 3.72 3.68 3.5 3.47 3.6 3.57 3.69 3.58 3.73 3.89 4.0599999999999996 4.2300000000000004 4.13 4.0999999999999996 4.1900000000000004 4.24 4.28 4.3099999999999996 4.16 4.16 4.1399999999999997 4.1500000000000004 4.1500000000000004 4.1399999999999997 4.2300000000000004 4.3499999999999996 4.38 4.3099999999999996 4.22 4.24 4.3 4.4400000000000004 4.29 4.3099999999999996 4.58 4.4800000000000004 4.28 4.32 4.53 4.6500000000000004 4.12 3.74 3.94 3.87 3.8 3.59 3.51 3.68 3.65 3.59 3.46 3.29 3.21 3.2 3.13 2.92 3 3.32 3.46 3.54 3.89 3.97 4 3.77 3.87 3.9 3.87 3.88 3.89 3.9 3.87 3.8 3.59 3.8 3.69 3.6 3.72 3.71 3.56 3.56 3.63 3.81 3.81 3.75 3.9 3.86 3.82 3.78 3.64 3.65 3.5 3.58 3.59 3.47 3.62 3.6 3.69 3.63 3.52 3.54 3.32 3.08 3.07 3.01 3.04 2.98 2.83 2.89 2.74 2.71 2.64 2.4700000000000002 2.54 2.52 2.3199999999999998 2.0299999999999998 1.98 1.98 1.87 1.97 1.97 2.0099999999999998 2.06 2.27 2.2599999999999998 2.16 2 1.96 2.19 2.04 1.99 2 2.08 1.96 2.13 2.17 2.1800000000000002 2.2000000000000002 2.06 2.09 2.0499999999999998 2.13 2.34 2.61 2.5499999999999998 2.4900000000000002 2.48 2.33 2.5 2.2599999999999998 2.37 2.54 2.41 2.38 2.39 2.42 2.38 2.2599999999999998 2.48 2.21 2.2000000000000002 2.2799999999999998 2.4 2.16 2.0299999999999998 1.91 1.97 2 1.81 1.84 2.04 2.0499999999999998 1.93 2.2400000000000002 2.2400000000000002 1.96 2.0299999999999998 1.89 1.81 1.98 2.0699999999999998 2.0499999999999998 2.12 1.94 1.88 1.85 1.79 1.71 1.76 1.85 1.82 1.74 1.69 1.54 1.65 1.46 1.52 1.52 1.46 1.32 1.28 1.35 1.46 1.65 1.63 1.76 1.6 1.45 1.55 1.49 1.49 1.72 1.98 1.74 1.93 2.02 2.27 2.37 2.19 1.98 1.91 1.85 1.55 1.52 1.43 1.27 0.91 1.38 1.62 1.44 1.71 1.17 1.46 2.66 3.46 1.81 1.45 1.1499999999999999 1.66 1.08 0.99 1.1200000000000001 1.28 0.88 0.79 0.59 0.49 0.69 0.54 0.34 0.19 0.11 0.26 0.03 0.14549999999999999 -0.30940000000000001 -0.2737 -0.3468 -0.18509999999999999 -0.1542 -0.1203 -0.26629999999999998 -0.19420000000000001 -0.36159999999999998 -0.60540000000000005 -0.71909999999999996 -1.2992999999999999 -1.2185999999999999 -1.3245 -1.3773 -1.3122 -1.4679 -1.5687 -1.8386 -1.7801 -1.6412 -1.9184000000000001 -1.6155999999999999 -1.8351 -2.0848 -1.8474999999999999 -1.7927 -1.8835999999999999 -1.8369 -2.1644000000000001 -2.65 -2.7892000000000001 -2.5114999999999998 30712 30741 30772 30802 30833 30863 30894 30925 30955 30986 31016 31047 31078 31106 31137 31167 31198 31228 31259 31290 31320 31351 31381 31412 31443 31471 31502 31532 31563 31593 31624 31655 31685 31716 31746 31777 31808 31836 31867 31897 31928 31958 31989 32020 32050 32081 32111 32142 32173 32202 32233 32263 32294 32324 32355 32386 32416 32447 32477 32508 32539 32567 32598 32628 32659 32689 32720 32751 32781 32812 32842 32873 32904 32932 32963 32993 33024 33054 33085 33116 33146 33177 33207 33238 33269 33297 33328 33358 33389 33419 33450 33481 33511 33542 33572 33603 33634 33663 33694 33724 33755 33785 33816 33847 33877 33908 33938 33969 34000 34028 34059 34089 34120 34150 34181 34212 34242 34273 34303 34334 34365 34393 34424 34454 34485 34515 34546 34577 34607 34638 34668 