Please see attachments. Thank you
>Chapter 4
/
11/1
0 Chapter 5. Tool Kit for
Bonds, Bond Valuation, and Interest Rates The value of any financial asset is the present value of the asset’s e
xpected future cash flows. The key inputs are
(1)the expected cash flows and
(2)the appropriate discount rate, given the bond’s risk, maturity, and other characteristics. The model developed here analyzes bonds in various ways.
BO
ND V
ALUATION (Section
5.
3)
A bond has a 15-year maturity, a
1 0%annual coupon, and a
$1,000par value. The required rate of return (or the yield to maturity) on the bond is
10%
, given its risk, maturity, liquidity, and other rates in the economy. What is a fair value for the bond, i.e., its market price? First, we list the key features of the bond as “model inputs”: Years
to Mat:
15
Coupon rate
: 10% Annual Pmt: $
100 Par value =FV:
$1,000
Required return, rd:
10%
The easiest way to solve this problem is to use Excel’s PV function. Click fx, then financial, then PV. Then fill in
the menu items as shown in our snapshot in the screen shown just below.
Value of bond =
$1,00
s on Actual Dates Thus far we have evaluated bonds assuming that we are at the beginning of an interest payment period. This is correct for new issues, but it is generally not correct for outstanding bonds. However, Excel has several date and time functions, and a bond valuation function that uses the calendar, so we can get exact valuations on any given date. Here is the data for MicroDrive’s bond as of the day it was issued. Settlement date (day on which you find bond price) = 1/5/
11 Maturitydate = 1/5/2
6 Coupon rate = 1 0.00% Required return, rd = 10.00% Redemption (100 means the bond pays 100% of its face value at maturity) = 100
Frequency (# payments per year) =
1
Ba
sis (1 is for actual number of days in month and year)
1
Click on fx on the formula bar (or click Insert and then Function). This gives you the “Insert Function” dialog box. To find a bond’s price, use the PRICE function (found in the “Financial” category of the “Insert Function dialog box). The PRICE function returns the price per
dollars of face value. Using PRICE function with inputs that are cell references: Value of bond based on $100 face value = $100.00 Value of bond in dollars based on $1,000 face value = $1,000.00 Using the PRICE function with inputs that are not cell references: Value of bond based on $100 face value =
=PRICE( DATE(
2011,1,5),DATE(2026,1,5),10%,10%,100,1,1) Value of bond based on $100 face value =
100.000Value of bond in dollars based on $1,000 face value = $1,000.00
Interest Rate Changes and Bond Prices Suppose the going interest rate changed from 10%, falling to 5%or rising to
15%. How would those changes affect the value of the bond? We could simply go to the input data section shown above, change the value for r from 10% to 5% and then 15%, and observe the changed values. An alternative is to set up a data table to show the bond’s value at a range of rates, i.e., to show the bond’s sensitivity to changes in interest rates. This is done below, and the values at 5% and 15% are boldfaced. Bond Value To make the data table, first type the headings, then type the rates in cells A
8 9:A93, and then put the formula =B41 in cell B88, then select the range A88:B93. Then click Data, What-IF-Analysis, and then Table to get the menu. The input data are in a column, so put the cursor on column and enter C20 the place where the going rate is inputted. Click OK to complete the operation and get the table. Going rate, r
:
$1,000
0%
0.00 5%
$1,5 18.98
10% $1,000.00
15%
07.63 20% $532.45 We can use the data table to construct a graph that shows the bond’s sensitivity to changing rates.
CHANGES IN BOND VALUES OVER TIME (Section
5.4
)
What happens to a bond price over time? To set up this problem, we will enter the different interest rates, and use the array of cash flows above. The following example operates under the precept that the bond is issued at par ($1,000) in year 0. From this point, the example sets three conditions for interest rates to follow: interest rates stay constant at 10%, interest rates fall to 5%, or interest rates rise to 15%. Then the price of the bond over the fifteen years of its life is determined for each of the scenarios. Suppose interest rates rose to 15% or fell to 5% immediately after the bond was issued, and they remained at the new level for the next 1 5 years
. What would happen to the price of the bond over time?
We could set up data tables to get the data for this problem, but instead we simply inserted the PV formula into the following matrix to calculate the value of the bond over time. Note that the formula takes the interest rate from the column heads, and the value of N from the left column. Note that the N = 0 values for the 5% and 15% rates are consistent with the results in the data table above. We can also plot the data, as shown in the graph below.
Value of Bond in Given Year:
N 5% 10% 15%
0
$1,000
$708 1 $1,495$1,000
$7 14 2 $1,470$1,000
$721 3 $1,443$1,000
$7 29 4 $1,415$1,000
$738 5 $1,386$1,000
$749 6 $1,355$1,000
$761 7 $1,323$1,000
$776 8 $1,289$1,000
$792 9 $1, 254
$1,000
$811 10 $1,2 16$1,000
$832 11 $1, 177
$1,000
$857 12 $1, 136
$1,000
$886 13 $1,093$1,000
$919 14 $1,048$1,000
$957 15 $1,000 $1,000 $1,000If rates fall, the bond goes to a premium, but it moves toward par as maturity approaches. The reverse hold if rates rise and the bond sells at a discount. If the going rate remains equal to the coupon rate, the bond will continue to sell at par. Note that the above graph assumes that interest rates stay constant after the initial change. That is most unlikely–interest rates fluctuate, and so do the prices of outstanding bonds. Market rate =
5%
N Bond Price
1 $1,494.93 6.5 8% – 1.58
% 5.00% 2
$1,469.68 6.6 9% – 1.69%
5.00%
3
0% –
1.80%
5.00%
4
5.00%
5
%
5.00%
6
%
5.00%
7
%
5.00%
8
%
5.00%
9
8 7.76% -2.76%
5.00%
10
7 7.98% –
2.98%
5.00%
11
2%
5.00%
12
5.00%
13
5.00%
14
5.00%
15 $1,000.00
5.00%
Market rate = 10%
N Bond Price Return Due to Coupon Payment Return Due to Price Change Total Return
0 $1,0001 $1,000 10.00% -0.00%
10.00%
2 $1,000 10.00% -0.00% 10.00%
3 $1,000 10.00% 0.00% 10.00%
4 $1,000 10.00% -0.00% 10.00%
5 $1,000 10.00% 0.00% 10.00%
6 $1,000 10.00% -0.00% 10.00%
7 $1,000 10.00% 0.00% 10.00%
8 $1,000 10.00% 0.00% 10.00%
9 $1,000 10.00% 0.00% 10.00%
10 $1,000 10.00% 0.00% 10.00%
11 $1,000 10.00% -0.00% 10.00%
12 $1,000 10.00% 0.00% 10.00%
13 $1,000 10.00% 0.00% 10.00%
14 $1,000 10.00% -0.00% 10.00%
15 $1,000 10.00% 0.00% 10.00%
Market rate = 15%
N Bond Price Return Due to Coupon Payment Return Due to Price Change Total Return
0 $707.63 1 $7 13.78 14.
13% 0.87% 15.00% 2
$72 0.84 14.01% 0.99%
15.00%
3
%
15.00%
4
%
15.00%
5
6%
15.00%
6
%
15.00%
7 $77
5.6
3
13.13% 1.87%
15.00%
8 $79 1.98 1 2.89% 2.11
%
15.00%
9
3% 2.37%
15.00%
10
% 2.67%
15.00%
11
% 2.99%
15.00%
12
% 3.33%
15.00%
13
1 1
1.29% 3.71%
15.00%
14
8% 4.
12% 15.00%
15 $1,000.00
4.55% 15.00%
BONDS WITH SEMIANNUAL COUPONS (Section
5.5
)
Since most bonds pay interest semiannually, we now look at the valuation of semiannual bonds. We must make three modifications to our original valuation model: (1) divide the coupon payment by 2, (2) multiply the years to maturity by 2, and (3)divide the nominal interest rate by 2. Problem: What is the price of a 15-year, 10% semi-annual coupon, $1,000 par value bond if the nominal rate (the
YTM) is 5%? The bond is not callable.
Use the Rate function with adjusted data to solve the problem.
Periods to maturity = 15*2 =
30
Christopher Buzzard: N=30, because of semi-annual compounding (15*2 = 30).
Coupon rate: 10%
Semiannual pmt = $100/2 = $50.00Bart Kreps: PMT=$50, because of semiannual payments
(100 ÷ 2) = 50 PV = $1,52 3.26 Current price
:
$1,000.00
Periodic rate = 5%/2 =
2.5%
Christopher Buzzard: I=2.5%, because of semi-annual compounding (5%/2 = 2.5%). Note that the bond is now more valuable, because interest payments come in faster. BOND YIELDS (Section 5.6) Yield
to Maturity
The YTM is defined as the rate of return that will be earned if a bond makes all scheduled payments and is held to maturity. The YTM is the same as the total rate of return discussed in the chapter, and it can also be interpreted as the “promised rate of return,” or the return to investors if all promised payments are made. The YTM for a bond that sells at par consists entirely of an interest yield. However, if the bond sells at any price other than its par value, the YTM consists of the interest yield together with a positive or negative capital gains yield. The YTM can be determined by solving the bond value formula for I. However, an easier method for finding it is to use Excel’s Rate function. Since the price of a bond is simply the sum of the present values of its cash flows, so we can use the time value of money techniques to solve these problems.
Problem: Suppose that you are offered a 14-year, 10% annual coupon, $1,000 par value bond at a price of $1,494.93. What is the Yield to Maturity of the bond?
Use the Rate function to solve the problem.
Years to Mat: 14
Coupon rate: 10%
Annual Pmt: $100.00 Going rate, r =YTM:
5.00%
Current price: $1,494.93
Par value = FV
: $1,000.00
The yield-to-maturity is the same as the expected rate of return only if (1) the probability of default is zero, and (2) the bond can not be called. If there is any chance of default, then there is a chance some payments may not be made. In this case, the expected rate of return will be less than the promised yield-to-maturity.
Finding the Yield to Maturity on Actual Dates
Thus far we have evaluated bonds assuming that we are at the beginning of an interest payment period. This is correct for new issues, but it is generally not correct for outstanding bonds. However, Excel has a function that uses the actual calendar when finding yields. Consider the bond above, with 1
s until maturity. Suppose the actual current date is 1/5/2012, so the bond matures on 1/5/2026. Here is the data for the bond. Settlement date (day on which you find bond price) =
01/05/12 Maturity date = 01/05/26Coupon rate = 10.00%
Price = bond price per $100 par value = $149.49 Redemption (100 means the bond pays 100% of its face value at maturity) = 100
Frequency (# payments per year) = 1
Basis (1 is for actual number of days in month and year) 1
) is found similarly to the YTM. The same formula is used, but years to maturity is replaced with years to call, and the maturity value is replaced with the call price. Problem: Suppose you purchase a 15-year, 10% annual coupon, $1,000 par value bond with a call provision after
10 years at a call price of $1,100. One year later, interest rates have fallen from 10% to 5% causing the value of the bond to rise to $1,494.93. What is the bond’s YTC? Note that this is the same bond as in the previous question, but now we assume it can be called.
Use the Rate function to solve the problem.
Years to call: 9Christopher Buzzard: N is equal to 9, because the bond can be called 10 years after issuance and one year has already gone by.
Coupon rate: 10%
Annual Pmt: $100.00 Rate = I = YTC = 4.21%Current price: $1,494.93
Call price = FV
$1,100.00
Par value $1,000.00
This bond’s YTM is 5%, but its YTC is only 4.21%. Which would an investor be more likely to actually earn?
This company could call the old bonds, which pay $100 per year, and replace them with bonds that pay somewhere in the vicinity of $50 (or maybe even only $42.10) per year. It would want to save that money, so it would in all likelihood call the bonds. In that case, investors would earn the YTC, so the YTC is the expected return on the bonds.
Current Yield
The current yield is the annual interest payment divided by the bond’s current price. The current yield provides information regarding the amount of cash income that a bond will generate in a given year. However, it does not account for any capital gains or losses that will be realized fi the bond is held to maturity or call.
Problem: What is the current yield on a $1,000 par value, 10% annual coupon bond that is currently selling for
$985?
Simply divide the annual interest payment by the price of the bond. Even if the bond made semiannual payments, we would still use the annual interest.
