Case responses

Chapter

Tool Kit			Chapter 5			10/27/15
			Bonds, Bond Valuation, and Interest Rates
The value of any financial asset is the present value of the asset's expected 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.
5-3 Bond Valuation
A bond has a 15-year maturity, a 9% annual coupon, and a $1,000 par 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?
We list the key features of the bond in the INPUT section of Table 5-1.
Figure 5-1
Finding the Value of MicroDrive Inc.'s Bond (VB)
INPUTS:
	Years to maturity = N =	15
	Coupon payment = INT =	$90
	Par value = M =	$1,000
	Required return = rd =	9%
1. Step-by-Step: Divide each cash flow by (1 + rd)t
Year (t)	Coupon Payment	PV of Coupon Payment	Par Value	PV of Par Value
1	$90	$82.57
2	$90	$75.75
3	$90	$69.50
4	$90	$63.76
5	$90	$58.49
6	$90	$53.66
7	$90	$49.23
8	$90	$45.17
9	$90	$41.44
10	$90	$38.02
11	$90	$34.88
12	$90	$32.00
13	$90	$29.36
14	$90	$26.93
15	$90	$24.71	$1,000	$274.54
	Total =	$725.46
			VB = PV of all coupon payments + PV of par value =	$1,000.00
	Inputs:	15	0		90	1000
2. Financial Calculator:		N	I/YR	PV	PMT	FV
	Output:			−$1,000.00
3. Excel:		PV function:	PVN =	=PV(Rate,Nper,Pmt,Fv,Type)
		Fixed inputs:	PVN =	=PV(9%,15,90,1000)		−$1,000.00
		Cell references:	PVN =	=PV(C24,C21,C22,C23)		−$1,000.00
Bond Prices 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) =				1/1/16
Maturity date =				12/31/30
Coupon rate =				9.00%
Required return, rd =				9.00%
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
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 $100 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 =				$999.99	See comment. Mike Ehrhardt: Note: the value based on the PRICE function is actually a bit lower than the par value because the function finds the price at the end of the settlement day, which means the times to the future payments are short by 1 day.
Using the PRICE function with inputs that are not cell references:
Value of bond based on $100 face value =				=PRICE(DATE(2016,1,1),DATE(2030,12,31),9%,9%,100,1,1)
Value of bond based on $100 face value =				100.00
Value of bond in dollars based on $1,000 face value =				$999.99	See comment. Mike Ehrhardt: Note: the value based on the PRICE function is actually a bit lower than the par value because the function finds the price at the end of the settlement day, which means the times to the future payments are short by 1 day.
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 the cells with the red font, and then put the formula =-G53 in cell B98, then select the range of yellow cells. 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 C24 the place where the going rate is inputted. Click OK to complete the operation and get the table.
Going rate, r:	$1,000
0%	$2,350.00
4%	$1,555.92
9%	$1,000.00
14%	$692.89
20%	$485.70
30%	$313.68
We can use the data table to construct a graph that shows the bond's sensitivity to changing rates.
5-4 Changes in Bond Values over Time
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 15 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	4%	9%	14%
15	$1,555.92	$1,000.00	$692.89
14	$1,528.16	$1,000.00	$699.90
13	$1,499.28	$1,000.00	$707.88
12	$1,469.25	$1,000.00	$716.99
11	$1,438.02	$1,000.00	$727.36
10	$1,405.54	$1,000.00	$739.19
9	$1,371.77	$1,000.00	$752.68
8	$1,336.64	$1,000.00	$768.06
7	$1,300.10	$1,000.00	$785.58
6	$1,262.11	$1,000.00	$805.57
5	$1,222.59	$1,000.00	$828.35
4	$1,181.49	$1,000.00	$854.31
3	$1,138.75	$1,000.00	$883.92
2	$1,094.30	$1,000.00	$917.67
1	$1,048.08	$1,000.00	$956.14
0	$1,000.00	$1,000.00	$1,000.00
Figure 5-2
Time Path of the Value of a 9% Coupon, $1,000 Par Value Bond When Interest Rates Are 4%, 9%, and 14%
									Series Titles:
									rd Falls and Stays at 4% (Premium Bond)
									rd = Coupon Rate = 9% (Par Bond)
									rd Rises and Stays at 14% (Discount Bond)
If 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 =	4%
Remaining Years Until Maturity	Years After Issue	Bond Price	Return Due to Coupon Payment	Return Due to Price Change	Total Return		Fall in Price from Previous Year
15	0	$1,555.92
14	1	$1,528.16	5.78%	-1.78%	4.00%
13	2	$1,499.28	5.89%	-1.89%	4.00%		$28.88
12	3	$1,469.25	6.00%	-2.00%	4.00%		$30.03
11	4	$1,438.02	6.13%	-2.13%	4.00%		$31.23
10	5	$1,405.54	6.26%	-2.26%	4.00%		$32.48
9	6	$1,371.77	6.40%	-2.40%	4.00%		$33.77
8	7	$1,336.64	6.56%	-2.56%	4.00%		$35.13
7	8	$1,300.10	6.73%	-2.73%	4.00%		$36.54
6	9	$1,262.11	6.92%	-2.92%	4.00%		$37.99
5	10	$1,222.59	7.13%	-3.13%	4.00%		$39.52
4	11	$1,181.49	7.36%	-3.36%	4.00%		$41.10
3	12	$1,138.75	7.62%	-3.62%	4.00%		$42.74
2	13	$1,094.30	7.90%	-3.90%	4.00%		$44.45
1	14	$1,048.08	8.22%	-4.22%	4.00%		$46.22
0	15	$1,000.00	8.59%	-4.59%	4.00%		$48.08
Market rate =	9%
Remaining Years Until Maturity	N	Bond Price	Return Due to Coupon Payment	Return Due to Price Change	Total Return		Fall in Price from Previous Year
15	0	$1,000.00
14	1	$1,000.00	9.00%	-0.00%	9.00%
13	2	$1,000.00	9.00%	0.00%	9.00%		$0.00
12	3	$1,000.00	9.00%	-0.00%	9.00%		$0.00
11	4	$1,000.00	9.00%	0.00%	9.00%		$0.00
10	5	$1,000.00	9.00%	-0.00%	9.00%		$0.00
9	6	$1,000.00	9.00%	0.00%	9.00%		$0.00
8	7	$1,000.00	9.00%	-0.00%	9.00%		$0.00
7	8	$1,000.00	9.00%	0.00%	9.00%		$0.00
6	9	$1,000.00	9.00%	-0.00%	9.00%		$0.00
5	10	$1,000.00	9.00%	0.00%	9.00%		$0.00
4	11	$1,000.00	9.00%	-0.00%	9.00%		$0.00
3	12	$1,000.00	9.00%	0.00%	9.00%		$0.00
2	13	$1,000.00	9.00%	0.00%	9.00%		$0.00
1	14	$1,000.00	9.00%	-0.00%	9.00%		$0.00
0	15	$1,000.00	9.00%	0.00%	9.00%		$0.00
Market rate =	14%
Remaining Years Until Maturity	N	Bond Price	Return Due to Coupon Payment	Return Due to Price Change	Total Return		Increase in Price from Previous Year
15	0	$692.89
14	1	$699.90	12.99%	1.01%	14.00%
13	2	$707.88	12.86%	1.14%	14.00%		$7.99
12	3	$716.99	12.71%	1.29%	14.00%		$9.10
11	4	$727.36	12.55%	1.45%	14.00%		$10.38
10	5	$739.19	12.37%	1.63%	14.00%		$11.83
9	6	$752.68	12.18%	1.82%	14.00%		$13.49
8	7	$768.06	11.96%	2.04%	14.00%		$15.38
7	8	$785.58	11.72%	2.28%	14.00%		$17.53
6	9	$805.57	11.46%	2.54%	14.00%		$19.98
5	10	$828.35	11.17%	2.83%	14.00%		$22.78
4	11	$854.31	10.87%	3.13%	14.00%		$25.97
3	12	$883.92	10.53%	3.47%	14.00%		$29.60
2	13	$917.67	10.18%	3.82%	14.00%		$33.75
1	14	$956.14	9.81%	4.19%	14.00%		$38.47
0	15	$1,000.00	9.41%	4.59%	14.00%		$43.86
5-5 Bonds with Semiannual Coupons
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.