34699 34730 34758 34789 34819 34850 34880 34911 34942 34972 35003 35033 35064 35095 35124 35155 35185 35216 35246 35277 35308 35338 35369 35399 35430 35461 35489 35520 35550 35581 35611 35642 35673 35703 35734 35764 35795 35826 35854 35885 35915 35946 35976 36007 36038 36068 36099 36129 36160 36191 36219 36250 36280 36311 36341 36372 36403 36433 36464 36494 36525 36556 36585 36616 36646 36677 36707 36738 36769 36799 36830 36860 36891 36922 36950 36981 37011 37042 37072 37103 37134 37164 37195 37225 37256 37287 37315 37346 37376 37407 37437 37468 37499 37529 37560 37590 37621 37652 37680 37711 37741 37772 37802 37833 37864 37894 37925 37955 37986 38017 38046 38077 38107 38138 38168 38199 38230 38260 38291 38321 38352 38383 38411 38442 38472 38503 38533 38564 38595 38625 38656 38686 38717 38748 38776 38807 38837 38868 38898 38929 38960 38990 39021 39051 39082 39113 39141 39172 39202 39233 39263 39294 39325 39355 39386 39416 39447 39478 39507 39538 39568 39599 39629 39660 39691 39721 39752 39782 39813 39844 39872 39903 39933 39964 39994 40025 40056 40086 40117 40147 40178 40209 40237 40268 40298 40329 40359 40390 40421 40451 40482 40512 40543 40574 40602 40633 40663 40694 40724 40755 40786 40816 40847 40877 40908 40939 40968 40999 41029 41060 41090 41121 41152 41182 41213 41243 41274 41305 41333 41364 41394 10.84 10.81 10.65 11.01 11.69 11.7 12.24 11.3 11.03 10.97 10.75 11.07 11.44 11.43 11.09 11.08 11.11 11.05 10.67 10.66 10.55 10.57 10.62 10.83 11.12 10.27 9.14 8.89 9.33 9.5500000000000007 9.6999999999999993 9.59 10.86 10.92 11.1 10.57 10.24 9.68 9.18 8.8800000000000008 8.7100000000000009 9.1999999999999993 9.86 10.37 10.26 9.460 0000000000009 9.31 9.61 9.3699999999999992 9.26 9.09 9.3699999999999992 9.4499999999999993 9.8000000000000007 9.7899999999999991 10.220000000000001 9.8800000000000008 9.61 10.16 10.11 9.73 9.9600000000000009 10 10.09 10.45 10.41 9.8800000000000008 10.02 10.46 10.43 10.71 10.41 11.11 11.63 12.52 13.18 12.18 11.65 11.77 12.01 12.14 11.5 10.92 11.04 10.26 10.220000000000001 10.14 10.3 10.48 10.56 10.18 9.9600000000000009 9.58 9.69 9.8699999999999992 9.73 9.39 9.26 9.9 9.16 8.89 9.11 9.3000000000000007 9.68 8.9600000000000009 8.08 8.5500000000000007 8.17 8.06 7.79 7.8 8.18 8.2100000000000009 7.7 7.42 6.82 6.96 6.92 6.66 6.24 6.36 7.04 7.65 7.99 8.67 8.8000000000000007 8.65 8.61 8.89 8.8000000000000007 8.5 8.75 8.6199999999999992 8.69 8.5500000000000007 8.49 7.96 8.49 8.23 8.1 8.15 7.96 7.58 7.44 7.51 8.01 8.1 8 8.0500000000000007 8.15 7.9 7.91 7.91 7.68 7.66 7.37 7.54 7.43 7.27 7.66 7.48 7.23 7.13 7 7.11 6.48 6.57 6.52 6.32 6.08 6.12 5.92 5.85 5.72 5.84 5.76 5.33 4.9000000000000004 5.07 4.68 4.38 4.1900000000000004 4.63 4.59 4.71 5 5.21 5.49 5.32 5.79 5.56 5.35 5.49 5.82 5.53 5.34 5.27 5.23 5.23 5.29 5. 