Par value $1,000.00
Coupon rate: 10% Current Yield = 1 0.15%
Annual Pmt: $100.00
Current price:
NTS OF MARKET INTEREST RATES (Section 5.7) Quoted market interest rate = rd =
r*+ IP + DRP + LP + MRP r* = Real risk-free rate of interest IP = Inflation premium DRP = Default risk premium LP = Liquidity premium MRP = Maturity risk premium THE REAL RISK-FREE RATE OF INTEREST, r* (Section 5.8) r* =
Real risk-free rate of interest
r* =
) r* =
1.54% (March 2009)THE INFLATION PREMIUM (IP) (Section
5.9
)
Maturity5 Years 20 Years Non-indexed U.S. Treasury Bond 1.91
% 3.93% TIPS
1.41% 2.44
% Inflation premium
0.50% 1.49% THE NOMINAL, OR QUOTED, RISK-FREE RATE OF INTEREST, rRF (Section 5.10) Nominal, or quoted, rate = rd = rRF + DRP + LP + MRP
THE DEFAULT RISK PREMIUM (DRP) (Section
5.11
)
Table 5-1 Rating Agencya Percent defaulting within:b Median Ratiosc Percent upgraded or downgraded in 2008:b S&P and Fitch Moody’s 1 year5 years
Return on capital Total debt/Total capital Down Up Yieldd (1) (2) (3) (4) (5) (6) (7) (8) (9) Investment grade bonds: AAA Aa
a
0.00 0.00
27.60 1
2.40 13.60NA
5.50 AA Aa 0 0.1 27 28.3 21.80
5.62 A A 0.1 0.6 17.5 37.58 1.8
5.79 BBB Baa 0.3
2.9
13.4 42.56.4 2.6
7.53 Junk bonds: BB Ba 1.4 8.2 11.353.7
15.16.8
11.62 B B 1.8 9.28.7
75.9 10.8 5.6 13.7
CCC
Caa
22.3
36.9
3.2
113.5 26.18.7
26.3 Notes: aThe ratings agencies also use “modifiers” for bonds rated below triple-A. S&P and Fitch use a plus and minus system; thus, A+ designates the strongest A-rated bonds and A– the weakest. Moody’s uses a 1, 2, or 3 designation, with 1 denoting the strongest and 3 the weakest; thus, within the double-A category, Aa1 is the best, Aa2 is average, and Aa3 is the weakest. bDefault data are from Fitch Ratings Global Corporate Finance 2008 Transition and Default Study, March 5, 2009: see http://www.fitchratings.com/corporate/reports/report_frame.cfm?rpt_id=428182. cMedian ratios are from Standard & Poor’s 2006 Corporate Ratings Criteria, April 23, 2007: see http://www2.standardandpoors.com/spf/pdf/fixedincome/Corporate_Ratings_2006 . dComposite yields for AAA, AA, and A bonds can be found at http://finance.yahoo.com/bonds/composite_bond_rates. Representative yields for BBB, BB, B, and CCC bonds can be found using the bond screener at http://screen.yahoo.com/bonds. .html. Bond spreads are the difference between the yield on a bond and the yield on some other bond of the same maturity. For a bond with good liquidity, its spread relative to a T-bond of similar maturity is a good estmat of the default risk premium. Figure 5-3: Bond Spreads Data for chart to right DATE AAA – T-bond BAA – T-bond 2009-022.40
5.21 2009-01 2.53 5.62
2008-12
2.63
6.01
2008-11
2.59
5.68
2008-10
2.47
5.07
2008-09
1.96
3.62
2008-08
1.75
3.26
2008-07
1.66
3.15
2008-06
1.58 2.97
2008-05
1.69
3.05 2008-041.87
3.29 2008-03 2.00 3.38 2008-02 1.79 3.08 2008-01 1.59 2.80 2007-12 1.39 2.55 2007-111.29
2.25 2007-101.13
1.95 2007-09 1.22 2.07
2007-08
1.12
1.98
2007-07
0.73
1.65
2007-06
0.69
1.60
2007-05
0.72
1.64
2007-04
0.78
1.70 2007-03 0.74 1.71 2007-02 0.67 1.56 2007-01 0.64 1.58
2006-12
0.76
1.66
2006-11
0.73 1.60
2006-10
0.78 1.69
2006-09
0.79
1.71
2006-08
0.80
1.71
2006-07
0.76 1.67
2006-06
0.78 1.67
THE LIQUIDITY PREMIUM (LP) (Section 5.12)
2006-05
0.84 1.64
2006-04
0.85
1.69
A differential of at least 2 percentage points (and perhaps up to 4 or 5 percentage points) exists between the least liquid and the most liquid financial assets of similar default risk and maturity.
2006-03
0.81
1.69
2006-02
0.78 1.70
2006-01
0.87
1.82 2005-12 0.90 1.85THE MATURITY RISK PREMIUM (MRP) (Section
5.13
)
2005-11 0.881.85
2005-10 0.89 1.84 Bonds are exposed to interest rate risk and reinvestment rate risk. The net effect is the maturity risk premium. 2005-09 0.93 1.83 2005-08 0.83 1.70
Interest Rate Risk
2005-07
0.88
1.77 2005-06 0.96 1.86 Interest Rate Risk is the risk of a decline in a bond’s price due to an increase in interest rates. Price sensitivity to interest rates is greater (1) the longer the maturity and (2) the smaller the coupon payment. Thus, if two bonds have the same coupon, the bond with the longer maturity will have more interest rate sensitivity, and if two bonds have the same maturity, the one with the smaller coupon payment will have more interest rate sensitivity. 2005-05 1.01 1.87
2005-04
0.99 1.71
2005-03
0.90 1.56
2005-02
1.03
1.65
2005-01
1.14
1.80
Compare the interest rate risk of two bonds, both of which have a 10% annual coupon and a $1,000 face value. The first bond matures in 1 year, the second in 25 years.
2004-12
1.24
1.92
2004-11
1.33
2.01
2004-10
1.37
2.11
Use the PV function, along with a two variable Data Table, to show the bonds’ price sensitivity.
2004-09
1.33
2.14 Coupon rate: 10% 2004-081.37
2.18 Payment $100.00 2004-07 1.32 2.12 Par value $1,000.00 2004-061.28
2.05 Maturity 1 2004-051.32
2.03 Going rate = r = YTM10%
2004-04 1.38 2.11
2004-03
1.50
2.28
Value of bond:
$1,000.00
2004-021.42
2.19 2004-011.39
2.29 2003-12 1.35 2.33
Value of the Bond Under Different Conditions
2003-11
1.35
2.36Going rate, r
Years to Maturity
2003-101.41 2.44
$1,000.00 1 25 2003-09 1.45 2.52 0% $1,100.00 $3,500.00 2003-08 1.43 2.56
5% $1,047.62
1.64
2.86 15% $956.52 $676.79 2003-051.65
2.81 20% $916.67 $505.24 2003-04 1.78 2.89
25%
$880.00
$40
2.27
2003-03
2.08
3.14
2003-02
2.05 3.16
Figure 5-4
2003-01
2.12
3.30 2002-122.18
3.42 2002-11 2.26 3.57 2002-102.38
3.79 2002-092.28
3.53 2002-082.11
3.32 2002-07 1.88 3.25 2002-061.70
3.02 2002-051.59
2.93 2002-04 1.55 2.82 2002-03 1.53 2.83 2002-021.60
2.98 2002-01 1.51 2.83
2001-12
1.68
2.96
2001-11
2.32
3.16
2001-10
2.46
3.34
2001-09
2.44 3.30
2001-08
2.05
2.88 2001-07 1.89 2.73 2001-06 1.90 2.69 2001-051.90
2.68 2001-04 2.06 2.93
2001-03
2.09
2.95
2001-02
2.00
2.77 2001-01 1.99 2.77
2000-12
1.97
2.78
2000-11
1.73
2.56
2000-10
1.81
2.60
THE TERM STRUCTURE OF INTEREST RATES (Section 5.14)
2000-09
1.82 2.55
2000-08
1.72
2.43
The term structure describes the relationship between long-term and short-term interest rates. Graphically, this relationship can be shown in what is known as the yield curve. In practice, the yield curve is relatively easy to obtain. It is published daily in the Wall Street Journal and can be accessed through the internet, via www. bloomberg.com. However, the “building block approach” to generating a yield curve is more complicated. We will see that later when we build our own yield curve.
2000-07
1.60
2.30 2000-06 1.57 2.38
2000-05
1.55 2.46
2000-04
1.65
2.41 2000-03 1.42 2.11
2000-02
1.16
1.77
Before jumping into the creation of our own yield curve, let’s look at some historical interest rate data and draw some historical yield curves.
2000-01
1.12 1.67
1999-12
1.27
1.91
1999-11
1.33 2.12
Maturity (yrs)
Mar-80
Feb-00
Mar-09
1999-10
1.44
2.27
0.5
2.28
1
2.21
5
6.7%
2.7% 1999-06 1.33 2.12
30
1.39 2.18
1999-04
1.46 2.30
From this data, we can plot three line graphs. Each line graph represents the U.S. Treasury yield curve at a
1999-03
1.39 2.30
different point in time.
1999-02
1.40 2.39
1999-01
1.52
2.57
Figure 5-5. U.S. Treasury Bond Interest Rates on Different Dates
Interest Rate Sensitivity
0.0 0.05 0.1 0.15 0.2 2500.0 1518.98290190903 1000.0 707.6314950684456 532.4527357594372
Price of Bond Over Time
Rate Drops to 5% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1518.98290190903 1494.932047004481 1469.678649354705 1443.16258182244 1415.320710913562 1386.086746459241 1355.391083782203 1323.160637971313 1289.318669869878 1253.784603363372 1216.473833531541 1177.297525208118 1136.162401468524 1092.97052154195 1047.619047619047 1000.0 Rate Stays at 10% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1000.0 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 999.9999999999999 1000.0 Rate Rises to 15% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 707.6314950684456 713.7762193287123 720.8426522280192 728.969050062222 738.3144075715553 749.0615687072888 761.420804013382 775.6339246153892 791.9790133076975 810.775865303852 832.3922450994299 857.2510818643444 885.8387441439962 918.7145557655954 956.5217391304349 1000.0
Mar-80 0.5 1.0 5.0 10.0 30.0 0.15 0.14 0.135 0.128 0.123 Feb-00 0.5 1.0 5.0 10.0 30.0 0.004 0.006 0.0169 0.0268 0.0369 Feb-05 0.5 1.0 5.0 10.0 30.0 0.0598 0.0619 0.0674 0.0668 0.0631
Years to Maturity
Interest Rate
(%)
1-Year 0.05 0.1 0.15 0.2 0.25 1047.619047619047 999.9999999999999 956.5217391304349 916.6666666666667 880.0 25-Year 0.05 0.1 0.15 0.2 0.25 1704.697228302238 999.9999999999999 676.792545736493 505.241298005198 402.2667359117775
Interest Rate, rd
Bond Value
($)
39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 2.4 2.53 2.63 2.59 2.47 1.96 1.75 1.66 1.58 1.69 1.87 2.0 1.79 1.59 1.39 1.29 1.13 1.22 1.12 0.73 0.69 0.72 0.779999999999999 0.74 0.67 0.64 0.760000000000001 0.73 0.779999999999999 0.79 0.8 0.76 0.779999999999999 0.84 0.85 0.81 0.779999999999999 0.87 0.9 0.88 0.89 0.93 0.83 0.88 0.96 1.01 0.99 0.9 1.03 1.14 1.24 1.33 1.37 1.33 1.37 1.32 1.28 1.32 1.38 1.5 1.42 1.39 1.35 1.35 1.41 1.45 1.43 1.51 1.64 1.65 1.78 2.08 2.05 2.12 2.18 2.26 2.38 2.28 2.11 1.88 1.7 1.59 1.55 1.53 1.6 1.51 1.68 2.32 2.46 2.44 2.05 1.89 1.9 1.9 2.06 2.09 2.0 1.99 1.97 1.73 1.81 1.82 1.72 1.6 1.57 1.55 1.65 1.42 1.16 1.12 1.27 1.33 1.44 1.47 1.46 1.4 1.33 1.39 1.46 1.39 1.4 1.52 39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 5.21 5.62 6.01 5.68 5.07 3.62 3.26 3.15 2.97 3.05 3.29 3.38 3.08 2.8 2.55 2.25 1.95 2.07 1.98 1.65 1.6 1.64 1.7 1.71 1.56 1.58 1.66 1.6 1.69 1.71 1.71 1.67 1.67 1.64 1.69 1.69 1.7 1.82 1.85 1.85 1.84 1.83 1.7 1.77 1.86 1.87 1.71 1.56 1.65 1.8 1.92 2.01 2.11 2.14 2.18 2.12 2.05 2.03 2.11 2.28 2.19 2.29 2.33 2.36 2.44 2.52 2.56 2.64 2.86 2.81 2.89 3.14 3.16 3.3 3.42 3.57 3.79 3.53 3.32 3.25 3.02 2.93 2.82 2.83 2.98 2.83 2.96 3.16 3.34 3.3 2.88 2.73 2.69 2.68 2.93 2.95 2.77 2.77 2.78 2.56 2.6 2.55 2.43 2.3 2.38 2.46 2.41 2.11 1.77 1.67 1.91 2.12 2.27 2.28 2.21 2.16 2.12 2.18 2.3 2.3 2.39 2.57
Spread
(%)
Interest Rate Sensitivity
0.0 0.05 0.1 0.15 0.2 2500.0 1518.98290190903 1000.0 707.6314950684456 532.4527357594372
Price of Bond Over Time