Suppose MicroDrive's bond pays interest semiannually. What is its price if the the price if there are still 15 years until maturity but rd has fallend to 4%?
Use the PV 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).
Semiannual pmt = $90/2 =		$45.00 Bart Kreps: PMT=$50, because of semiannual payments (100 ÷ 2) = 50
Current price:		$1,000.00
Periodic rate = 4%/2 =		2.0% Christopher Buzzard: I=2.5%, because of semi-annual compounding (5%/2 = 2.5%).
	PV =	$1,559.91	if semiannual payments
	PV =	$1,555.92	if annual payments
Note that the bond is now more valuable with semiannual paymens because interest payments come in slightly earlier.
5-6 Bond Yields
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, 9% annual coupon, $1,000 par value bond at a price of $1,528.16.
Use the Rate function to solve the problem.
Years to Mat:	14
Coupon rate:	9%
Annual Pmt:	$90.00
Current price:	$1,528.16
Par value = FV:	$1,000.00
	Going rate, rd =YTM=	4.00%
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 14 years until maturity. Suppose the actual current date is 12/31/2016, so the bond matures on 12/31/2030.
Here is the data for the bond.
Settlement date (day on which you find bond price) =				12/31/16
Maturity date =				12/31/30
Coupon rate =				9.00%
Price = bond price per $100 par value =				$152.82
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
Using the YIELD function with inputs that are cell references:
			Yield to maturity =	4.0%	=YIELD(E336,E337,E338,E339,E340,E341,E342)
Yield to Call
The yield to call is the rate of return investors will receive if their bonds are called. If the issuer has the right to call the bonds, and if interest rates fall, then it would be logical for the issuer to call the bonds and replace them with new bonds that carry a lower coupon. The yield to call (YTC) 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, 9% 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 9% to 4% causing the value of the bond to rise to $1,528.16. 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:	9 Christopher 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:	9%
Annual Pmt:	$90.00
Current price:	$1,528.16
Call price = FV	$1,100.00
Par value	$1,000.00
	Rate = I = YTC =	3.15%	=RATE(B362,B364,-B365,B366)
This bond's YTM is 4%, but its YTC is only 3.15%. Which would an investor be more likely to actually earn?
This company could call the old bonds, which pay $90 per year, and replace them with bonds that pay somewhere in the vicinity of $40 (or maybe even only $31.50) 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, 9% 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:	9%
Annual Pmt:	$90.00
Current price:	$985.00
	Current Yield =	9.14%
The current yield provides information on a bond's cash return, but it gives no indication of the bond's total return. To see this, consider a zero coupon bond. Since zeros pay no coupon, the current yield is zero because there is no interest income. However, the zero appreciates through time, and its total return clearly exceeds zero.
5-7 The Pre-Tax Cost of Debt: Determinants of Market Interest Rates
Quoted market interest rate = rd = r* + IP + MRP + DRP + LP
r* =	Real risk-free rate of interest
IP =	Inflation premium
MRP =	Maturity risk premium
DRP =	Default risk premium
LP =	Liquidity premium
5-8 The Risk-Free Interest Rate: Nominal (rRF) and Real (r*)
	rRF =	Market rate on a U.S. Treasury security
	rRF (short-term)=	Market rate on a U.S. Treasury bill
	rRF (long-term)=	Market rate on a U.S. Treasury bond
	r* =	Real risk-free rate of interest
	r* ≈	Yield on short-term (1-year) U.S. Treasury Inflation-Protected Security (TIPS)
	r* ≈	-0.56%	February, 2015
5-9 The Inflation Premium (IP)
				Maturity
			1 Year	5 Years	20 Years
		Non-indexed U.S. Treasury Bond	0.22%	1.52%	2.40%
		TIPS	-0.56%	-0.07%	0.32%
		Inflation premium	0.78%	1.59%	2.08%	February, 2015
The exact premium would found by solving (1+r*)(1+IP) = (1+rd)
				Maturity
			1 Year	5 Years	20 Years
		Inflation premium	0.78%	1.59%	2.07%
5-10 The Maturity Risk Premium (MRP)
Bonds are exposed to interest rate risk and reinvestment rate risk. The net effect is the maturity risk premium.
Interest Rate Risk
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.
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.
Use the PV function, along with a two variable Data Table, to show the bonds' price sensitivity.