4 5.27 5.22 4.91 4.8899999999999997 4.7699999999999996 4.8 4.8 5.14 5.24 5.33 5.09 4.9400000000000004 4.96 4.58 4.6900000000000004 5.09 4.88 4.9800000000000004 5.31 5.21 5.28 5.03 4.9400000000000004 4.66 4.42 4.6100000000000003 4.71 4.41 4.29 4.21 4.34 4.4000000000000004 4.1500000000000004 4.25 4.5999999999999996 4.67 4.5999999999999996 5.05 5.08 4.8 4.8899999999999997 4.7699999999999996 4.76 5 5.17 5.12 5.12 4.9400000000000004 4.84 4.74 4.5999999999999996 4.53 4.58 4.71 4.6900000000000004 4.5199999999999996 4.32 4.18 4.33 4.16 4.29 4.33 4.22 4.0999999999999996 4.1399999999999997 4.18 4.4000000000000004 4.6399999999999997 4.5999999999999996 4.72 4.62 4.5199999999999996 4.53 4.51 4.5 4.7300000000000004 4.96 4.78 4.96 5.04 5.25 5.48 5.23 5.03 5.0199999999999996 4.9400000000000004 4.68 4.5599999999999996 4.51 4.54 4.41 4.75 5.05 5.23 4.8899999999999997 4.5599999999999996 4.519999999 9999996 4.6500000000000004 3.97 3.35 3.96 3.69 3.23 3.53 3.7 3.63 3.82 3.54 3.61 3.67 3.6 4.07 3.99 4.07 4.0199999999999996 3.96 3.65 3.45 3.4405999999999999 2.9196 3.0388999999999999 3.1783000000000001 3.3262999999999998 3.4914000000000001 3.7494999999999998 3.7616999999999998 3.7715000000000001 3.5880999999999998 3.4407000000000001 3.5232999999999999 3.0539000000000001 2.8022999999999998 2.4352999999999998 2.4828999999999999 2.3532999999999999 2.0423 2.0339 2.1819999999999999 2.25 2.1825000000000001 1.6272 1.8133999999999999 1.5634999999999999 1.5874999999999999 1.6485000000000001 1.825 1.7466999999999999 1.8273999999999999 2.2376 2.1520999999999999 1.8331999999999999 1.7403999999999999Yield (%)
Default Risk
Default or Credit Risk - The risk that a bond issuer may default on its bonds
Default premium - The additional yield on a bond that investors require for bearing credit risk
Investment grade - Bonds rated Baa or above by Moody’s or BBB or above by Standard & Poor’s
Junk bonds - Bond with a rating below Baa or BBB
6- ‹#›
Default Risk
| Moody' s | Standard & Poor's | Safety |
| Aaa | AAA | The strongest rating; ability to repay interest and principal is very strong |
| Aa | AA | Very strong likelihood that interest and principal will be repaid |
| A | A | Strong ability to repay, but some vulnerability to changes in circumstances |
| Baa | BBB | Adequate capacity to repay; more vulnerability to changes in economic circumstances |
| Ba | BB | Considerable uncertainty about ability to repay |
| B | B | Likelihood of interest and principal payments over sustained periods is questionable |
| Caa | CCC | Bonds in the Caa/CCC and Ca/CC classes may already be in default or in danger of imminent default |
| Ca | CC | |
| C | C | C-rated bonds offer little prospect for interest or principal on the debt ever to be repaid |
6- ‹#›
Default Risk
Annual cost (CDS spread) of insuring eurozone government debt
6- ‹#›
Default Risk
Yield spreads between corporate Baa and Aaa bonds
6- ‹#›
Corporate Bonds
Zero coupons
Floating rate bonds
Convertible bonds
6- ‹#›
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Valuing bonds using a spreadsheet
7.25 % coupon7.25 % semi-annual coupon
maturing May 2016maturing May 2016
Settlement date5/15/135/15/13
Maturity date5/15/165/15/16
Annual coupon rate0.07250.0725
Yield to maturity0.00350.0035
Redemption value (% of face value)100100
Coupon payments per year12