Rate Drops to 5% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1518.98290190903 1494.932047004481 1469.678649354705 1443.16258182244 1415.320710913562 1386.086746459241 1355.391083782203 1323.160637971313 1289.318669869878 1253.784603363372 1216.473833531541 1177.297525208118 1136.162401468524 1092.97052154195 1047.619047619047 1000.0 Rate Stays at 10% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1000.0 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 999.9999999999999 1000.0 Rate Rises to 15% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 707.6314950684456 713.7762193287123 720.8426522280192 728.969050062222 738.3144075715553 749.0615687072888 761.420804013382 775.6339246153892 791.9790133076975 810.775865303852 832.3922450994299 857.2510818643444 885.8387441439962 918.7145557655954 956.5217391304349 1000.0
Mar-80 0.5 1.0 5.0 10.0 30.0 0.15 0.14 0.135 0.128 0.123 Feb-00 0.5 1.0 5.0 10.0 30.0 0.004 0.006 0.0169 0.0268 0.0369 Feb-05 0.5 1.0 5.0 10.0 30.0 0.0598 0.0619 0.0674 0.0668 0.0631 Years to Maturity
Interest Rate
(%)
1-Year 0.05 0.1 0.15 0.2 0.25 1047.619047619047 999.9999999999999 956.5217391304349 916.6666666666667 880.0 25-Year 0.05 0.1 0.15 0.2 0.25 1704.697228302238 999.9999999999999 676.792545736493 505.241298005198 402.2667359117775 Interest Rate, rd
Bond Value
($)
39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 2.4 2.53 2.63 2.59 2.47 1.96 1.75 1.66 1.58 1.69 1.87 2.0 1.79 1.59 1.39 1.29 1.13 1.22 1.12 0.73 0.69 0.72 0.779999999999999 0.74 0.67 0.64 0.760000000000001 0.73 0.779999999999999 0.79 0.8 0.76 0.779999999999999 0.84 0.85 0.81 0.779999999999999 0.87 0.9 0.88 0.89 0.93 0.83 0.88 0.96 1.01 0.99 0.9 1.03 1.14 1.24 1.33 1.37 1.33 1.37 1.32 1.28 1.32 1.38 1.5 1.42 1.39 1.35 1.35 1.41 1.45 1.43 1.51 1.64 1.65 1.78 2.08 2.05 2.12 2.18 2.26 2.38 2.28 2.11 1.88 1.7 1.59 1.55 1.53 1.6 1.51 1.68 2.32 2.46 2.44 2.05 1.89 1.9 1.9 2.06 2.09 2.0 1.99 1.97 1.73 1.81 1.82 1.72 1.6 1.57 1.55 1.65 1.42 1.16 1.12 1.27 1.33 1.44 1.47 1.46 1.4 1.33 1.39 1.46 1.39 1.4 1.52 39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 5.21 5.62 6.01 5.68 5.07 3.62 3.26 3.15 2.97 3.05 3.29 3.38 3.08 2.8 2.55 2.25 1.95 2.07 1.98 1.65 1.6 1.64 1.7 1.71 1.56 1.58 1.66 1.6 1.69 1.71 1.71 1.67 1.67 1.64 1.69 1.69 1.7 1.82 1.85 1.85 1.84 1.83 1.7 1.77 1.86 1.87 1.71 1.56 1.65 1.8 1.92 2.01 2.11 2.14 2.18 2.12 2.05 2.03 2.11 2.28 2.19 2.29 2.33 2.36 2.44 2.52 2.56 2.64 2.86 2.81 2.89 3.14 3.16 3.3 3.42 3.57 3.79 3.53 3.32 3.25 3.02 2.93 2.82 2.83 2.98 2.83 2.96 3.16 3.34 3.3 2.88 2.73 2.69 2.68 2.93 2.95 2.77 2.77 2.78 2.56 2.6 2.55 2.43 2.3 2.38 2.46 2.41 2.11 1.77 1.67 1.91 2.12 2.27 2.28 2.21 2.16 2.12 2.18 2.3 2.3 2.39 2.57
Spread
(%)
Interest Rate Sensitivity
0.0 0.05 0.1 0.15 0.2 2500.0 1518.98290190903 1000.0 707.6314950684456 532.4527357594372
Price of Bond Over Time
Rate Drops to 5% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1518.98290190903 1494.932047004481 1469.678649354705 1443.16258182244 1415.320710913562 1386.086746459241 1355.391083782203 1323.160637971313 1289.318669869878 1253.784603363372 1216.473833531541 1177.297525208118 1136.162401468524 1092.97052154195 1047.619047619047 1000.0 Rate Stays at 10% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1000.0 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 999.9999999999999 1000.0 Rate Rises to 15% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 707.6314950684456 713.7762193287123 720.8426522280192 728.969050062222 738.3144075715553 749.0615687072888 761.420804013382 775.6339246153892 791.9790133076975 810.775865303852 832.3922450994299 857.2510818643444 885.8387441439962 918.7145557655954 956.5217391304349 1000.0
Mar-80 0.5 1.0 5.0 10.0 30.0 0.15 0.14 0.135 0.128 0.123 Feb-00 0.5 1.0 5.0 10.0 30.0 0.004 0.006 0.0169 0.0268 0.0369 Feb-05 0.5 1.0 5.0 10.0 30.0 0.0598 0.0619 0.0674 0.0668 0.0631 Years to Maturity
Interest Rate
(%)
1-Year 0.05 0.1 0.15 0.2 0.25 1047.619047619047 999.9999999999999 956.5217391304349 916.6666666666667 880.0 25-Year 0.05 0.1 0.15 0.2 0.25 1704.697228302238 999.9999999999999 676.792545736493 505.241298005198 402.2667359117775 Interest Rate, rd
Bond Value
($)
39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 2.4 2.53 2.63 2.59 2.47 1.96 1.75 1.66 1.58 1.69 1.87 2.0 1.79 1.59 1.39 1.29 1.13 1.22 1.12 0.73 0.69 0.72 0.779999999999999 0.74 0.67 0.64 0.760000000000001 0.73 0.779999999999999 0.79 0.8 0.76 0.779999999999999 0.84 0.85 0.81 0.779999999999999 0.87 0.9 0.88 0.89 0.93 0.83 0.88 0.96 1.01 0.99 0.9 1.03 1.14 1.24 1.33 1.37 1.33 1.37 1.32 1.28 1.32 1.38 1.5 1.42 1.39 1.35 1.35 1.41 1.45 1.43 1.51 1.64 1.65 1.78 2.08 2.05 2.12 2.18 2.26 2.38 2.28 2.11 1.88 1.7 1.59 1.55 1.53 1.6 1.51 1.68 2.32 2.46 2.44 2.05 1.89 1.9 1.9 2.06 2.09 2.0 1.99 1.97 1.73 1.81 1.82 1.72 1.6 1.57 1.55 1.65 1.42 1.16 1.12 1.27 1.33 1.44 1.47 1.46 1.4 1.33 1.39 1.46 1.39 1.4 1.52 39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 5.21 5.62 6.01 5.68 5.07 3.62 3.26 3.15 2.97 3.05 3.29 3.38 3.08 2.8 2.55 2.25 1.95 2.07 1.98 1.65 1.6 1.64 1.7 1.71 1.56 1.58 1.66 1.6 1.69 1.71 1.71 1.67 1.67 1.64 1.69 1.69 1.7 1.82 1.85 1.85 1.84 1.83 1.7 1.77 1.86 1.87 1.71 1.56 1.65 1.8 1.92 2.01 2.11 2.14 2.18 2.12 2.05 2.03 2.11 2.28 2.19 2.29 2.33 2.36 2.44 2.52 2.56 2.64 2.86 2.81 2.89 3.14 3.16 3.3 3.42 3.57 3.79 3.53 3.32 3.25 3.02 2.93 2.82 2.83 2.98 2.83 2.96 3.16 3.34 3.3 2.88 2.73 2.69 2.68 2.93 2.95 2.77 2.77 2.78 2.56 2.6 2.55 2.43 2.3 2.38 2.46 2.41 2.11 1.77 1.67 1.91 2.12 2.27 2.28 2.21 2.16 2.12 2.18 2.3 2.3 2.39 2.57
Spread
(%)
Interest Rate Sensitivity
0.0 0.05 0.1 0.15 0.2 2500.0 1518.98290190903 1000.0 707.6314950684456 532.4527357594372
Price of Bond Over Time
Rate Drops to 5% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1518.98290190903 1494.932047004481 1469.678649354705 1443.16258182244 1415.320710913562 1386.086746459241 1355.391083782203 1323.160637971313 1289.318669869878 1253.784603363372 1216.473833531541 1177.297525208118 1136.162401468524 1092.97052154195 1047.619047619047 1000.0 Rate Stays at 10% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1000.0 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 999.9999999999999 1000.0 Rate Rises to 15% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 707.6314950684456 713.7762193287123 720.8426522280192 728.969050062222 738.3144075715553 749.0615687072888 761.420804013382 775.6339246153892 791.9790133076975 810.775865303852 832.3922450994299 857.2510818643444 885.8387441439962 918.7145557655954 956.5217391304349 1000.0
Mar-80 0.5 1.0 5.0 10.0 30.0 0.15 0.14 0.135 0.128 0.123 Feb-00 0.5 1.0 5.0 10.0 30.0 0.004 0.006 0.0169 0.0268 0.0369 Feb-05 0.5 1.0 5.0 10.0 30.0 0.0598 0.0619 0.0674 0.0668 0.0631 Years to Maturity
Interest Rate
(%)
1-Year 0.05 0.1 0.15 0.2 0.25 1047.619047619047 999.9999999999999 956.5217391304349 916.6666666666667 880.0 25-Year 0.05 0.1 0.15 0.2 0.25 1704.697228302238 999.9999999999999 676.792545736493 505.241298005198 402.2667359117775 Interest Rate, rd
Bond Value
($)
39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 2.4 2.53 2.63 2.59 2.47 1.96 1.75 1.66 1.58 1.69 1.87 2.0 1.79 1.59 1.39 1.29 1.13 1.22 1.12 0.73 0.69 0.72 0.779999999999999 0.74 0.67 0.64 0.760000000000001 0.73 0.779999999999999 0.79 0.8 0.76 0.779999999999999 0.84 0.85 0.81 0.779999999999999 0.87 0.9 0.88 0.89 0.93 0.83 0.88 0.96 1.01 0.99 0.9 1.03 1.14 1.24 1.33 1.37 1.33 1.37 1.32 1.28 1.32 1.38 1.5 1.42 1.39 1.35 1.35 1.41 1.45 1.43 1.51 1.64 1.65 1.78 2.08 2.05 2.12 2.18 2.26 2.38 2.28 2.11 1.88 1.7 1.59 1.55 1.53 1.6 1.51 1.68 2.32 2.46 2.44 2.05 1.89 1.9 1.9 2.06 2.09 2.0 1.99 1.97 1.73 1.81 1.82 1.72 1.6 1.57 1.55 1.65 1.42 1.16 1.12 1.27 1.33 1.44 1.47 1.46 1.4 1.33 1.39 1.46 1.39 1.4 1.52 39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 5.21 5.62 6.01 5.68 5.07 3.62 3.26 3.15 2.97 3.05 3.29 3.38 3.08 2.8 2.55 2.25 1.95 2.07 1.98 1.65 1.6 1.64 1.7 1.71 1.56 1.58 1.66 1.6 1.69 1.71 1.71 1.67 1.67 1.64 1.69 1.69 1.7 1.82 1.85 1.85 1.84 1.83 1.7 1.77 1.86 1.87 1.71 1.56 1.65 1.8 1.92 2.01 2.11 2.14 2.18 2.12 2.05 2.03 2.11 2.28 2.19 2.29 2.33 2.36 2.44 2.52 2.56 2.64 2.86 2.81 2.89 3.14 3.16 3.3 3.42 3.57 3.79 3.53 3.32 3.25 3.02 2.93 2.82 2.83 2.98 2.83 2.96 3.16 3.34 3.3 2.88 2.73 2.69 2.68 2.93 2.95 2.77 2.77 2.78 2.56 2.6 2.55 2.43 2.3 2.38 2.46 2.41 2.11 1.77 1.67 1.91 2.12 2.27 2.28 2.21 2.16 2.12 2.18 2.3 2.3 2.39 2.57
Spread
(%)
Interest Rate Sensitivity
0.0 0.05 0.1 0.15 0.2 2500.0 1518.98290190903 1000.0 707.6314950684456 532.4527357594372
Price of Bond Over Time
Rate Drops to 5% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1518.98290190903 1494.932047004481 1469.678649354705 1443.16258182244 1415.320710913562 1386.086746459241 1355.391083782203 1323.160637971313 1289.318669869878 1253.784603363372 1216.473833531541 1177.297525208118 1136.162401468524 1092.97052154195 1047.619047619047 1000.0 Rate Stays at 10% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1000.0 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 999.9999999999999 1000.0 Rate Rises to 15% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 707.6314950684456 713.7762193287123 720.8426522280192 728.969050062222 738.3144075715553 749.0615687072888 761.420804013382 775.6339246153892 791.9790133076975 810.775865303852 832.3922450994299 857.2510818643444 885.8387441439962 918.7145557655954 956.5217391304349 1000.0
Mar-80 0.5 1.0 5.0 10.0 30.0 0.15 0.14 0.135 0.128 0.123 Feb-00 0.5 1.0 5.0 10.0 30.0 0.004 0.006 0.0169 0.0268 0.0369 Feb-05 0.5 1.0 5.0 10.0 30.0 0.0598 0.0619 0.0674 0.0668 0.0631 Years to Maturity
Interest Rate
(%)
1-Year 0.05 0.1 0.15 0.2 0.25 1047.619047619047 999.9999999999999 956.5217391304349 916.6666666666667 880.0 25-Year 0.05 0.1 0.15 0.2 0.25 1704.697228302238 999.9999999999999 676.792545736493 505.241298005198 402.2667359117775 Interest Rate, rd
Bond Value
($)