Coupon rate:		10%
Payment		$100.00
Par value		$1,000.00
Maturity		1
Going rate = r = YTM		10%
Value of bond:		$1,000.00
	Value of the Bond Under Different Conditions
Going rate, r	Years to Maturity
$1,000.00	1	25
0%	$1,100.00	$3,500.00
5%	$1,047.62	$1,704.70
10%	$1,000.00	$1,000.00
15%	$956.52	$676.79
20%	$916.67	$505.24
25%	$880.00	$402.27
Figure 5-3
Value of Long- and Short-Term 10% Annual Coupon Bonds at Different Market Interest Rates
5-11 The Default Risk Premium (DRP)
Table 5-1
Bond Ratings, Default Risk, and Yields
Rating Agencya		Percent defaulting within:b		Median Ratiosc		Percent upgraded or downgraded in 2013:b
S&P and Fitch	Moody’s	1 year	5 years	Return on capital	Total debt/Total capital	Down	Up	Yieldd				Spreads
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)		T-bond	2.11
Investment grade bonds:										AAA	2.67	0.56
AAA	Aaa	0.00	0.00	27.6	12.4	0.00	NA	2.67		AA	2.83	0.72
AA	Aa	0.03	0.19	27.0	28.3	0.95	0.00	2.83		A	3.02	0.91
A	A	0.08	0.71	17.5	37.5	4.19	2.03	3.02		BBB	4.29	2.18
BBB	Baa	0.19	2.36	13.4	42.5	3.91	1.37	4.29
Junk bonds:										BB	5.74	3.63
BB	Ba	1.09	6.95	11.3	53.7	4.60	5.57	5.74		B	6.06	3.95
B	B	1.94	10.88	8.7	75.9	3.69	5.37	6.06		CCC	8.08	5.97
CCC	Caa	23.51	39.58	3.2	113.5	29.41	8.82	8.08
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, downgrades, and upgrades are from Fitch Ratings Global Corporate Finance 2013 Transition and Default Study, March 17, 2014: see www.fitchratings.com/creditdesk/reports/report_frame.cfm?rpt_id=738797.
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.pdf.
dComposite yields for 10-year AAA, AA, and A bonds can be found at http://finance.yahoo.com/bonds/composite_bond_rates. Representative yields for 10-year BBB, BB, B, and CCC bonds can be found using the bond screener at http://screener.finance.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.
																			Keep start date at 2001.
Figure 5-4																			This uses the FRED add-in available at https://research.stlouisfed.org/fred-addin/install_windows.html
Bond Spreads																			Data for Figure 5-4
																			Sources: FRED monthly data. http://research.stlouisfed.org/fred2/
							Data for chart to right		Data for chart to right		Data for chart to right		Data for chart to right		Data for chart to right		Data for chart to right		DATE	AAA-Bond Ehrhardt, Michael C: Ehrhardt, Michael C: Moody's Aaa bond. Monthly, average of daily values.		BAA Bond Ehrhardt, Michael C: Ehrhardt, Michael C: Moody's Baa bond. Monthly, average of daily values.		10-Year T-bond Ehrhardt, Michael C: Ehrhardt, Michael C: DGS10. Monthly, average of daily values. Note: same data used in box on fear and rationality.	AAA - T-bond	BAA - T-bond
																			2001-01	7.15	1/1/01	7.93	2001-01-01	5.16	1.99	2.77
																			2001-02	7.10	2/1/01	7.87	2001-02-01	5.10	2.00	2.77
																			2001-03	6.98	3/1/01	7.84	2001-03-01	4.89	2.09	2.95
																			2001-04	7.20	4/1/01	8.07	2001-04-01	5.14	2.06	2.93
																			2001-05	7.29	5/1/01	8.07	2001-05-01	5.39	1.90	2.68
																			2001-06	7.18	6/1/01	7.97	2001-06-01	5.28	1.90	2.69
																			2001-07	7.13	7/1/01	7.97	2001-07-01	5.24	1.89	2.73
																			2001-08	7.02	8/1/01	7.85	2001-08-01	4.97	2.05	2.88
																			2001-09	7.17	9/1/01	8.03	2001-09-01	4.73	2.44	3.30
																			2001-10	7.03	10/1/01	7.91	2001-10-01	4.57	2.46	3.34
																			2001-11	6.97	11/1/01	7.81	2001-11-01	4.65	2.32	3.16
																			2001-12	6.77	12/1/01	8.05	2001-12-01	5.09	1.68	2.96
																			2002-01	6.55	1/1/02	7.87	2002-01-01	5.04	1.51	2.83
																			2002-02	6.51	2/1/02	7.89	2002-02-01	4.91	1.60	2.98
																			2002-03	6.81	3/1/02	8.11	2002-03-01	5.28	1.53	2.83
																			2002-04	6.76	4/1/02	8.03	2002-04-01	5.21	1.55	2.82
																			2002-05	6.75	5/1/02	8.09	2002-05-01	5.16	1.59	2.93
																			2002-06	6.63	6/1/02	7.95	2002-06-01	4.93	1.70	3.02
																			2002-07	6.53	7/1/02	7.90	2002-07-01	4.65	1.88	3.25