Bond price (% of par)120.556 120.574
=PRICE(B7,B8,B9,B10,B11,B12)
Sheet1
| Valuing bonds using a spreadsheet | |||
| 7.25 % coupon | 7.25 % semi-annual coupon | ||
| maturing May 2016 | maturing May 2016 | ||
| Settlement date | 5/15/13 | 5/15/13 | |
| Maturity date | 5/15/16 | 5/15/16 | |
| Annual coupon rate | 0.0725 | 0.0725 | |
| Yield to maturity | 0.0035 | 0.0035 | |
| Redemption value (% of face value) | 100 | 100 | |
| Coupon payments per year | 1 | 2 | |
| Bond price (% of par) | 120.556 | 120.574 | |
| =PRICE(B7,B8,B9,B10,B11,B12) |
Sheet2
Sheet3
600 700 800 900 1,000 1,100 1,200 1,300 1,400302520151050Bond PriceTime to Maturity
Chart1
| 30 | 30 |
| 29 | 29 |
| 28 | 28 |
| 27 | 27 |
| 26 | 26 |
| 25 | 25 |
| 24 | 24 |
| 23 | 23 |
| 22 | 22 |
| 21 | 21 |
| 20 | 20 |
| 19 | 19 |
| 18 | 18 |
| 17 | 17 |
| 16 | 16 |
| 15 | 15 |
| 14 | 14 |
| 13 | 13 |
| 12 | 12 |
| 11 | 11 |
| 10 | 10 |
| 9 | 9 |
| 8 | 8 |
| 7 | 7 |
| 6 | 6 |
| 5 | 5 |
| 4 | 4 |
| 3 | 3 |
| 2 | 2 |
| 1 | 1 |
| 0 | 0 |
Sheet1
| PV(rate,nper,pmt,fv,type) | |||||
| FV(rate,nper,pmt,pv,type) | |||||
| time | yield | hi yireld | |||
| 1,344 | 662 | 30 | 0.032 | 0.08 | 30 |
| 1,337 | 665 | 29 | 0.032 | 0.08 | 29 |
| 1,330 | 668 | 28 | 0.032 | 0.08 | 28 |
| 1,322 | 672 | 27 | 0.032 | 0.08 | 27 |
| 1,315 | 676 | 26 | 0.032 | 0.08 | 26 |
| 1,307 | 680 | 25 | 0.032 | 0.08 | 25 |
| 1,298 | 684 | 24 | 0.032 | 0.08 | 24 |
| 1,290 | 689 | 23 | 0.032 | 0.08 | 23 |
| 1,281 | 694 | 22 | 0.032 | 0.08 | 22 |
| 1,272 | 699 | 21 | 0.032 | 0.08 | 21 |
| 1,263 | 705 | 20 | 0.032 | 0.08 | 20 |
| 1,253 | 712 | 19 | 0.032 | 0.08 | 19 |
| 1,243 | 719 | 18 | 0.032 | 0.08 | 18 |
| 1,233 | 726 | 17 | 0.032 | 0.08 | 17 |
| 1,223 | 734 | 16 | 0.032 | 0.08 | 16 |
| 1,212 | 743 | 15 | 0.032 | 0.08 | 15 |
| 1,201 | 753 | 14 | 0.032 | 0.08 | 14 |
| 1,189 | 763 | 13 | 0.032 | 0.08 | 13 |
| 1,177 | 774 | 12 | 0.032 | 0.08 | 12 |
| 1,165 | 786 | 11 | 0.032 | 0.08 | 11 |
| 1,152 | 799 | 10 | 0.032 | 0.08 | 10 |
| 1,139 | 813 | 9 | 0.032 | 0.08 | 9 |
| 1,125 | 828 | 8 | 0.032 | 0.08 | 8 |
| 1,111 | 844 | 7 | 0.032 | 0.08 | 7 |
| 1,097 | 861 | 6 | 0.032 | 0.08 | 6 |
| 1,082 | 880 | 5 | 0.032 | 0.08 | 5 |
| 1,067 | 901 | 4 | 0.032 | 0.08 | 4 |
| 1,051 | 923 | 3 | 0.032 | 0.08 | 3 |
| 1,034 | 947 | 2 | 0.032 | 0.08 | 2 |
| 1,017 | 972 | 1 | 0.032 | 0.08 | 1 |
| 1,000 | 1,000 | 0 | 0.032 | 0.08 | 0 |
Sheet2
Sheet3
Annual couponsSemiannual coupons
Settlement date5/15/135/15/13
Maturity date5/15/165/15/16
Annual coupon rate0.07250.0725
Bond price120.556120.556
Redemption value (% of face value)100100
Coupon payments per year12
Yield to maturity (decimal)0.0350 0.0355
=YIELD(B3,B4,B5,B6,B7,B8)
Sheet1
| Annual coupons | Semiannual coupons | ||
| Settlement date | 5/15/13 | 5/15/13 | |
| Maturity date | 5/15/16 | 5/15/16 | |
| Annual coupon rate | 0.0725 | 0.0725 | |
| Bond price | 120.556 | 120.556 | |
| Redemption value (% of face value) | 100 | 100 | |
| Coupon payments per year | 1 | 2 | |
| Yield to maturity (decimal) | 0.0350 | 0.0355 | |
| =YIELD(B3,B4,B5,B6,B7,B8) |