39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 2.4 2.53 2.63 2.59 2.47 1.96 1.75 1.66 1.58 1.69 1.87 2.0 1.79 1.59 1.39 1.29 1.13 1.22 1.12 0.73 0.69 0.72 0.779999999999999 0.74 0.67 0.64 0.760000000000001 0.73 0.779999999999999 0.79 0.8 0.76 0.779999999999999 0.84 0.85 0.81 0.779999999999999 0.87 0.9 0.88 0.89 0.93 0.83 0.88 0.96 1.01 0.99 0.9 1.03 1.14 1.24 1.33 1.37 1.33 1.37 1.32 1.28 1.32 1.38 1.5 1.42 1.39 1.35 1.35 1.41 1.45 1.43 1.51 1.64 1.65 1.78 2.08 2.05 2.12 2.18 2.26 2.38 2.28 2.11 1.88 1.7 1.59 1.55 1.53 1.6 1.51 1.68 2.32 2.46 2.44 2.05 1.89 1.9 1.9 2.06 2.09 2.0 1.99 1.97 1.73 1.81 1.82 1.72 1.6 1.57 1.55 1.65 1.42 1.16 1.12 1.27 1.33 1.44 1.47 1.46 1.4 1.33 1.39 1.46 1.39 1.4 1.52 39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 5.21 5.62 6.01 5.68 5.07 3.62 3.26 3.15 2.97 3.05 3.29 3.38 3.08 2.8 2.55 2.25 1.95 2.07 1.98 1.65 1.6 1.64 1.7 1.71 1.56 1.58 1.66 1.6 1.69 1.71 1.71 1.67 1.67 1.64 1.69 1.69 1.7 1.82 1.85 1.85 1.84 1.83 1.7 1.77 1.86 1.87 1.71 1.56 1.65 1.8 1.92 2.01 2.11 2.14 2.18 2.12 2.05 2.03 2.11 2.28 2.19 2.29 2.33 2.36 2.44 2.52 2.56 2.64 2.86 2.81 2.89 3.14 3.16 3.3 3.42 3.57 3.79 3.53 3.32 3.25 3.02 2.93 2.82 2.83 2.98 2.83 2.96 3.16 3.34 3.3 2.88 2.73 2.69 2.68 2.93 2.95 2.77 2.77 2.78 2.56 2.6 2.55 2.43 2.3 2.38 2.46 2.41 2.11 1.77 1.67 1.91 2.12 2.27 2.28 2.21 2.16 2.12 2.18 2.3 2.3 2.39 2.57
Spread
(%)
Interest Rate Sensitivity
0.0 0.05 0.1 0.15 0.2 2500.0 1518.98290190903 1000.0 707.6314950684456 532.4527357594372
Price of Bond Over Time
Rate Drops to 5% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1518.98290190903 1494.932047004481 1469.678649354705 1443.16258182244 1415.320710913562 1386.086746459241 1355.391083782203 1323.160637971313 1289.318669869878 1253.784603363372 1216.473833531541 1177.297525208118 1136.162401468524 1092.97052154195 1047.619047619047 1000.0 Rate Stays at 10% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1000.0 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 999.9999999999999 1000.0 Rate Rises to 15% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 707.6314950684456 713.7762193287123 720.8426522280192 728.969050062222 738.3144075715553 749.0615687072888 761.420804013382 775.6339246153892 791.9790133076975 810.775865303852 832.3922450994299 857.2510818643444 885.8387441439962 918.7145557655954 956.5217391304349 1000.0
Mar-80 0.5 1.0 5.0 10.0 30.0 0.15 0.14 0.135 0.128 0.123 Feb-00 0.5 1.0 5.0 10.0 30.0 0.004 0.006 0.0169 0.0268 0.0369 Feb-05 0.5 1.0 5.0 10.0 30.0 0.0598 0.0619 0.0674 0.0668 0.0631 Years to Maturity
Interest Rate
(%)
1-Year 0.05 0.1 0.15 0.2 0.25 1047.619047619047 999.9999999999999 956.5217391304349 916.6666666666667 880.0 25-Year 0.05 0.1 0.15 0.2 0.25 1704.697228302238 999.9999999999999 676.792545736493 505.241298005198 402.2667359117775 Interest Rate, rd
Bond Value
($)
39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 2.4 2.53 2.63 2.59 2.47 1.96 1.75 1.66 1.58 1.69 1.87 2.0 1.79 1.59 1.39 1.29 1.13 1.22 1.12 0.73 0.69 0.72 0.779999999999999 0.74 0.67 0.64 0.760000000000001 0.73 0.779999999999999 0.79 0.8 0.76 0.779999999999999 0.84 0.85 0.81 0.779999999999999 0.87 0.9 0.88 0.89 0.93 0.83 0.88 0.96 1.01 0.99 0.9 1.03 1.14 1.24 1.33 1.37 1.33 1.37 1.32 1.28 1.32 1.38 1.5 1.42 1.39 1.35 1.35 1.41 1.45 1.43 1.51 1.64 1.65 1.78 2.08 2.05 2.12 2.18 2.26 2.38 2.28 2.11 1.88 1.7 1.59 1.55 1.53 1.6 1.51 1.68 2.32 2.46 2.44 2.05 1.89 1.9 1.9 2.06 2.09 2.0 1.99 1.97 1.73 1.81 1.82 1.72 1.6 1.57 1.55 1.65 1.42 1.16 1.12 1.27 1.33 1.44 1.47 1.46 1.4 1.33 1.39 1.46 1.39 1.4 1.52 39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 5.21 5.62 6.01 5.68 5.07 3.62 3.26 3.15 2.97 3.05 3.29 3.38 3.08 2.8 2.55 2.25 1.95 2.07 1.98 1.65 1.6 1.64 1.7 1.71 1.56 1.58 1.66 1.6 1.69 1.71 1.71 1.67 1.67 1.64 1.69 1.69 1.7 1.82 1.85 1.85 1.84 1.83 1.7 1.77 1.86 1.87 1.71 1.56 1.65 1.8 1.92 2.01 2.11 2.14 2.18 2.12 2.05 2.03 2.11 2.28 2.19 2.29 2.33 2.36 2.44 2.52 2.56 2.64 2.86 2.81 2.89 3.14 3.16 3.3 3.42 3.57 3.79 3.53 3.32 3.25 3.02 2.93 2.82 2.83 2.98 2.83 2.96 3.16 3.34 3.3 2.88 2.73 2.69 2.68 2.93 2.95 2.77 2.77 2.78 2.56 2.6 2.55 2.43 2.3 2.38 2.46 2.41 2.11 1.77 1.67 1.91 2.12 2.27 2.28 2.21 2.16 2.12 2.18 2.3 2.3 2.39 2.57
Spread
(%)
Interest Rate Sensitivity
0.0 0.05 0.1 0.15 0.2 2500.0 1518.98290190903 1000.0 707.6314950684456 532.4527357594372
Price of Bond Over Time
Rate Drops to 5% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1518.98290190903 1494.932047004481 1469.678649354705 1443.16258182244 1415.320710913562 1386.086746459241 1355.391083782203 1323.160637971313 1289.318669869878 1253.784603363372 1216.473833531541 1177.297525208118 1136.162401468524 1092.97052154195 1047.619047619047 1000.0 Rate Stays at 10% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1000.0 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 999.9999999999999 1000.0 Rate Rises to 15% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 707.6314950684456 713.7762193287123 720.8426522280192 728.969050062222 738.3144075715553 749.0615687072888 761.420804013382 775.6339246153892 791.9790133076975 810.775865303852 832.3922450994299 857.2510818643444 885.8387441439962 918.7145557655954 956.5217391304349 1000.0
Mar-80 0.5 1.0 5.0 10.0 30.0 0.15 0.14 0.135 0.128 0.123 Feb-00 0.5 1.0 5.0 10.0 30.0 0.004 0.006 0.0169 0.0268 0.0369 Feb-05 0.5 1.0 5.0 10.0 30.0 0.0598 0.0619 0.0674 0.0668 0.0631 Years to Maturity
Interest Rate
(%)
1-Year 0.05 0.1 0.15 0.2 0.25 1047.619047619047 999.9999999999999 956.5217391304349 916.6666666666667 880.0 25-Year 0.05 0.1 0.15 0.2 0.25 1704.697228302238 999.9999999999999 676.792545736493 505.241298005198 402.2667359117775 Interest Rate, rd
Bond Value
($)
39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 2.4 2.53 2.63 2.59 2.47 1.96 1.75 1.66 1.58 1.69 1.87 2.0 1.79 1.59 1.39 1.29 1.13 1.22 1.12 0.73 0.69 0.72 0.779999999999999 0.74 0.67 0.64 0.760000000000001 0.73 0.779999999999999 0.79 0.8 0.76 0.779999999999999 0.84 0.85 0.81 0.779999999999999 0.87 0.9 0.88 0.89 0.93 0.83 0.88 0.96 1.01 0.99 0.9 1.03 1.14 1.24 1.33 1.37 1.33 1.37 1.32 1.28 1.32 1.38 1.5 1.42 1.39 1.35 1.35 1.41 1.45 1.43 1.51 1.64 1.65 1.78 2.08 2.05 2.12 2.18 2.26 2.38 2.28 2.11 1.88 1.7 1.59 1.55 1.53 1.6 1.51 1.68 2.32 2.46 2.44 2.05 1.89 1.9 1.9 2.06 2.09 2.0 1.99 1.97 1.73 1.81 1.82 1.72 1.6 1.57 1.55 1.65 1.42 1.16 1.12 1.27 1.33 1.44 1.47 1.46 1.4 1.33 1.39 1.46 1.39 1.4 1.52 39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 5.21 5.62 6.01 5.68 5.07 3.62 3.26 3.15 2.97 3.05 3.29 3.38 3.08 2.8 2.55 2.25 1.95 2.07 1.98 1.65 1.6 1.64 1.7 1.71 1.56 1.58 1.66 1.6 1.69 1.71 1.71 1.67 1.67 1.64 1.69 1.69 1.7 1.82 1.85 1.85 1.84 1.83 1.7 1.77 1.86 1.87 1.71 1.56 1.65 1.8 1.92 2.01 2.11 2.14 2.18 2.12 2.05 2.03 2.11 2.28 2.19 2.29 2.33 2.36 2.44 2.52 2.56 2.64 2.86 2.81 2.89 3.14 3.16 3.3 3.42 3.57 3.79 3.53 3.32 3.25 3.02 2.93 2.82 2.83 2.98 2.83 2.96 3.16 3.34 3.3 2.88 2.73 2.69 2.68 2.93 2.95 2.77 2.77 2.78 2.56 2.6 2.55 2.43 2.3 2.38 2.46 2.41 2.11 1.77 1.67 1.91 2.12 2.27 2.28 2.21 2.16 2.12 2.18 2.3 2.3 2.39 2.57
Spread
(%)
Interest Rate Sensitivity
0.0 0.05 0.1 0.15 0.2 2500.0 1518.98290190903 1000.0 707.6314950684456 532.4527357594372
Price of Bond Over Time
Rate Drops to 5% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1518.98290190903 1494.932047004481 1469.678649354705 1443.16258182244 1415.320710913562 1386.086746459241 1355.391083782203 1323.160637971313 1289.318669869878 1253.784603363372 1216.473833531541 1177.297525208118 1136.162401468524 1092.97052154195 1047.619047619047 1000.0 Rate Stays at 10% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1000.0 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 999.9999999999999 1000.0 Rate Rises to 15% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 707.6314950684456 713.7762193287123 720.8426522280192 728.969050062222 738.3144075715553 749.0615687072888 761.420804013382 775.6339246153892 791.9790133076975 810.775865303852 832.3922450994299 857.2510818643444 885.8387441439962 918.7145557655954 956.5217391304349 1000.0
Mar-80 0.5 1.0 5.0 10.0 30.0 0.15 0.14 0.135 0.128 0.123 Feb-00 0.5 1.0 5.0 10.0 30.0 0.004 0.006 0.0169 0.0268 0.0369 Feb-05 0.5 1.0 5.0 10.0 30.0 0.0598 0.0619 0.0674 0.0668 0.0631 Years to Maturity
Interest Rate
(%)
1-Year 0.05 0.1 0.15 0.2 0.25 1047.619047619047 999.9999999999999 956.5217391304349 916.6666666666667 880.0 25-Year 0.05 0.1 0.15 0.2 0.25 1704.697228302238 999.9999999999999 676.792545736493 505.241298005198 402.2667359117775 Interest Rate, rd
Bond Value
($)
39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 2.4 2.53 2.63 2.59 2.47 1.96 1.75 1.66 1.58 1.69 1.87 2.0 1.79 1.59 1.39 1.29 1.13 1.22 1.12 0.73 0.69 0.72 0.779999999999999 0.74 0.67 0.64 0.760000000000001 0.73 0.779999999999999 0.79 0.8 0.76 0.779999999999999 0.84 0.85 0.81 0.779999999999999 0.87 0.9 0.88 0.89 0.93 0.83 0.88 0.96 1.01 0.99 0.9 1.03 1.14 1.24 1.33 1.37 1.33 1.37 1.32 1.28 1.32 1.38 1.5 1.42 1.39 1.35 1.35 1.41 1.45 1.43 1.51 1.64 1.65 1.78 2.08 2.05 2.12 2.18 2.26 2.38 2.28 2.11 1.88 1.7 1.59 1.55 1.53 1.6 1.51 1.68 2.32 2.46 2.44 2.05 1.89 1.9 1.9 2.06 2.09 2.0 1.99 1.97 1.73 1.81 1.82 1.72 1.6 1.57 1.55 1.65 1.42 1.16 1.12 1.27 1.33 1.44 1.47 1.46 1.4 1.33 1.39 1.46 1.39 1.4 1.52 39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 5.21 5.62 6.01 5.68 5.07 3.62 3.26 3.15 2.97 3.05 3.29 3.38 3.08 2.8 2.55 2.25 1.95 2.07 1.98 1.65 1.6 1.64 1.7 1.71 1.56 1.58 1.66 1.6 1.69 1.71 1.71 1.67 1.67 1.64 1.69 1.69 1.7 1.82 1.85 1.85 1.84 1.83 1.7 1.77 1.86 1.87 1.71 1.56 1.65 1.8 1.92 2.01 2.11 2.14 2.18 2.12 2.05 2.03 2.11 2.28 2.19 2.29 2.33 2.36 2.44 2.52 2.56 2.64 2.86 2.81 2.89 3.14 3.16 3.3 3.42 3.57 3.79 3.53 3.32 3.25 3.02 2.93 2.82 2.83 2.98 2.83 2.96 3.16 3.34 3.3 2.88 2.73 2.69 2.68 2.93 2.95 2.77 2.77 2.78 2.56 2.6 2.55 2.43 2.3 2.38 2.46 2.41 2.11 1.77 1.67 1.91 2.12 2.27 2.28 2.21 2.16 2.12 2.18 2.3 2.3 2.39 2.57
Spread
(%)
Yield Curve for March 1980
Interest Rate Sensitivity
0.0 0.05 0.1 0.15 0.2 2500.0 1518.98290190903 1000.0 707.6314950684456 532.4527357594372
Price of Bond Over Time
Rate Drops to 5% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1518.98290190903 1494.932047004481 1469.678649354705 1443.16258182244 1415.320710913562 1386.086746459241 1355.391083782203 1323.160637971313 1289.318669869878 1253.784603363372 1216.473833531541 1177.297525208118 1136.162401468524 1092.97052154195 1047.619047619047 1000.0 Rate Stays at 10% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1000.0 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 999.9999999999999 1000.0 Rate Rises to 15% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 707.6314950684456 713.7762193287123 720.8426522280192 728.969050062222 738.3144075715553 749.0615687072888 761.420804013382 775.6339246153892 791.9790133076975 810.775865303852 832.3922450994299 857.2510818643444 885.8387441439962 918.7145557655954 956.5217391304349 1000.0