																			2002-08	6.37	8/1/02	7.58	2002-08-01	4.26	2.11	3.32
																			2002-09	6.15	9/1/02	7.40	2002-09-01	3.87	2.28	3.53
																			2002-10	6.32	10/1/02	7.73	2002-10-01	3.94	2.38	3.79
																			2002-11	6.31	11/1/02	7.62	2002-11-01	4.05	2.26	3.57
																			2002-12	6.21	12/1/02	7.45	2002-12-01	4.03	2.18	3.42
																			2003-01	6.17	1/1/03	7.35	2003-01-01	4.05	2.12	3.30
																			2003-02	5.95	2/1/03	7.06	2003-02-01	3.90	2.05	3.16
																			2003-03	5.89	3/1/03	6.95	2003-03-01	3.81	2.08	3.14
																			2003-04	5.74	4/1/03	6.85	2003-04-01	3.96	1.78	2.89
																			2003-05	5.22	5/1/03	6.38	2003-05-01	3.57	1.65	2.81
																			2003-06	4.97	6/1/03	6.19	2003-06-01	3.33	1.64	2.86
																			2003-07	5.49	7/1/03	6.62	2003-07-01	3.98	1.51	2.64
								Data for box on spreads during financial crisis.											2003-08	5.88	8/1/03	7.01	2003-08-01	4.45	1.43	2.56
BofA Merrill Lynch US High Yield Master II Effective Yield and TED Spread								Month	10-Year T-bond Ehrhardt, Michael C: Ehrhardt, Michael C: DGS10. Monthly, average of daily values. Note: same data used in Figure 5-4.		BofA Merrill Lynch US High Yield Master II Effective Yield Ehrhardt, Michael C: Ehrhardt, Michael C: BAMLH0A0HYM2EY. Monthly, average of daily.		3-month LIBOR Ehrhardt, Michael C: Ehrhardt, Michael C: USD3MTD156N. Monthly, average of daily.	Christopher Buzzard: N is equal to 9, because the bond can be called 10 years after issuance and one year has already gone by.														3-month T-Bill Ehrhardt, Michael C: Ehrhardt, Michael C: TB3MS. Monthly.					Ehrhardt, Michael C: Ehrhardt, Michael C: Moody's Aaa bond. Monthly, average of daily values.		Ehrhardt, Michael C: Ehrhardt, Michael C: Moody's Baa bond. Monthly, average of daily values.		Ehrhardt, Michael C: Ehrhardt, Michael C: DGS10. Monthly, average of daily values. Note: same data used in box on fear and rationality.	Mike Ehrhardt: Note: the value based on the PRICE function is actually a bit lower than the par value because the function finds the price at the end of the settlement day, which means the times to the future payments are short by 1 day.	Mike Ehrhardt: Note: the value based on the PRICE function is actually a bit lower than the par value because the function finds the price at the end of the settlement day, which means the times to the future payments are short by 1 day.	Christopher Buzzard: N=30, because of semi-annual compounding (15*2 = 30).	Bart Kreps: PMT=$50, because of semiannual payments (100 ÷ 2) = 50	Christopher Buzzard: I=2.5%, because of semi-annual compounding (5%/2 = 2.5%).														Hi-Yield Spread	TED Spread: 3-month LIBOR - 3-month T-Bill		2003-09	5.72	9/1/03	6.79	2003-09-01	4.27	1.45	2.52
					Data to Right of Chart			2001-01	5.16	1/1/01	13.56	1/1/01	5.70	1/1/01	5.15	8.40	0.55		2003-10	5.70	10/1/03	6.73	2003-10-01	4.29	1.41	2.44
								2001-02	5.10	2/1/01	12.66	2/1/01	5.35	2/1/01	4.88	7.56	0.47		2003-11	5.65	11/1/03	6.66	2003-11-01	4.30	1.35	2.36
								2001-03	4.89	3/1/01	12.74	3/1/01	4.96	3/1/01	4.42	7.85	0.54		2003-12	5.62	12/1/03	6.60	2003-12-01	4.27	1.35	2.33
								2001-04	5.14	4/1/01	13.37	4/1/01	4.61	4/1/01	3.87	8.23	0.74		2004-01	5.54	1/1/04	6.44	2004-01-01	4.15	1.39	2.29
								2001-05	5.39	5/1/01	12.78	5/1/01	4.10	5/1/01	3.62	7.39	0.48		2004-02	5.50	2/1/04	6.27	2004-02-01	4.08	1.42	2.19
								2001-06	5.28	6/1/01	13.03	6/1/01	3.83	6/1/01	3.49	7.75	0.34		2004-03	5.33	3/1/04	6.11	2004-03-01	3.83	1.50	2.28
								2001-07	5.24	7/1/01	13.17	7/1/01	3.75	7/1/01	3.51	7.93	0.24		2004-04	5.73	4/1/04	6.46	2004-04-01	4.35	1.38	2.11
								2001-08	4.97	8/1/01	12.71	8/1/01	3.57	8/1/01	3.36	7.74	0.21		2004-05	6.04	5/1/04	6.75	2004-05-01	4.72	1.32	2.03
								2001-09	4.73	9/1/01	13.51	9/1/01	3.03	9/1/01	2.64	8.78	0.39		2004-06	6.01	6/1/04	6.78	2004-06-01	4.73	1.28	2.05
								2001-10	4.57	10/1/01	13.81	10/1/01	2.40	10/1/01	2.16	9.24	0.24		2004-07	5.82	7/1/04	6.62	2004-07-01	4.50	1.32	2.12