Mar-80 0.5 1.0 5.0 10.0 30.0 0.15 0.14 0.135 0.128 0.123 Feb-00 0.5 1.0 5.0 10.0 30.0 0.004 0.006 0.0169 0.0268 0.0369 Feb-05 0.5 1.0 5.0 10.0 30.0 0.0598 0.0619 0.0674 0.0668 0.0631 Years to Maturity
Interest Rate
(%)
1-Year 0.05 0.1 0.15 0.2 0.25 1047.619047619047 999.9999999999999 956.5217391304349 916.6666666666667 880.0 25-Year 0.05 0.1 0.15 0.2 0.25 1704.697228302238 999.9999999999999 676.792545736493 505.241298005198 402.2667359117775 Interest Rate, rd
Bond Value
($)
39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 2.4 2.53 2.63 2.59 2.47 1.96 1.75 1.66 1.58 1.69 1.87 2.0 1.79 1.59 1.39 1.29 1.13 1.22 1.12 0.73 0.69 0.72 0.779999999999999 0.74 0.67 0.64 0.760000000000001 0.73 0.779999999999999 0.79 0.8 0.76 0.779999999999999 0.84 0.85 0.81 0.779999999999999 0.87 0.9 0.88 0.89 0.93 0.83 0.88 0.96 1.01 0.99 0.9 1.03 1.14 1.24 1.33 1.37 1.33 1.37 1.32 1.28 1.32 1.38 1.5 1.42 1.39 1.35 1.35 1.41 1.45 1.43 1.51 1.64 1.65 1.78 2.08 2.05 2.12 2.18 2.26 2.38 2.28 2.11 1.88 1.7 1.59 1.55 1.53 1.6 1.51 1.68 2.32 2.46 2.44 2.05 1.89 1.9 1.9 2.06 2.09 2.0 1.99 1.97 1.73 1.81 1.82 1.72 1.6 1.57 1.55 1.65 1.42 1.16 1.12 1.27 1.33 1.44 1.47 1.46 1.4 1.33 1.39 1.46 1.39 1.4 1.52 39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 5.21 5.62 6.01 5.68 5.07 3.62 3.26 3.15 2.97 3.05 3.29 3.38 3.08 2.8 2.55 2.25 1.95 2.07 1.98 1.65 1.6 1.64 1.7 1.71 1.56 1.58 1.66 1.6 1.69 1.71 1.71 1.67 1.67 1.64 1.69 1.69 1.7 1.82 1.85 1.85 1.84 1.83 1.7 1.77 1.86 1.87 1.71 1.56 1.65 1.8 1.92 2.01 2.11 2.14 2.18 2.12 2.05 2.03 2.11 2.28 2.19 2.29 2.33 2.36 2.44 2.52 2.56 2.64 2.86 2.81 2.89 3.14 3.16 3.3 3.42 3.57 3.79 3.53 3.32 3.25 3.02 2.93 2.82 2.83 2.98 2.83 2.96 3.16 3.34 3.3 2.88 2.73 2.69 2.68 2.93 2.95 2.77 2.77 2.78 2.56 2.6 2.55 2.43 2.3 2.38 2.46 2.41 2.11 1.77 1.67 1.91 2.12 2.27 2.28 2.21 2.16 2.12 2.18 2.3 2.3 2.39 2.57
Spread
(%)
Yield Curve for February 2000
Interest Rate Sensitivity
0.0 0.05 0.1 0.15 0.2 2500.0 1518.98290190903 1000.0 707.6314950684456 532.4527357594372
Price of Bond Over Time
Rate Drops to 5% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1518.98290190903 1494.932047004481 1469.678649354705 1443.16258182244 1415.320710913562 1386.086746459241 1355.391083782203 1323.160637971313 1289.318669869878 1253.784603363372 1216.473833531541 1177.297525208118 1136.162401468524 1092.97052154195 1047.619047619047 1000.0 Rate Stays at 10% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1000.0 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 999.9999999999999 1000.0 Rate Rises to 15% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 707.6314950684456 713.7762193287123 720.8426522280192 728.969050062222 738.3144075715553 749.0615687072888 761.420804013382 775.6339246153892 791.9790133076975 810.775865303852 832.3922450994299 857.2510818643444 885.8387441439962 918.7145557655954 956.5217391304349 1000.0
Mar-80 0.5 1.0 5.0 10.0 30.0 0.15 0.14 0.135 0.128 0.123 Feb-00 0.5 1.0 5.0 10.0 30.0 0.004 0.006 0.0169 0.0268 0.0369 Feb-05 0.5 1.0 5.0 10.0 30.0 0.0598 0.0619 0.0674 0.0668 0.0631 Years to Maturity
Interest Rate
(%)
1-Year 0.05 0.1 0.15 0.2 0.25 1047.619047619047 999.9999999999999 956.5217391304349 916.6666666666667 880.0 25-Year 0.05 0.1 0.15 0.2 0.25 1704.697228302238 999.9999999999999 676.792545736493 505.241298005198 402.2667359117775 Interest Rate, rd
Bond Value
($)
39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 2.4 2.53 2.63 2.59 2.47 1.96 1.75 1.66 1.58 1.69 1.87 2.0 1.79 1.59 1.39 1.29 1.13 1.22 1.12 0.73 0.69 0.72 0.779999999999999 0.74 0.67 0.64 0.760000000000001 0.73 0.779999999999999 0.79 0.8 0.76 0.779999999999999 0.84 0.85 0.81 0.779999999999999 0.87 0.9 0.88 0.89 0.93 0.83 0.88 0.96 1.01 0.99 0.9 1.03 1.14 1.24 1.33 1.37 1.33 1.37 1.32 1.28 1.32 1.38 1.5 1.42 1.39 1.35 1.35 1.41 1.45 1.43 1.51 1.64 1.65 1.78 2.08 2.05 2.12 2.18 2.26 2.38 2.28 2.11 1.88 1.7 1.59 1.55 1.53 1.6 1.51 1.68 2.32 2.46 2.44 2.05 1.89 1.9 1.9 2.06 2.09 2.0 1.99 1.97 1.73 1.81 1.82 1.72 1.6 1.57 1.55 1.65 1.42 1.16 1.12 1.27 1.33 1.44 1.47 1.46 1.4 1.33 1.39 1.46 1.39 1.4 1.52 39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 5.21 5.62 6.01 5.68 5.07 3.62 3.26 3.15 2.97 3.05 3.29 3.38 3.08 2.8 2.55 2.25 1.95 2.07 1.98 1.65 1.6 1.64 1.7 1.71 1.56 1.58 1.66 1.6 1.69 1.71 1.71 1.67 1.67 1.64 1.69 1.69 1.7 1.82 1.85 1.85 1.84 1.83 1.7 1.77 1.86 1.87 1.71 1.56 1.65 1.8 1.92 2.01 2.11 2.14 2.18 2.12 2.05 2.03 2.11 2.28 2.19 2.29 2.33 2.36 2.44 2.52 2.56 2.64 2.86 2.81 2.89 3.14 3.16 3.3 3.42 3.57 3.79 3.53 3.32 3.25 3.02 2.93 2.82 2.83 2.98 2.83 2.96 3.16 3.34 3.3 2.88 2.73 2.69 2.68 2.93 2.95 2.77 2.77 2.78 2.56 2.6 2.55 2.43 2.3 2.38 2.46 2.41 2.11 1.77 1.67 1.91 2.12 2.27 2.28 2.21 2.16 2.12 2.18 2.3 2.3 2.39 2.57
Spread
(%)
Yield Curve for March 2009
Interest Rate Sensitivity
0.0 0.05 0.1 0.15 0.2 2500.0 1518.98290190903 1000.0 707.6314950684456 532.4527357594372
Price of Bond Over Time
Rate Drops to 5% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1518.98290190903 1494.932047004481 1469.678649354705 1443.16258182244 1415.320710913562 1386.086746459241 1355.391083782203 1323.160637971313 1289.318669869878 1253.784603363372 1216.473833531541 1177.297525208118 1136.162401468524 1092.97052154195 1047.619047619047 1000.0 Rate Stays at 10% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1000.0 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 999.9999999999999 1000.0 Rate Rises to 15% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 707.6314950684456 713.7762193287123 720.8426522280192 728.969050062222 738.3144075715553 749.0615687072888 761.420804013382 775.6339246153892 791.9790133076975 810.775865303852 832.3922450994299 857.2510818643444 885.8387441439962 918.7145557655954 956.5217391304349 1000.0
Mar-80 0.5 1.0 5.0 10.0 30.0 0.15 0.14 0.135 0.128 0.123 Feb-00 0.5 1.0 5.0 10.0 30.0 0.004 0.006 0.0169 0.0268 0.0369 Feb-05 0.5 1.0 5.0 10.0 30.0 0.0598 0.0619 0.0674 0.0668 0.0631 Years to Maturity
Interest Rate
(%)
1-Year 0.05 0.1 0.15 0.2 0.25 1047.619047619047 999.9999999999999 956.5217391304349 916.6666666666667 880.0 25-Year 0.05 0.1 0.15 0.2 0.25 1704.697228302238 999.9999999999999 676.792545736493 505.241298005198 402.2667359117775 Interest Rate, rd
Bond Value
($)
39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 2.4 2.53 2.63 2.59 2.47 1.96 1.75 1.66 1.58 1.69 1.87 2.0 1.79 1.59 1.39 1.29 1.13 1.22 1.12 0.73 0.69 0.72 0.779999999999999 0.74 0.67 0.64 0.760000000000001 0.73 0.779999999999999 0.79 0.8 0.76 0.779999999999999 0.84 0.85 0.81 0.779999999999999 0.87 0.9 0.88 0.89 0.93 0.83 0.88 0.96 1.01 0.99 0.9 1.03 1.14 1.24 1.33 1.37 1.33 1.37 1.32 1.28 1.32 1.38 1.5 1.42 1.39 1.35 1.35 1.41 1.45 1.43 1.51 1.64 1.65 1.78 2.08 2.05 2.12 2.18 2.26 2.38 2.28 2.11 1.88 1.7 1.59 1.55 1.53 1.6 1.51 1.68 2.32 2.46 2.44 2.05 1.89 1.9 1.9 2.06 2.09 2.0 1.99 1.97 1.73 1.81 1.82 1.72 1.6 1.57 1.55 1.65 1.42 1.16 1.12 1.27 1.33 1.44 1.47 1.46 1.4 1.33 1.39 1.46 1.39 1.4 1.52 39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 5.21 5.62 6.01 5.68 5.07 3.62 3.26 3.15 2.97 3.05 3.29 3.38 3.08 2.8 2.55 2.25 1.95 2.07 1.98 1.65 1.6 1.64 1.7 1.71 1.56 1.58 1.66 1.6 1.69 1.71 1.71 1.67 1.67 1.64 1.69 1.69 1.7 1.82 1.85 1.85 1.84 1.83 1.7 1.77 1.86 1.87 1.71 1.56 1.65 1.8 1.92 2.01 2.11 2.14 2.18 2.12 2.05 2.03 2.11 2.28 2.19 2.29 2.33 2.36 2.44 2.52 2.56 2.64 2.86 2.81 2.89 3.14 3.16 3.3 3.42 3.57 3.79 3.53 3.32 3.25 3.02 2.93 2.82 2.83 2.98 2.83 2.96 3.16 3.34 3.3 2.88 2.73 2.69 2.68 2.93 2.95 2.77 2.77 2.78 2.56 2.6 2.55 2.43 2.3 2.38 2.46 2.41 2.11 1.77 1.67 1.91 2.12 2.27 2.28 2.21 2.16 2.12 2.18 2.3 2.3 2.39 2.57
Spread
(%)
Interest Rate Sensitivity
0.0 0.05 0.1 0.15 0.2 2500.0 1518.98290190903 1000.0 707.6314950684456 532.4527357594372
Price of Bond Over Time
Rate Drops to 5% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1518.98290190903 1494.932047004481 1469.678649354705 1443.16258182244 1415.320710913562 1386.086746459241 1355.391083782203 1323.160637971313 1289.318669869878 1253.784603363372 1216.473833531541 1177.297525208118 1136.162401468524 1092.97052154195 1047.619047619047 1000.0 Rate Stays at 10% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1000.0 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 999.9999999999999 1000.0 Rate Rises to 15% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 707.6314950684456 713.7762193287123 720.8426522280192 728.969050062222 738.3144075715553 749.0615687072888 761.420804013382 775.6339246153892 791.9790133076975 810.775865303852 832.3922450994299 857.2510818643444 885.8387441439962 918.7145557655954 956.5217391304349 1000.0
Mar-80 0.5 1.0 5.0 10.0 30.0 0.15 0.14 0.135 0.128 0.123 Feb-00 0.5 1.0 5.0 10.0 30.0 0.004 0.006 0.0169 0.0268 0.0369 Feb-05 0.5 1.0 5.0 10.0 30.0 0.0598 0.0619 0.0674 0.0668 0.0631 Years to Maturity
Interest Rate
(%)
1-Year 0.05 0.1 0.15 0.2 0.25 1047.619047619047 999.9999999999999 956.5217391304349 916.6666666666667 880.0 25-Year 0.05 0.1 0.15 0.2 0.25 1704.697228302238 999.9999999999999 676.792545736493 505.241298005198 402.2667359117775 Interest Rate, rd
Bond Value
($)
39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 2.4 2.53 2.63 2.59 2.47 1.96 1.75 1.66 1.58 1.69 1.87 2.0 1.79 1.59 1.39 1.29 1.13 1.22 1.12 0.73 0.69 0.72 0.779999999999999 0.74 0.67 0.64 0.760000000000001 0.73 0.779999999999999 0.79 0.8 0.76 0.779999999999999 0.84 0.85 0.81 0.779999999999999 0.87 0.9 0.88 0.89 0.93 0.83 0.88 0.96 1.01 0.99 0.9 1.03 1.14 1.24 1.33 1.37 1.33 1.37 1.32 1.28 1.32 1.38 1.5 1.42 1.39 1.35 1.35 1.41 1.45 1.43 1.51 1.64 1.65 1.78 2.08 2.05 2.12 2.18 2.26 2.38 2.28 2.11 1.88 1.7 1.59 1.55 1.53 1.6 1.51 1.68 2.32 2.46 2.44 2.05 1.89 1.9 1.9 2.06 2.09 2.0 1.99 1.97 1.73 1.81 1.82 1.72 1.6 1.57 1.55 1.65 1.42 1.16 1.12 1.27 1.33 1.44 1.47 1.46 1.4 1.33 1.39 1.46 1.39 1.4 1.52 39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 5.21 5.62 6.01 5.68 5.07 3.62 3.26 3.15 2.97 3.05 3.29 3.38 3.08 2.8 2.55 2.25 1.95 2.07 1.98 1.65 1.6 1.64 1.7 1.71 1.56 1.58 1.66 1.6 1.69 1.71 1.71 1.67 1.67 1.64 1.69 1.69 1.7 1.82 1.85 1.85 1.84 1.83 1.7 1.77 1.86 1.87 1.71 1.56 1.65 1.8 1.92 2.01 2.11 2.14 2.18 2.12 2.05 2.03 2.11 2.28 2.19 2.29 2.33 2.36 2.44 2.52 2.56 2.64 2.86 2.81 2.89 3.14 3.16 3.3 3.42 3.57 3.79 3.53 3.32 3.25 3.02 2.93 2.82 2.83 2.98 2.83 2.96 3.16 3.34 3.3 2.88 2.73 2.69 2.68 2.93 2.95 2.77 2.77 2.78 2.56 2.6 2.55 2.43 2.3 2.38 2.46 2.41 2.11 1.77 1.67 1.91 2.12 2.27 2.28 2.21 2.16 2.12 2.18 2.3 2.3 2.39 2.57