								2001-11	4.65	11/1/01	12.92	11/1/01	2.10	11/1/01	1.87	8.27	0.23		2004-08	5.65	8/1/04	6.46	2004-08-01	4.28	1.37	2.18
								2001-12	5.09	12/1/01	12.85	12/1/01	1.92	12/1/01	1.69	7.76	0.23		2004-09	5.46	9/1/04	6.27	2004-09-01	4.13	1.33	2.14
								2002-01	5.04	1/1/02	12.63	1/1/02	1.82	1/1/02	1.65	7.59	0.17		2004-10	5.47	10/1/04	6.21	2004-10-01	4.10	1.37	2.11
								2002-02	4.91	2/1/02	12.46	2/1/02	1.90	2/1/02	1.73	7.55	0.17		2004-11	5.52	11/1/04	6.20	2004-11-01	4.19	1.33	2.01
								2002-03	5.28	3/1/02	12.15	3/1/02	1.99	3/1/02	1.79	6.87	0.20		2004-12	5.47	12/1/04	6.15	2004-12-01	4.23	1.24	1.92
								2002-04	5.21	4/1/02	11.85	4/1/02	1.97	4/1/02	1.72	6.64	0.25		2005-01	5.36	1/1/05	6.02	2005-01-01	4.22	1.14	1.80
								2002-05	5.16	5/1/02	11.58	5/1/02	1.90	5/1/02	1.73	6.42	0.17		2005-02	5.20	2/1/05	5.82	2005-02-01	4.17	1.03	1.65
								2002-06	4.93	6/1/02	12.23	6/1/02	1.88	6/1/02	1.70	7.30	0.18		2005-03	5.40	3/1/05	6.06	2005-03-01	4.50	0.90	1.56
								2002-07	4.65	7/1/02	13.30	7/1/02	1.85	7/1/02	1.68	8.65	0.17		2005-04	5.33	4/1/05	6.05	2005-04-01	4.34	0.99	1.71
								2002-08	4.26	8/1/02	13.30	8/1/02	1.77	8/1/02	1.62	9.04	0.15		2005-05	5.15	5/1/05	6.01	2005-05-01	4.14	1.01	1.87
								2002-09	3.87	9/1/02	13.08	9/1/02	1.80	9/1/02	1.63	9.21	0.17		2005-06	4.96	6/1/05	5.86	2005-06-01	4.00	0.96	1.86
								2002-10	3.94	10/1/02	13.86	10/1/02	1.78	10/1/02	1.58	9.92	0.20		2005-07	5.06	7/1/05	5.95	2005-07-01	4.18	0.88	1.77
								2002-11	4.05	11/1/02	12.87	11/1/02	1.46	11/1/02	1.23	8.82	0.23		2005-08	5.09	8/1/05	5.96	2005-08-01	4.26	0.83	1.70
5-12 The Liquidity Premium (LP)								2002-12	4.03	12/1/02	12.19	12/1/02	1.41	12/1/02	1.19	8.16	0.22		2005-09	5.13	9/1/05	6.03	2005-09-01	4.20	0.93	1.83
								2003-01	4.05	1/1/03	11.41	1/1/03	1.37	1/1/03	1.17	7.36	0.20		2005-10	5.35	10/1/05	6.30	2005-10-01	4.46	0.89	1.84
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.								2003-02	3.90	2/1/03	11.50	2/1/03	1.34	2/1/03	1.17	7.60	0.17		2005-11	5.42	11/1/05	6.39	2005-11-01	4.54	0.88	1.85
								2003-03	3.81	3/1/03	11.05	3/1/03	1.29	3/1/03	1.13	7.24	0.16		2005-12	5.37	12/1/05	6.32	2005-12-01	4.47	0.90	1.85
								2003-04	3.96	4/1/03	10.16	4/1/03	1.30	4/1/03	1.13	6.20	0.17		2006-01	5.29	1/1/06	6.24	2006-01-01	4.42	0.87	1.82
								2003-05	3.57	5/1/03	9.39	5/1/03	1.28	5/1/03	1.07	5.82	0.21		2006-02	5.35	2/1/06	6.27	2006-02-01	4.57	0.78	1.70
								2003-06	3.33	6/1/03	8.90	6/1/03	1.12	6/1/03	0.92	5.57	0.20		2006-03	5.53	3/1/06	6.41	2006-03-01	4.72	0.81	1.69
5-13 The Term Structure of Interest Rates								2003-07	3.98	7/1/03	8.96	7/1/03	1.11	7/1/03	0.90	4.98	0.21		2006-04	5.84	4/1/06	6.68	2006-04-01	4.99	0.85	1.69
								2003-08	4.45	8/1/03	9.40	8/1/03	1.13	8/1/03	0.95	4.95	0.18		2006-05	5.95	5/1/06	6.75	2006-05-01	5.11	0.84	1.64
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.								2003-09	4.27	9/1/03	8.79	9/1/03	1.14	9/1/03	0.94	4.52	0.20		2006-06	5.89	6/1/06	6.78	2006-06-01	5.11	0.78	1.67
								2003-10	4.29	10/1/03	8.35	10/1/03	1.16	10/1/03	0.92	4.06	0.24		2006-07	5.85	7/1/06	6.76	2006-07-01	5.09	0.76	1.67
								2003-11	4.30	11/1/03	8.13	11/1/03	1.17	11/1/03	0.93	3.83	0.24		2006-08	5.68	8/1/06	6.59	2006-08-01	4.88	0.80	1.71
								2003-12	4.27	12/1/03	7.78	12/1/03	1.17	12/1/03	0.90	3.51	0.27		2006-09	5.51	9/1/06	6.43	2006-09-01	4.72	0.79	1.71
								2004-01	4.15	1/1/04	7.31	1/1/04	1.13	1/1/04	0.88	3.16	0.25		2006-10	5.51	10/1/06	6.42	2006-10-01	4.73	0.78	1.69
								2004-02	4.08	2/1/04	7.55	2/1/04	1.12	2/1/04	0.93	3.47	0.19		2006-11	5.33	11/1/06	6.20	2006-11-01	4.60	0.73	1.60
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.								2004-03	3.83	3/1/04	7.47	3/1/04	1.11	3/1/04	0.94	3.64	0.17		2006-12	5.32	12/1/06	6.22	2006-12-01	4.56	0.76	1.66
								2004-04	4.35	4/1/04	7.60	4/1/04	1.15	4/1/04	0.94	3.25	0.21		2007-01	5.40	1/1/07	6.34	2007-01-01	4.76	0.64	1.58
								2004-05	4.72	5/1/04	8.30	5/1/04	1.25	5/1/04	1.02	3.58	0.23		2007-02	5.39	2/1/07	6.28	2007-02-01	4.72	0.67	1.56
	Maturity (yrs)	Mar-80	Feb-00	Feb-15				2004-06	4.73	6/1/04	8.18	6/1/04	1.50	6/1/04	1.27	3.45	0.23		2007-03	5.30	3/1/07	6.27	2007-03-01	4.56	0.74	1.71
	0.5	15.0%	6.0%	0.07%				2004-07	4.50	7/1/04	7.92	7/1/04	1.63	7/1/04	1.33	3.42	0.30		2007-04	5.47	4/1/07	6.39	2007-04-01	4.69	0.78	1.70
	1	14.0%	6.2%	0.23%				2004-08	4.28	8/1/04	7.79	8/1/04	1.73	8/1/04	1.48	3.51	0.25		2007-05	5.47	5/1/07	6.39	2007-05-01	4.75	0.72	1.64
	5	13.5%	6.7%	1.52%				2004-09	4.13	9/1/04	7.49	9/1/04	1.90	9/1/04	1.65	3.36	0.25		2007-06	5.79	6/1/07	6.70	2007-06-01	5.10	0.69	1.60
	10	12.8%	6.7%	2.11%				2004-10	4.10	10/1/04	7.34	10/1/04	2.08	10/1/04	1.76	3.24	0.32		2007-07	5.73	7/1/07	6.65	2007-07-01	5.00	0.73	1.65
	30	12.3%	6.3%	2.73%				2004-11	4.19	11/1/04	7.06	11/1/04	2.31	11/1/04	2.07	2.87	0.24		2007-08	5.79	8/1/07	6.65	2007-08-01	4.67	1.12	1.98
								2004-12	4.23	12/1/04	6.95	12/1/04	2.50	12/1/04	2.19	2.72	0.31		2007-09	5.74	9/1/07	6.59	2007-09-01	4.52	1.22	2.07
From this data, we can plot three line graphs. Each line graph represents the U.S. Treasury yield curve at a different point in time.								2005-01	4.22	1/1/05	7.11	1/1/05	2.67	1/1/05	2.33	2.89	0.34		2007-10	5.66	10/1/07	6.48	2007-10-01	4.53	1.13	1.95
								2005-02	4.17	2/1/05	6.97	2/1/05	2.82	2/1/05	2.54	2.80	0.28		2007-11	5.44	11/1/07	6.40	2007-11-01	4.15	1.29	2.25
								2005-03	4.50	3/1/05	7.27	3/1/05	3.02	3/1/05	2.74	2.77	0.28		2007-12	5.49	12/1/07	6.65	2007-12-01	4.10	1.39	2.55
Figure 5-5								2005-04	4.34	4/1/05	7.91	4/1/05	3.15	4/1/05	2.78	3.57	0.37		2008-01	5.33	1/1/08	6.54	2008-01-01	3.74	1.59	2.80
U.S. Treasury Bond Interest Rates on Different Dates								2005-05	4.14	5/1/05	8.20	5/1/05	3.27	5/1/05	2.84	4.06	0.43		2008-02	5.53	2/1/08	6.82	2008-02-01	3.74	1.79	3.08
								2005-06	4.00	6/1/05	7.77	6/1/05	3.43	6/1/05	2.97	3.77	0.46		2008-03	5.51	3/1/08	6.89	2008-03-01	3.51	2.00	3.38
								2005-07	4.18	7/1/05	7.57	7/1/05	3.61	7/1/05	3.22	3.39	0.39		2008-04	5.55	4/1/08	6.97	2008-04-01	3.68	1.87	3.29
								2005-08	4.26	8/1/05	7.56	8/1/05	3.80	8/1/05	3.44	3.30	0.36		2008-05	5.57	5/1/08	6.93	2008-05-01	3.88	1.69	3.05
								2005-09	4.20	9/1/05	7.74	9/1/05	3.91	9/1/05	3.42	3.54	0.49		2008-06	5.68	6/1/08	7.07	2008-06-01	4.10	1.58	2.97
								2005-10	4.46	10/1/05	8.00	10/1/05	4.17	10/1/05	3.71	3.54	0.46		2008-07	5.67	7/1/08	7.16	2008-07-01	4.01	1.66	3.15
								2005-11	4.54	11/1/05	8.14	11/1/05	4.35	11/1/05	3.88	3.60	0.47		2008-08	5.64	8/1/08	7.15	2008-08-01	3.89	1.75	3.26
								2005-12	4.47	12/1/05	8.12	12/1/05	4.49	12/1/05	3.89	3.65	0.60		2008-09	5.65	9/1/08	7.31	2008-09-01	3.69	1.96	3.62
								2006-01	4.42	1/1/06	7.96	1/1/06	4.61	1/1/06	4.24	3.54	0.37		2008-10	6.28	10/1/08	8.88	2008-10-01	3.81	2.47	5.07
								2006-02	4.57	2/1/06	7.96	2/1/06	4.76	2/1/06	4.43	3.39	0.33		2008-11	6.12	11/1/08	9.21	2008-11-01	3.53	2.59	5.68
								2006-03	4.72	3/1/06	8.03	3/1/06	4.92	3/1/06	4.51	3.31	0.41		2008-12	5.05	12/1/08	8.43	2008-12-01	2.42	2.63	6.01
								2006-04	4.99	4/1/06	8.04	4/1/06	5.07	4/1/06	4.60	3.05	0.47		2009-01	5.05	1/1/09	8.14	2009-01-01	2.52	2.53	5.62
								2006-05	5.11	5/1/06	8.09	5/1/06	5.19	5/1/06	4.72	2.98	0.47		2009-02	5.27	2/1/09	8.08	2009-02-01	2.87	2.40	5.21
								2006-06	5.11	6/1/06	8.40	6/1/06	5.38	6/1/06	4.79	3.29	0.59		2009-03	5.50	3/1/09	8.42	2009-03-01	2.82	2.68	5.60
								2006-07	5.09	7/1/06	8.47	7/1/06	5.50	7/1/06	4.95	3.38	0.55		2009-04	5.39	4/1/09	8.39	2009-04-01	2.93	2.46	5.46
								2006-08	4.88	8/1/06	8.30	8/1/06	5.42	8/1/06	4.96	3.42	0.46		2009-05	5.54	5/1/09	8.06	2009-05-01	3.29	2.25	4.77
								2006-09	4.72	9/1/06	8.15	9/1/06	5.38	9/1/06	4.81	3.43	0.57		2009-06	5.61	6/1/09	7.50	2009-06-01	3.72	1.89	3.78
								2006-10	4.73	10/1/06	7.99	10/1/06	5.37	10/1/06	4.92	3.26	0.45		2009-07	5.41	7/1/09	7.09	2009-07-01	3.56	1.85	3.53
								2006-11	4.60	11/1/06	7.76	11/1/06	5.37	11/1/06	4.94	3.16	0.43		2009-08	5.26	8/1/09	6.58	2009-08-01	3.59	1.67	2.99
								2006-12	4.56	12/1/06	7.59	12/1/06	5.36	12/1/06	4.85	3.03	0.51		2009-09	5.13	9/1/09	6.31	2009-09-01	3.40	1.73	2.91
								2007-01	4.76	1/1/07	7.55	1/1/07	5.36	1/1/07	4.98	2.79	0.38		2009-10	5.15	10/1/09	6.29	2009-10-01	3.39	1.76	2.90