Spread
(%)
Interest Rate Sensitivity
0.0 0.05 0.1 0.15 0.2 2500.0 1518.98290190903 1000.0 707.6314950684456 532.4527357594372
Price of Bond Over Time
Rate Drops to 5% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1518.98290190903 1494.932047004481 1469.678649354705 1443.16258182244 1415.320710913562 1386.086746459241 1355.391083782203 1323.160637971313 1289.318669869878 1253.784603363372 1216.473833531541 1177.297525208118 1136.162401468524 1092.97052154195 1047.619047619047 1000.0 Rate Stays at 10% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1000.0 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 999.9999999999999 1000.0 Rate Rises to 15% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 707.6314950684456 713.7762193287123 720.8426522280192 728.969050062222 738.3144075715553 749.0615687072888 761.420804013382 775.6339246153892 791.9790133076975 810.775865303852 832.3922450994299 857.2510818643444 885.8387441439962 918.7145557655954 956.5217391304349 1000.0
Mar-80 0.5 1.0 5.0 10.0 30.0 0.15 0.14 0.135 0.128 0.123 Feb-00 0.5 1.0 5.0 10.0 30.0 0.004 0.006 0.0169 0.0268 0.0369 Feb-05 0.5 1.0 5.0 10.0 30.0 0.0598 0.0619 0.0674 0.0668 0.0631 Years to Maturity
Interest Rate
(%)
1-Year 0.05 0.1 0.15 0.2 0.25 1047.619047619047 999.9999999999999 956.5217391304349 916.6666666666667 880.0 25-Year 0.05 0.1 0.15 0.2 0.25 1704.697228302238 999.9999999999999 676.792545736493 505.241298005198 402.2667359117775 Interest Rate, rd
Bond Value
($)
39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 2.4 2.53 2.63 2.59 2.47 1.96 1.75 1.66 1.58 1.69 1.87 2.0 1.79 1.59 1.39 1.29 1.13 1.22 1.12 0.73 0.69 0.72 0.779999999999999 0.74 0.67 0.64 0.760000000000001 0.73 0.779999999999999 0.79 0.8 0.76 0.779999999999999 0.84 0.85 0.81 0.779999999999999 0.87 0.9 0.88 0.89 0.93 0.83 0.88 0.96 1.01 0.99 0.9 1.03 1.14 1.24 1.33 1.37 1.33 1.37 1.32 1.28 1.32 1.38 1.5 1.42 1.39 1.35 1.35 1.41 1.45 1.43 1.51 1.64 1.65 1.78 2.08 2.05 2.12 2.18 2.26 2.38 2.28 2.11 1.88 1.7 1.59 1.55 1.53 1.6 1.51 1.68 2.32 2.46 2.44 2.05 1.89 1.9 1.9 2.06 2.09 2.0 1.99 1.97 1.73 1.81 1.82 1.72 1.6 1.57 1.55 1.65 1.42 1.16 1.12 1.27 1.33 1.44 1.47 1.46 1.4 1.33 1.39 1.46 1.39 1.4 1.52 39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 5.21 5.62 6.01 5.68 5.07 3.62 3.26 3.15 2.97 3.05 3.29 3.38 3.08 2.8 2.55 2.25 1.95 2.07 1.98 1.65 1.6 1.64 1.7 1.71 1.56 1.58 1.66 1.6 1.69 1.71 1.71 1.67 1.67 1.64 1.69 1.69 1.7 1.82 1.85 1.85 1.84 1.83 1.7 1.77 1.86 1.87 1.71 1.56 1.65 1.8 1.92 2.01 2.11 2.14 2.18 2.12 2.05 2.03 2.11 2.28 2.19 2.29 2.33 2.36 2.44 2.52 2.56 2.64 2.86 2.81 2.89 3.14 3.16 3.3 3.42 3.57 3.79 3.53 3.32 3.25 3.02 2.93 2.82 2.83 2.98 2.83 2.96 3.16 3.34 3.3 2.88 2.73 2.69 2.68 2.93 2.95 2.77 2.77 2.78 2.56 2.6 2.55 2.43 2.3 2.38 2.46 2.41 2.11 1.77 1.67 1.91 2.12 2.27 2.28 2.21 2.16 2.12 2.18 2.3 2.3 2.39 2.57
Spread
(%)
Interest Rate Sensitivity
0.0 0.05 0.1 0.15 0.2 2500.0 1518.98290190903 1000.0 707.6314950684456 532.4527357594372
Price of Bond Over Time
Rate Drops to 5% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1518.98290190903 1494.932047004481 1469.678649354705 1443.16258182244 1415.320710913562 1386.086746459241 1355.391083782203 1323.160637971313 1289.318669869878 1253.784603363372 1216.473833531541 1177.297525208118 1136.162401468524 1092.97052154195 1047.619047619047 1000.0 Rate Stays at 10% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1000.0 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 999.9999999999999 1000.0 Rate Rises to 15% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 707.6314950684456 713.7762193287123 720.8426522280192 728.969050062222 738.3144075715553 749.0615687072888 761.420804013382 775.6339246153892 791.9790133076975 810.775865303852 832.3922450994299 857.2510818643444 885.8387441439962 918.7145557655954 956.5217391304349 1000.0
Mar-80 0.5 1.0 5.0 10.0 30.0 0.15 0.14 0.135 0.128 0.123 Feb-00 0.5 1.0 5.0 10.0 30.0 0.004 0.006 0.0169 0.0268 0.0369 Feb-05 0.5 1.0 5.0 10.0 30.0 0.0598 0.0619 0.0674 0.0668 0.0631 Years to Maturity
Interest Rate
(%)
1-Year 0.05 0.1 0.15 0.2 0.25 1047.619047619047 999.9999999999999 956.5217391304349 916.6666666666667 880.0 25-Year 0.05 0.1 0.15 0.2 0.25 1704.697228302238 999.9999999999999 676.792545736493 505.241298005198 402.2667359117775 Interest Rate, rd
Bond Value
($)
39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 2.4 2.53 2.63 2.59 2.47 1.96 1.75 1.66 1.58 1.69 1.87 2.0 1.79 1.59 1.39 1.29 1.13 1.22 1.12 0.73 0.69 0.72 0.779999999999999 0.74 0.67 0.64 0.760000000000001 0.73 0.779999999999999 0.79 0.8 0.76 0.779999999999999 0.84 0.85 0.81 0.779999999999999 0.87 0.9 0.88 0.89 0.93 0.83 0.88 0.96 1.01 0.99 0.9 1.03 1.14 1.24 1.33 1.37 1.33 1.37 1.32 1.28 1.32 1.38 1.5 1.42 1.39 1.35 1.35 1.41 1.45 1.43 1.51 1.64 1.65 1.78 2.08 2.05 2.12 2.18 2.26 2.38 2.28 2.11 1.88 1.7 1.59 1.55 1.53 1.6 1.51 1.68 2.32 2.46 2.44 2.05 1.89 1.9 1.9 2.06 2.09 2.0 1.99 1.97 1.73 1.81 1.82 1.72 1.6 1.57 1.55 1.65 1.42 1.16 1.12 1.27 1.33 1.44 1.47 1.46 1.4 1.33 1.39 1.46 1.39 1.4 1.52 39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 5.21 5.62 6.01 5.68 5.07 3.62 3.26 3.15 2.97 3.05 3.29 3.38 3.08 2.8 2.55 2.25 1.95 2.07 1.98 1.65 1.6 1.64 1.7 1.71 1.56 1.58 1.66 1.6 1.69 1.71 1.71 1.67 1.67 1.64 1.69 1.69 1.7 1.82 1.85 1.85 1.84 1.83 1.7 1.77 1.86 1.87 1.71 1.56 1.65 1.8 1.92 2.01 2.11 2.14 2.18 2.12 2.05 2.03 2.11 2.28 2.19 2.29 2.33 2.36 2.44 2.52 2.56 2.64 2.86 2.81 2.89 3.14 3.16 3.3 3.42 3.57 3.79 3.53 3.32 3.25 3.02 2.93 2.82 2.83 2.98 2.83 2.96 3.16 3.34 3.3 2.88 2.73 2.69 2.68 2.93 2.95 2.77 2.77 2.78 2.56 2.6 2.55 2.43 2.3 2.38 2.46 2.41 2.11 1.77 1.67 1.91 2.12 2.27 2.28 2.21 2.16 2.12 2.18 2.3 2.3 2.39 2.57
Spread
(%)
Interest Rate Sensitivity
0.0 0.05 0.1 0.15 0.2 2500.0 1518.98290190903 1000.0 707.6314950684456 532.4527357594372
Price of Bond Over Time
Rate Drops to 5% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1518.98290190903 1494.932047004481 1469.678649354705 1443.16258182244 1415.320710913562 1386.086746459241 1355.391083782203 1323.160637971313 1289.318669869878 1253.784603363372 1216.473833531541 1177.297525208118 1136.162401468524 1092.97052154195 1047.619047619047 1000.0 Rate Stays at 10% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1000.0 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 999.9999999999999 1000.0 Rate Rises to 15% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 707.6314950684456 713.7762193287123 720.8426522280192 728.969050062222 738.3144075715553 749.0615687072888 761.420804013382 775.6339246153892 791.9790133076975 810.775865303852 832.3922450994299 857.2510818643444 885.8387441439962 918.7145557655954 956.5217391304349 1000.0
Mar-80 0.5 1.0 5.0 10.0 30.0 0.15 0.14 0.135 0.128 0.123 Feb-00 0.5 1.0 5.0 10.0 30.0 0.004 0.006 0.0169 0.0268 0.0369 Feb-05 0.5 1.0 5.0 10.0 30.0 0.0598 0.0619 0.0674 0.0668 0.0631 Years to Maturity
Interest Rate
(%)
1-Year 0.05 0.1 0.15 0.2 0.25 1047.619047619047 999.9999999999999 956.5217391304349 916.6666666666667 880.0 25-Year 0.05 0.1 0.15 0.2 0.25 1704.697228302238 999.9999999999999 676.792545736493 505.241298005198 402.2667359117775 Interest Rate, rd
Bond Value
($)
39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 2.4 2.53 2.63 2.59 2.47 1.96 1.75 1.66 1.58 1.69 1.87 2.0 1.79 1.59 1.39 1.29 1.13 1.22 1.12 0.73 0.69 0.72 0.779999999999999 0.74 0.67 0.64 0.760000000000001 0.73 0.779999999999999 0.79 0.8 0.76 0.779999999999999 0.84 0.85 0.81 0.779999999999999 0.87 0.9 0.88 0.89 0.93 0.83 0.88 0.96 1.01 0.99 0.9 1.03 1.14 1.24 1.33 1.37 1.33 1.37 1.32 1.28 1.32 1.38 1.5 1.42 1.39 1.35 1.35 1.41 1.45 1.43 1.51 1.64 1.65 1.78 2.08 2.05 2.12 2.18 2.26 2.38 2.28 2.11 1.88 1.7 1.59 1.55 1.53 1.6 1.51 1.68 2.32 2.46 2.44 2.05 1.89 1.9 1.9 2.06 2.09 2.0 1.99 1.97 1.73 1.81 1.82 1.72 1.6 1.57 1.55 1.65 1.42 1.16 1.12 1.27 1.33 1.44 1.47 1.46 1.4 1.33 1.39 1.46 1.39 1.4 1.52 39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 5.21 5.62 6.01 5.68 5.07 3.62 3.26 3.15 2.97 3.05 3.29 3.38 3.08 2.8 2.55 2.25 1.95 2.07 1.98 1.65 1.6 1.64 1.7 1.71 1.56 1.58 1.66 1.6 1.69 1.71 1.71 1.67 1.67 1.64 1.69 1.69 1.7 1.82 1.85 1.85 1.84 1.83 1.7 1.77 1.86 1.87 1.71 1.56 1.65 1.8 1.92 2.01 2.11 2.14 2.18 2.12 2.05 2.03 2.11 2.28 2.19 2.29 2.33 2.36 2.44 2.52 2.56 2.64 2.86 2.81 2.89 3.14 3.16 3.3 3.42 3.57 3.79 3.53 3.32 3.25 3.02 2.93 2.82 2.83 2.98 2.83 2.96 3.16 3.34 3.3 2.88 2.73 2.69 2.68 2.93 2.95 2.77 2.77 2.78 2.56 2.6 2.55 2.43 2.3 2.38 2.46 2.41 2.11 1.77 1.67 1.91 2.12 2.27 2.28 2.21 2.16 2.12 2.18 2.3 2.3 2.39 2.57
Spread
(%)
Interest Rate Sensitivity
0.0 0.05 0.1 0.15 0.2 2500.0 1518.98290190903 1000.0 707.6314950684456 532.4527357594372
Price of Bond Over Time
Rate Drops to 5% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1518.98290190903 1494.932047004481 1469.678649354705 1443.16258182244 1415.320710913562 1386.086746459241 1355.391083782203 1323.160637971313 1289.318669869878 1253.784603363372 1216.473833531541 1177.297525208118 1136.162401468524 1092.97052154195 1047.619047619047 1000.0 Rate Stays at 10% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 1000.0 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 999.9999999999999 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 999.9999999999999 1000.0 Rate Rises to 15% 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 707.6314950684456 713.7762193287123 720.8426522280192 728.969050062222 738.3144075715553 749.0615687072888 761.420804013382 775.6339246153892 791.9790133076975 810.775865303852 832.3922450994299 857.2510818643444 885.8387441439962 918.7145557655954 956.5217391304349 1000.0