								2007-02	4.72	2/1/07	7.37	2/1/07	5.36	2/1/07	5.03	2.65	0.33		2009-11	5.19	11/1/09	6.32	2009-11-01	3.40	1.79	2.92
								2007-03	4.56	3/1/07	7.43	3/1/07	5.35	3/1/07	4.94	2.87	0.41		2009-12	5.26	12/1/09	6.37	2009-12-01	3.59	1.67	2.78
								2007-04	4.69	4/1/07	7.41	4/1/07	5.35	4/1/07	4.87	2.72	0.48		2010-01	5.26	1/1/10	6.25	2010-01-01	3.73	1.53	2.52
								2007-05	4.75	5/1/07	7.32	5/1/07	5.36	5/1/07	4.73	2.57	0.63		2010-02	5.35	2/1/10	6.34	2010-02-01	3.69	1.66	2.65
								2007-06	5.10	6/1/07	7.68	6/1/07	5.36	6/1/07	4.61	2.58	0.75		2010-03	5.27	3/1/10	6.27	2010-03-01	3.73	1.54	2.54
								2007-07	5.00	7/1/07	8.30	7/1/07	5.36	7/1/07	4.82	3.30	0.54		2010-04	5.29	4/1/10	6.25	2010-04-01	3.85	1.44	2.40
								2007-08	4.67	8/1/07	8.88	8/1/07	5.48	8/1/07	4.20	4.21	1.28		2010-05	4.96	5/1/10	6.05	2010-05-01	3.42	1.54	2.63
								2007-09	4.52	9/1/07	8.76	9/1/07	5.49	9/1/07	3.89	4.24	1.60		2010-06	4.88	6/1/10	6.23	2010-06-01	3.20	1.68	3.03
								2007-10	4.53	10/1/07	8.48	10/1/07	5.15	10/1/07	3.90	3.95	1.25		2010-07	4.72	7/1/10	6.01	2010-07-01	3.01	1.71	3.00
								2007-11	4.15	11/1/07	9.15	11/1/07	4.96	11/1/07	3.27	5.00	1.69		2010-08	4.49	8/1/10	5.66	2010-08-01	2.70	1.79	2.96
								2007-12	4.10	12/1/07	9.40	12/1/07	4.98	12/1/07	3.00	5.30	1.98		2010-09	4.53	9/1/10	5.66	2010-09-01	2.65	1.88	3.01
								2008-01	3.74	1/1/08	10.02	1/1/08	3.92	1/1/08	2.75	6.28	1.17		2010-10	4.68	10/1/10	5.72	2010-10-01	2.54	2.14	3.18
								2008-02	3.74	2/1/08	10.31	2/1/08	3.09	2/1/08	2.12	6.57	0.97		2010-11	4.87	11/1/10	5.92	2010-11-01	2.76	2.11	3.16
								2008-03	3.51	3/1/08	10.82	3/1/08	2.78	3/1/08	1.26	7.31	1.52		2010-12	5.02	12/1/10	6.10	2010-12-01	3.29	1.73	2.81
								2008-04	3.68	4/1/08	10.41	4/1/08	2.79	4/1/08	1.29	6.73	1.50		2011-01	5.04	1/1/11	6.09	2011-01-01	3.39	1.65	2.70
								2008-05	3.88	5/1/08	10.02	5/1/08	2.69	5/1/08	1.73	6.14	0.96		2011-02	5.22	2/1/11	6.15	2011-02-01	3.58	1.64	2.57
								2008-06	4.10	6/1/08	10.34	6/1/08	2.77	6/1/08	1.86	6.24	0.91		2011-03	5.13	3/1/11	6.03	2011-03-01	3.41	1.72	2.62
								2008-07	4.01	7/1/08	11.18	7/1/08	2.79	7/1/08	1.63	7.17	1.16		2011-04	5.16	4/1/11	6.02	2011-04-01	3.46	1.70	2.56
								2008-08	3.89	8/1/08	11.46	8/1/08	2.81	8/1/08	1.72	7.57	1.09		2011-05	4.96	5/1/11	5.78	2011-05-01	3.17	1.79	2.61
								2008-09	3.69	9/1/08	12.18	9/1/08	3.12	9/1/08	1.13	8.49	1.99		2011-06	4.99	6/1/11	5.75	2011-06-01	3.00	1.99	2.75
								2008-10	3.81	10/1/08	17.79	10/1/08	4.06	10/1/08	0.67	13.98	3.39		2011-07	4.93	7/1/11	5.76	2011-07-01	3.00	1.93	2.76
								2008-11	3.53	11/1/08	20.32	11/1/08	2.28	11/1/08	0.19	16.79	2.09		2011-08	4.37	8/1/11	5.36	2011-08-01	2.30	2.07	3.06
								2008-12	2.42	12/1/08	21.82	12/1/08	1.83	12/1/08	0.03	19.40	1.80		2011-09	4.09	9/1/11	5.27	2011-09-01	1.98	2.11	3.29
								2009-01	2.52	1/1/09	18.36	1/1/09	1.21	1/1/09	0.13	15.84	1.08		2011-10	3.98	10/1/11	5.37	2011-10-01	2.15	1.83	3.22
								2009-02	2.87	2/1/09	18.47	2/1/09	1.24	2/1/09	0.30	15.60	0.94		2011-11	3.87	11/1/11	5.14	2011-11-01	2.01	1.86	3.13
								2009-03	2.82	3/1/09	19.72	3/1/09	1.27	3/1/09	0.21	16.90	1.06		2011-12	3.93	12/1/11	5.25	2011-12-01	1.98	1.95	3.27
								2009-04	2.93	4/1/09	17.50	4/1/09	1.11	4/1/09	0.16	14.57	0.95		2012-01	3.85	1/1/12	5.23	2012-01-01	1.97	1.88	3.26
								2009-05	3.29	5/1/09	14.68	5/1/09	0.82	5/1/09	0.18	11.39	0.64		2012-02	3.85	2/1/12	5.14	2012-02-01	1.97	1.88	3.17
								2009-06	3.72	6/1/09	13.42	6/1/09	0.62	6/1/09	0.18	9.70	0.44		2012-03	3.99	3/1/12	5.23	2012-03-01	2.17	1.82	3.06
								2009-07	3.56	7/1/09	12.71	7/1/09	0.52	7/1/09	0.18	9.15	0.34		2012-04	3.96	4/1/12	5.19	2012-04-01	2.05	1.91	3.14
								2009-08	3.59	8/1/09	11.51	8/1/09	0.42	8/1/09	0.17	7.92	0.25		2012-05	3.80	5/1/12	5.07	2012-05-01	1.80	2.00	3.27
								2009-09	3.40	9/1/09	10.77	9/1/09	0.30	9/1/09	0.12	7.37	0.18		2012-06	3.64	6/1/12	5.02	2012-06-01	1.62	2.02	3.40
								2009-10	3.39	10/1/09	10.04	10/1/09	0.28	10/1/09	0.07	6.65	0.21		2012-07	3.40	7/1/12	4.87	2012-07-01	1.53	1.87	3.34
								2009-11	3.40	11/1/09	9.83	11/1/09	0.27	11/1/09	0.05	6.43	0.22		2012-08	3.48	8/1/12	4.91	2012-08-01	1.68	1.80	3.23