Mar-80 0.5 1.0 5.0 10.0 30.0 0.15 0.14 0.135 0.128 0.123 Feb-00 0.5 1.0 5.0 10.0 30.0 0.004 0.006 0.0169 0.0268 0.0369 Feb-05 0.5 1.0 5.0 10.0 30.0 0.0598 0.0619 0.0674 0.0668 0.0631 Years to Maturity
Interest Rate
(%)
1-Year 0.05 0.1 0.15 0.2 0.25 1047.619047619047 999.9999999999999 956.5217391304349 916.6666666666667 880.0 25-Year 0.05 0.1 0.15 0.2 0.25 1704.697228302238 999.9999999999999 676.792545736493 505.241298005198 402.2667359117775 Interest Rate, rd
Bond Value
($)
39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 2.4 2.53 2.63 2.59 2.47 1.96 1.75 1.66 1.58 1.69 1.87 2.0 1.79 1.59 1.39 1.29 1.13 1.22 1.12 0.73 0.69 0.72 0.779999999999999 0.74 0.67 0.64 0.760000000000001 0.73 0.779999999999999 0.79 0.8 0.76 0.779999999999999 0.84 0.85 0.81 0.779999999999999 0.87 0.9 0.88 0.89 0.93 0.83 0.88 0.96 1.01 0.99 0.9 1.03 1.14 1.24 1.33 1.37 1.33 1.37 1.32 1.28 1.32 1.38 1.5 1.42 1.39 1.35 1.35 1.41 1.45 1.43 1.51 1.64 1.65 1.78 2.08 2.05 2.12 2.18 2.26 2.38 2.28 2.11 1.88 1.7 1.59 1.55 1.53 1.6 1.51 1.68 2.32 2.46 2.44 2.05 1.89 1.9 1.9 2.06 2.09 2.0 1.99 1.97 1.73 1.81 1.82 1.72 1.6 1.57 1.55 1.65 1.42 1.16 1.12 1.27 1.33 1.44 1.47 1.46 1.4 1.33 1.39 1.46 1.39 1.4 1.52 39845.0 39814.0 39783.0 39753.0 39722.0 39692.0 39661.0 39630.0 39600.0 39569.0 39539.0 39508.0 39479.0 39448.0 39417.0 39387.0 39356.0 39326.0 39295.0 39264.0 39234.0 39203.0 39173.0 39142.0 39114.0 39083.0 39052.0 39022.0 38991.0 38961.0 38930.0 38899.0 38869.0 38838.0 38808.0 38777.0 38749.0 38718.0 38687.0 38657.0 38626.0 38596.0 38565.0 38534.0 38504.0 38473.0 38443.0 38412.0 38384.0 38353.0 38322.0 38292.0 38261.0 38231.0 38200.0 38169.0 38139.0 38108.0 38078.0 38047.0 38018.0 37987.0 37956.0 37926.0 37895.0 37865.0 37834.0 37803.0 37773.0 37742.0 37712.0 37681.0 37653.0 37622.0 37591.0 37561.0 37530.0 37500.0 37469.0 37438.0 37408.0 37377.0 37347.0 37316.0 37288.0 37257.0 37226.0 37196.0 37165.0 37135.0 37104.0 37073.0 37043.0 37012.0 36982.0 36951.0 36923.0 36892.0 36861.0 36831.0 36800.0 36770.0 36739.0 36708.0 36678.0 36647.0 36617.0 36586.0 36557.0 36526.0 36495.0 36465.0 36434.0 36404.0 36373.0 36342.0 36312.0 36281.0 36251.0 36220.0 36192.0 36161.0 5.21 5.62 6.01 5.68 5.07 3.62 3.26 3.15 2.97 3.05 3.29 3.38 3.08 2.8 2.55 2.25 1.95 2.07 1.98 1.65 1.6 1.64 1.7 1.71 1.56 1.58 1.66 1.6 1.69 1.71 1.71 1.67 1.67 1.64 1.69 1.69 1.7 1.82 1.85 1.85 1.84 1.83 1.7 1.77 1.86 1.87 1.71 1.56 1.65 1.8 1.92 2.01 2.11 2.14 2.18 2.12 2.05 2.03 2.11 2.28 2.19 2.29 2.33 2.36 2.44 2.52 2.56 2.64 2.86 2.81 2.89 3.14 3.16 3.3 3.42 3.57 3.79 3.53 3.32 3.25 3.02 2.93 2.82 2.83 2.98 2.83 2.96 3.16 3.34 3.3 2.88 2.73 2.69 2.68 2.93 2.95 2.77 2.77 2.78 2.56 2.6 2.55 2.43 2.3 2.38 2.46 2.41 2.11 1.77 1.67 1.91 2.12 2.27 2.28 2.21 2.16 2.12 2.18 2.3 2.3 2.39 2.57
Spread
(%)
Web 5A
. Find the issue price of Vandenburg’s bonds, construct a table to analyze the cash flows attributable to one of the bonds, and determine the after-tax cost of debt for the issue. Then, indicate the total par value of the issue.
$1,000
6%
5
40%
Years 0 1 2 3 4 5
5 4 3 2 1 0
$747.26
$1,000.00
$0.00 $0.00 $0.00 $0.00
$747.26 $17.93 $19.01 $20.15 $21.36
= = bonds.
=
4/11/10 | |||||||||
Web Extension 5A: Zero Coupon Bonds | |||||||||
Vandenburg Corporation needs to issue $50 million to finance a project, and it has decided to raise the funds by issuing $1,000 par value, zero coupon bonds. The going interest rate on such debt is 6%, and the corporate tax rate is | 40% | ||||||||
This example analyzes the after-tax cost of issuing zero coupon debt. | |||||||||
Table 5A-1 | |||||||||
Input Data | |||||||||
Amount needed = | $50,000,000 | ||||||||
Maturity value= | |||||||||
Pre-tax market interest rate, rd = | |||||||||
Maturity (in years) = | |||||||||
Corporate tax rate = | |||||||||
Coupon payment (assuming annual payments) = | $0 | ||||||||
Issue Price = | PV of payments at rd = | $747.26 | |||||||
Analysis: | |||||||||
(1) Remaining years | |||||||||
(2) Year-end accrued value | Michael C. Ehrhardt: This the PV of all remaining payments, discounted at the pre-tax market interest rate, rd | $792.09 | $839.62 | $890.00 | $943.40 | ||||
(3) Interest payment | $0.00 | ||||||||
(4) Implied interest | |||||||||
deduction on discount | $44.84 | $47.53 | $50.38 | $53.40 | $56.60 | ||||
(5) Tax savings | $17.93 | $19.01 | $20.15 | $21.36 | $22.64 | ||||
(6) Cash flow | ($977.36) | ||||||||
After-tax cost of debt = | 3.60% | ||||||||
Number of $1,000 zeros the company must issue to raise $50 million |
|||||||||
Amount needed/Price per bond | |||||||||
66,911.279 | |||||||||
Face amount of bonds = # bonds x $1,000 | $66,911,279 |
&F &A
Michael C. Ehrhardt Page &P &D
Web 5C
20
.0
$1,000
1 $90
82.57
$1,000.00
Maturity 9%
1
$1,000.00
9.00%
$4,224.11
$5,775.89
$4,224.11
$10,000.00
1% 2% 3% 4% 5% 6% 7% 8% 9% $5,775.89 $4,224.11 $10,000.00 $0.00
10% 12% 13% 15%
4/24/09 | ||||||||||||||||||||
Web Extension 5C. Tool Kit for Duration | ||||||||||||||||||||
Duration is a measure of risk for bonds. The following example illustrates its calculation. | ||||||||||||||||||||
Figure 5C-1 Duration | ||||||||||||||||||||
Inputs | ||||||||||||||||||||
Years to maturity = | ||||||||||||||||||||
9.00% | ||||||||||||||||||||
Annual payment = | $90 | |||||||||||||||||||
Par value = FV = | ||||||||||||||||||||
t (1) |
CFt (2) |
PV of CFt (3) |
t(PV of CFt) (4) |
|||||||||||||||||
$ | 82.57 | |||||||||||||||||||
$75.75 | 151.50 | |||||||||||||||||||
$69.50 | 208.49 | |||||||||||||||||||
$63.76 | 255.03 | |||||||||||||||||||
$58.49 | 292.47 | |||||||||||||||||||
$53.66 | 321.98 | |||||||||||||||||||
$49.23 | 344.63 | |||||||||||||||||||
$45.17 | 361.34 | |||||||||||||||||||
$41.44 | 372.95 | |||||||||||||||||||
$38.02 | 380.17 | |||||||||||||||||||
$34.88 | 383.66 | |||||||||||||||||||
$32.00 | 383.98 | |||||||||||||||||||
$29.36 | 381.63 | |||||||||||||||||||
$26.93 | 377.05 | |||||||||||||||||||
$24.71 | 370.63 | |||||||||||||||||||
$22.67 | 362.69 | |||||||||||||||||||
$20.80 | 353.54 | |||||||||||||||||||
$19.08 | 343.43 | |||||||||||||||||||
$17.50 | 332.58 | |||||||||||||||||||
$1,090 | $194.49 | 3,889.79 | ||||||||||||||||||
VB = | Sum of t(PV of CFt) = |
$9,950.11 | ||||||||||||||||||
Duration = | Sum of t(PV of CFt) / VB = | 9.95 | ||||||||||||||||||
Finding Duration with the Excel Formula | ||||||||||||||||||||
Settlement date = | 1/1/09 | |||||||||||||||||||
12/31/28 | ||||||||||||||||||||
Coupon = | ||||||||||||||||||||
Frequency = | ||||||||||||||||||||
Consider the amount that would accumulate during the first 10 years, if all coupons are reinvested at the original interest rate of 9%. To do this, first find the amount that would be in the account at 10 years (including the 10-year coupon). Then we find the value of the bond at year 10 based on the payments from 11 and on. | ||||||||||||||||||||
Duration of Bond = | 9.95011 | |||||||||||||||||||
Target value at year 10 = |
$10,000.00 | |||||||||||||||||||
FV of reinvested coupons at year 10 if no change in rates = | $1,367.36 | |||||||||||||||||||
PV at year 10 of remaining payments if no change in rates = | ||||||||||||||||||||
Total value at year 10 if no change in rates = | $2,367.36 | |||||||||||||||||||
Value of bonds to be purchased to provide target at 10 years = | $4,224.11 | |||||||||||||||||||
Number of bonds purchased = | 4.22 | |||||||||||||||||||
Now find the value at year 10 if the market interest rate (shown below) changes immediately after time zero, based on the total number of bonds that were purchased. | ||||||||||||||||||||
Interest rate = | ||||||||||||||||||||
FV at year 10 = | $5,775.89 | |||||||||||||||||||
PV of payments beyond year 10 discounted back to year 10 = | ||||||||||||||||||||
The total value of the position at time 9.95011 is the value of the reinvested coupon and the current value of the bond. | ||||||||||||||||||||
Value of reinvested coupons: | ||||||||||||||||||||
Current value of bond: | ||||||||||||||||||||
Total value of position = | ||||||||||||||||||||
As the table below shows, the total value of a position at a future time equal to the orginal duration will not fall if interest rates change. For example, if rates go up, the value of reinvested coupons increases and the value of the bond at the future date (t=duration) falls, but the net affect is an increase in total value. If rates go down, the value of reinvested coupons goes down, but the future value of the bond goes up, for a net increase in value. Thus, if the desired time horizon is equal to the bond’s duration, the value of the position will not fall if interest rates change. | ||||||||||||||||||||
Reinvested Coupons | Current Price at t=Duration | Total Value | Change in Total Value from Original Target | |||||||||||||||||
$3,977.42 | $7,424.73 | $11,402.15 | $1,402.15 | |||||||||||||||||
$4,162.75 | $6,880.15 | $11,042.90 | $1,042.90 | |||||||||||||||||
$4,358.22 | $6,386.06 | $10,744.28 | $744.28 | |||||||||||||||||
$4,564.36 | $5,937.17 | $10,501.53 | $501.53 | |||||||||||||||||
$4,781.73 | $5,528.81 | $10,310.54 | $310.54 | |||||||||||||||||
$5,010.94 | $5,156.80 | $10,167.74 | $167.74 | |||||||||||||||||
$5,252.60 | $4,817.48 | $10,070.07 | $70.07 | |||||||||||||||||
$5,507.35 | $4,507.55 | $10,014.90 | $14.90 | |||||||||||||||||
$6,058.93 | $3,964.55 | $10,023.48 | $23.48 | |||||||||||||||||
11% | $6,357.20 | $3,726.57 | $10,083.77 | $83.77 | ||||||||||||||||
$6,671.50 | $3,508.09 | $10,179.59 | $179.59 | |||||||||||||||||
$7,002.63 | $3,307.27 | $10,309.90 | $309.90 | |||||||||||||||||
14% | $7,351.45 | $3,122.44 | $10,473.89 | $473.89 | ||||||||||||||||
$7,718.86 | $2,952.12 | $10,670.98 | $670.98 | |||||||||||||||||
16% | $8,105.78 | $2,794.98 | $10,900.76 | $900.76 |
&F &A
Michael C. Ehrhardt Page &P &D
Web 5D
s from now on a 2-year bond would be denoted by 3r2.
s from now =
s from now =
Maturity Maturity Yield1 year 1 2 year 2 3 year 3 4 year 4 5 year 5 10 year 10 20 year 20
30
x
= (
x (1 + 1r1)
= ( (1+ r2)2 x
= ( 1.1090 x (1 + 2r1)
= ( (1+ r3)3 x
= ( 1.1736 x (1 + 3r1)
= ( (1+ r4)4 x
= ( 1.2459 x (1 + 4r1)
= ( (1+ r5)5 x
= ( 1.3213 x (1 + 5r5)5
= ( (1+ r10)10 x
= ( 1.7375 x (1 + 10r10)10
= ( (1+ r20)20 x
= ( 3.2132 x (1 + 20r10)10
QUESTIONS
and it was zero for the 1-year bond?
1-year Treasury yield 7.0%
2-year Treasury yield 9.0%
1-year rate, 1 year from now
3/28/09 | ||||||||||||||||||
Web Extension 5D. The Pure Expectations Theory and Estimation of Forward Rates | ||||||||||||||||||
The shape of the yield curve depends primarily on two key factors: (1) expectations about future inflation and (2) perceptions about the relative riskiness of securities of different maturities. The first factor is the basis for the Pure Expectations Hypothesis. If the relationship between expectations for future inflation and bond yields is controlling, i. e., if no maturity premiums existed, then the pure expectations theory posits that forward interest rates can be predicted by “backing them out of the yield curve.” Essentially, under the pure expectations theory, long-term security rates are a weighted average of the yields on all the shorter maturities that make up the longer maturity. This calculation will hold true, providing that the MRP=0 assumption is valid. | ||||||||||||||||||
For instance, if the yield on a 1-year bond is 5% and that on a 2-year bond is 6%, the rate on a 1-year bond one year from now should be 7%, because (1.06)2 = (1.05)(1.07). | ||||||||||||||||||
Generally, r designates the rate, or yield, and our notation involves two subscripts. The first subscript denotes when in the future we expect the yield to exist, and the second denotes the maturity of the security. For instance, the rate expected | 3 year | |||||||||||||||||
Assuming that expectations theory holds, use the yield information below to back out the following forward rates from the yield curve. | ||||||||||||||||||
Expected forward rates, in words: | Symbol: | |||||||||||||||||
Yield on 1-year bond 1 year from now = | 1r1 | |||||||||||||||||
Yield on 1-year bond | 2 year | 2r1 | ||||||||||||||||
Yield on 1-year bond 3 years from now = | 3r1 | |||||||||||||||||
Yield on 1-year bond 4 years from now = | 4r1 | |||||||||||||||||
Yield on 5-year bond 5 years from now = | 5r5 | |||||||||||||||||
Yield on 10-year bond 10 years from now = | 10r10 | |||||||||||||||||
Yield on 20-year bond 10 years from now = | 10r20 | |||||||||||||||||
Yield on 10-year bond | 20 year | 20r10 | ||||||||||||||||
5.02% | ||||||||||||||||||
5.31% | ||||||||||||||||||
5.48% | ||||||||||||||||||
5.65% | ||||||||||||||||||
5.73% | ||||||||||||||||||
5.68% | ||||||||||||||||||
6.01% | ||||||||||||||||||
30 year | 5.92% | |||||||||||||||||
(1+ r2)2 | = ( | (1 + r1) | (1 + 1r1) | |||||||||||||||
1.1090 | 1.0502 | |||||||||||||||||
5.60% | ||||||||||||||||||
(1+ r3)3 | (1 + 2r1) | |||||||||||||||||
1.1736 | ||||||||||||||||||
5.82% | ||||||||||||||||||
(1+ r4)4 | (1 + 3r1) | |||||||||||||||||
1.2459 | ||||||||||||||||||
6.16% | ||||||||||||||||||
(1+ r5)5 | (1 + 4r1) | |||||||||||||||||
1.3213 | ||||||||||||||||||
6.05% | ||||||||||||||||||
(1+ r10)10 | (1 + 5r5)5 | |||||||||||||||||
1.7375 | ||||||||||||||||||
5.63% | ||||||||||||||||||
(1+ r20)20 | (1 + 10r10)10 | |||||||||||||||||
3.2132 | ||||||||||||||||||
6.34% | ||||||||||||||||||
(1+ r30)30 | (1 + 20r10)10 | |||||||||||||||||
5.6149 | ||||||||||||||||||
5.74% | ||||||||||||||||||
The data used to construct the yield curve are readily available, and forward rates can be calculated as shown above. Bond traders and corporate borrowers can use this information for hedging in the futures market. For example, if a company plans to build a new plant two years from now and wants to be assured of getting the required funds at a specified rate, then it can buy a bond futures contract that will enable it to “lock in” the cost of debt for the project. The treasurer would go through the process described above to determine what the rate two years hence should be on bonds with the desired maturity. | ||||||||||||||||||
SOLUTIONS TO SELF-TEST | ||||||||||||||||||
4a Assume the interest rate on a 1-year T-bond is currently 7% and the rate on a 2-year bond is 9%. If the maturity risk premium is zero, what is a reasonable forecast of the rate on a 1-year bond next year? | ||||||||||||||||||
1-year Treasury yield | 7.0% | |||||||||||||||||
2-year Treasury yield | 9.0% | |||||||||||||||||
Maturity Risk Premium | 0.0% | |||||||||||||||||
1-year rate, 1 year from now | 11.04% | |||||||||||||||||
4b What would the forecast be if the maturity risk premium on the 2-year bond were | 0.5% | |||||||||||||||||
10.02% |
5.3
SOLUTIONS TO SELF-TEST, and a market interest rate of 9%. What is its price?
Years to Maturity 6 $80
9%
Coupon rate 10%
Annual Payment $100
Par value $1,000
Going rate, rd 7%Value of bond =
SECTION 5.3 | ||||||||
A bond that matures in six years has a par value of $1,000, an annual coupon payment of | $80 | |||||||
Annual Payment | ||||||||
Going rate, rd | ||||||||
$955.14 | ||||||||
A bond that matures in 18 years has a par value of $1,000, an annual coupon of 10%, and a market interest rate of 7%. What is its price? | ||||||||
$1,301.77 |
5.4
SOLUTIONS TO SELF-TEST
Years to Maturity 29Coupon rate 8%
Annual Payment $80
Par value $1,000
Value of bond =
Years to Maturity 29
Coupon rate 8%
Annual Payment $80
Par value $1,000
Value of bond =
SECTION 5.4 |
Last year a firm issued 30-year, 8% annual coupon bonds at a par value of $1,000. (1) Suppose that one year later the going rate drops to 6%. What is the new price of the bonds, assuming that they now have 29 years to maturity? |
$1,271.81 |
Suppose instead that one year after issue the going interest rate increases to 10% (rather than 6%). What is the price? |
$812.61 |
5.5
SOLUTIONS TO SELF-TEST
2
Coupon rate 8% 4%
Annual Payment $80 $40
Par value $1,000 $1,000
Going rate, rd 6% Value of bond =
SECTION 5.5 | |
A bond has a 25-year maturity, an 8% annual coupon paid semiannually, and a face value of $1,000. The going nominal annual interest rate (rd) is 6%. What is the bond’s price? | |
Coupons per year | |
Annual values | Semiannual Inputs |
3.0% | |
$1,255.67 | $1,257.30 |
5.6
SOLUTIONS TO SELF-TEST
Years to Maturity 8Annual Payment Current price Par value = FV $1,000.00
Annual Payment $80.00
Current price $850.00
. It pays a
annual coupon and has a 20-year maturity, but it can be called in 5 years at
. What are its YTM and its YTC? Is it likely to be called if interest rates don’t change?
Years to Maturity 20 5
Current price $1,250 Current price $1,250
Par value = FV $1,000 Call price $1,110
YTM
YTC
SECTION 5.6 | |||||
A bond currently sells for $850. It has an eight-year maturity, an annual coupon of $80, and a par value of $1,000. What is its yield to maturity? What is its current yield? | |||||
$80.00 | |||||
$850.00 | |||||
Going rate, rd =YTM: | 10.90% | ||||
Current yield: | 9.41% | ||||
A bond currently sells for | $1,250 | $110 | $1,110 | ||
Years to Call | |||||
8.38% | 6.85% | ||||
The company will probably call the bond, because the YTC is less than the YTM. |
5.9
SOLUTIONS TO SELF-TEST
5%
3%
SECTION 5.9 | |
The yield on a 15-year TIPS is 3 percent and the yield on a 15-year Treasury bond is 5 percent. What is the inflation premium for a 15-year security | |
Yield on T-Bond | |
Yield on TIPS | |
5.11
SOLUTIONS TO SELF-TEST
Yield on T-Bond 6.0%
SECTION 5.11 |
A 10-year T-bond has a yield of 4.5 percent. A corporate bond with a rating of AA has a yield of 6.0 percent. If the corporate bond has excellent liquidty, what is an estimate of the corporate bond’s default risk premium? |
4.5% |
Yield on corporate bond |
1.5% |
5.13
r* 3.0% 2.5%
1.0%
SECTION 5.13 | ||
SOLUTIONS TO SELF-TEST QUESTIONS | ||
Assume that the real risk-free rate is r* = 3% and the average expected inflation rate is 2.5% for the foreseeable future. The DRP and LP for a bond are each 1%, and the applicable MRP is 2%. What is the bond’s yield? | ||
Inflation Premium | ||
Default Risk Premium | 1.0% | |
Liquidity Premium | ||
2.0% | ||
9.5% |
td>>Ch0
5P24 Build a Model
13
year,
semiannual coupon bond with a par value of
may be called in 5 years at a call price of
. The bond sells for
. (Assume that the bond has just been issued.)
20
2
:
8%
$1,000
$1,100
$1,040
5
– Hint: Write formula in words.
Cap. Gain/loss yield = (Answer)
This is a nominal rate, not the effective rate. Nominal rates are generally quoted.
8%
$0.00
$0.00 $0.00 $0.00
$0.00 $0.00 $0.00
$0.00 $0.00 $0.00
$0.00 $0.00 $0.00
$0.00 $0.00 $0.00
$0.00 $0.00 $0.00
$0.00 $0.00 $0.00
$0.00 $0.00 $0.00
Spring 1, | 20 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
7/22/12 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Chapter 5. Ch 05 P24 Build a Model | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Except for charts and answers that must be written, only Excel formulas that use cell references or functions will be accepted for credit. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Numeric answers in cells will not be accepted. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
A 20 | – | 8% | $1,000 | $1,040 | $1,100 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Basic Input Data: | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Years to maturity: | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Periods per year: | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Periods to maturity: | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Coupon rate | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Par value: | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Periodic payment: | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Current price | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Call price: | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Years till callable: | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Periods till callable: | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
a. What is the bond’s yield to maturity? | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Periodic YTM = | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Annualized Nominal YTM = | Hint: | This is a nominal rate, not the effective rate. Nominal rates are generally quoted. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
b. What is the bond’s current yield? | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Current yield = | Hint: Write formula in words. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Hint: Cell formulas should refer to Input Section | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
(Answer) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
c. What is the bond’s capital gain or loss yield? | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Cap. Gain/loss yield = | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Note that this is an economic loss, not a loss for tax purposes. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
d. What is the bond’s yield to call? | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Here we can again use the Rate function, but with data related to the call. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Peridodic YTC = | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Annualized Nominal YTC = | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
The YTC is lower than the YTM because if the bond is called, the buyer will lose the difference between the call price and the current price in just 4 years, and that loss will offset much of the interest imcome. Note too that the bond is likely to be called and replaced, hence that the YTC will probably be earned. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
NOW ANSWER THE FOLLOWING NEW QUESTIONS: | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
e. How would the price of the bond be affected by changing the going market interest rate? (Hint: Conduct a sensitivity analysis of price to changes in the going market interest rate for the bond. Assume that the bond will be called if and only if the going rate of interest falls below the coupon rate. That is an oversimplification, but assume it anyway for purposes of this problem.) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Nominal market rate, r: | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Value of bond if it’s not called: | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Value of bond if it’s called: | The bond would not be called unless r | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
We can use the two valuation formulas to find values under different r’s, in a 2-output data table, and then use an IF | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
statement to determine which value is appropriate: | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Value of Bond If: | Actual value, | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Not called | Called | considering | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Rate, r | $0.00 | call likehood: | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
0% | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
2% | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
4% | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
6% | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
10% | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
12% | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
14% | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
16% | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
f. Now assume the date is 10/25/2010. Assume further that a 12%, 10-year bond was issued on 7/1/2010, pays interest semiannually (January 1 and July 1), and sells for $1,100. Use your spreadsheet to find the bond’s yield. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Refer to this chapter’s Tool Kit for information about how to use Excel’s bond valuation functions. The model finds the price of a bond, but the procedures for finding the yield are similar. Begin by setting up the input data as shown below: | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Basic info: | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Settlement (today) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Maturity | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Current price (% of par) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Redemption (% of par value) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Frequency (for semiannual) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Basis (360 or 365 day year) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Yield to Maturity: | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Hint: Use the Yield function. For dates, either refer to cells in Basic Info above, or enter the date in quotes, such as “10/25/2010”. |
Sheet2
7/22/121. The real risk-free rate is 2%. Inflation is expected to be 3% this year and 6% during the next 2 years.
Assume that the maturity risk premium is zero.
What is the yield on 2-year Treasury securities? Round your answer to two decimal places.
%
What is the yield on 3-year Treasury securities? Round your answer to two decimal places.
%
2. Thatcher Corporation’s bonds will mature in 16 years. The bonds have a face value of $1,000 and an
7.5% coupon rate, paid semiannually. The price of the bonds is $1,100. The bonds are callable in 5 years at
a call price of $1,050. Round your answers to two decimal places.
What is their yield to maturity?
%
What is their yield to call?
%
3. The real risk-free rate is 2%, and inflation is expected to be 2% for the next 2 years. A 2-year Treasury
security yields 5.1%. What is the maturity risk premium for the 2-year security?
%
4. Assume that the real risk-free rate, r*, is 2% and that inflation is expected to be 7% in Year 1, 6% in
Year 2, and 3% thereafter. Assume also that all Treasury securities are highly liquid and free of default risk.
If 2-year and 5-year Treasury notes both yield 10%, what is the difference in the maturity risk premiums
(MRPs) on the two notes; that is, what is MRP5 minus MRP2? Round your answer to two decimal places.
%
5. Jackson Corporation’s bonds have 6 years remaining to maturity. Interest is paid annually, the bonds
have a $1,000 par value, and the coupon interest rate is 12%. The bonds have a yield to maturity of 11%.
What is the current market price of these bonds? Round your answer to the nearest cent.
$
6. Renfro Rentals has issued bonds that have a 11% coupon rate, payable semiannually. The bonds mature
in 18 years, have a face value of $1,000, and a yield to maturity of 7.5%. What is the price of the bonds?
Round your answer to the nearest cent.
$
7. Wilson Wonders’s bonds have 12 years remaining to maturity. Interest is paid annually, the bonds have a
$1,000 par value, and the coupon interest rate is 10%. The bonds sell at a price of $850. What is their yield
to maturity? Round your answer to two decimal places.
%
8. A bond that matures in 10 years sells for $1,190.The bond has a face value of $1,000 and a yield to
maturity of 9.7489%. The bond pays coupons semiannually. What is the bond’s current yield? Round your
answer to two decimal places.
%