								2009-12	3.59	12/1/09	9.33	12/1/09	0.25	12/1/09	0.05	5.74	0.20		2012-09	3.49	9/1/12	4.84	2012-09-01	1.72	1.77	3.12
								2010-01	3.73	1/1/10	8.72	1/1/10	0.25	1/1/10	0.06	4.99	0.19		2012-10	3.47	10/1/12	4.58	2012-10-01	1.75	1.72	2.83
								2010-02	3.69	2/1/10	9.14	2/1/10	0.25	2/1/10	0.11	5.45	0.14		2012-11	3.50	11/1/12	4.51	2012-11-01	1.65	1.85	2.86
								2010-03	3.73	3/1/10	8.63	3/1/10	0.26842	3/1/10	0.15	4.90	0.12		2012-12	3.65	12/1/12	4.63	2012-12-01	1.72	1.93	2.91
								2010-04	3.85	4/1/10	8.23	4/1/10	0.31161	4/1/10	0.16	4.38	0.15		2013-01	3.80	1/1/13	4.73	2013-01-01	1.91	1.89	2.82
								2010-05	3.42	5/1/10	8.79	5/1/10	0.45851	5/1/10	0.16	5.37	0.30		2013-02	3.90	2/1/13	4.85	2013-02-01	1.98	1.92	2.87
								2010-06	3.20	6/1/10	9.13	6/1/10	0.5369	6/1/10	0.12	5.93	0.42		2013-03	3.93	3/1/13	4.85	2013-03-01	1.96	1.97	2.89
								2010-07	3.01	7/1/10	8.64	7/1/10	0.51033	7/1/10	0.16	5.63	0.35		2013-04	3.73	4/1/13	4.59	2013-04-01	1.76	1.97	2.83
								2010-08	2.70	8/1/10	8.33	8/1/10	0.36255	8/1/10	0.16	5.63	0.20		2013-05	3.89	5/1/13	4.73	2013-05-01	1.93	1.96	2.80
								2010-09	2.65	9/1/10	8.01	9/1/10	0.29137	9/1/10	0.15	5.36	0.14		2013-06	4.27	6/1/13	5.19	2013-06-01	2.30	1.97	2.89
								2010-10	2.54	10/1/10	7.45	10/1/10	0.28884	10/1/10	0.13	4.91	0.16		2013-07	4.34	7/1/13	5.32	2013-07-01	2.58	1.76	2.74
								2010-11	2.76	11/1/10	7.47	11/1/10	0.28712	11/1/10	0.14	4.71	0.15		2013-08	4.54	8/1/13	5.42	2013-08-01	2.74	1.80	2.68
								2010-12	3.29	12/1/10	7.67	12/1/10	0.30272	12/1/10	0.14	4.38	0.16		2013-09	4.64	9/1/13	5.47	2013-09-01	2.81	1.83	2.66
								2011-01	3.39	1/1/11	7.31	1/1/11	0.30341	1/1/11	0.15	3.92	0.15		2013-10	4.53	10/1/13	5.31	2013-10-01	2.62	1.91	2.69
								2011-02	3.58	2/1/11	7.06	2/1/11	0.3119	2/1/11	0.13	3.48	0.18		2013-11	4.63	11/1/13	5.38	2013-11-01	2.72	1.91	2.66
								2011-03	3.41	3/1/11	7.12	3/1/11	0.30843	3/1/11	0.1	3.71	0.21		2013-12	4.62	12/1/13	5.38	2013-12-01	2.90	1.72	2.48
								2011-04	3.46	4/1/11	6.99	4/1/11	0.28138	4/1/11	0.06	3.53	0.22		2014-01	4.49	1/1/14	5.19	2014-01-01	2.86	1.63	2.33
								2011-05	3.17	5/1/11	6.89	5/1/11	0.26071	5/1/11	0.04	3.72	0.22		2014-02	4.45	2/1/14	5.10	2014-02-01	2.71	1.74	2.39
								2011-06	3.00	6/1/11	7.33	6/1/11	0.24782	6/1/11	0.04	4.33	0.21		2014-03	4.38	3/1/14	5.06	2014-03-01	2.72	1.66	2.34
								2011-07	3.00	7/1/11	7.26	7/1/11	0.24991	7/1/11	0.04	4.26	0.21		2014-04	4.24	4/1/14	4.90	2014-04-01	2.71	1.53	2.19
								2011-08	2.30	8/1/11	8.26	8/1/11	0.29324	8/1/11	0.02	5.96	0.27		2014-05	4.16	5/1/14	4.76	2014-05-01	2.56	1.60	2.20
								2011-09	1.98	9/1/11	8.77	9/1/11	0.35023	9/1/11	0.01	6.79	0.34		2014-06	4.25	6/1/14	4.80	2014-06-01	2.60	1.65	2.20
								2011-10	2.15	10/1/11	9.15	10/1/11	0.40648	10/1/11	0.02	7.00	0.39		2014-07	4.16	7/1/14	4.73	2014-07-01	2.54	1.62	2.19
								2011-11	2.01	11/1/11	8.7	11/1/11	0.47529	11/1/11	0.01	6.69	0.47		2014-08	4.08	8/1/14	4.69	2014-08-01	2.42	1.66	2.27
								2011-12	1.98	12/1/11	8.59	12/1/11	0.55574	12/1/11	0.01	6.61	0.55		2014-09	4.11	9/1/14	4.80	2014-09-01	2.53	1.58	2.27
								2012-01	1.97	1/1/12	7.9	1/1/12	0.5659	1/1/12	0.03	5.93	0.54		2014-10	3.92	10/1/14	4.69	2014-10-01	2.30	1.62	2.39
								2012-02	1.97	2/1/12	7.31	2/1/12	0.50324	2/1/12	0.09	5.34	0.41		2014-11	3.92	11/1/14	4.79	2014-11-01	2.33	1.59	2.46
								2012-03	2.17	3/1/12	7.2	3/1/12	0.47329	3/1/12	0.08	5.03	0.39		2014-12	3.79	12/1/14	4.74	2014-12-01	2.21	1.58	2.53
								2012-04	2.05	4/1/12	7.27	4/1/12	0.46681	4/1/12	0.08	5.22	0.39		2015-01	3.46	1/1/15	4.45	2015-01-01	1.88	1.58	2.57
								2012-05	1.80	5/1/12	7.3	5/1/12	0.46653	5/1/12	0.09	5.50	0.38
								2012-06	1.62	6/1/12	7.7	6/1/12	0.46559	6/1/12	0.09	6.08	0.38
								2012-07	1.53	7/1/12	7.19	7/1/12	0.45355	7/1/12	0.1	5.66	0.35
								2012-08	1.68	8/1/12	6.85	8/1/12	0.4326	8/1/12	0.1	5.17	0.33
								2012-09	1.72	9/1/12	6.53	9/1/12	0.38563	9/1/12	0.11	4.81	0.28
								2012-10	1.75	10/1/12	6.44	10/1/12	0.33049	10/1/12	0.1	4.69	0.23
								2012-11	1.65	11/1/12	6.61	11/1/12	0.31102	11/1/12	0.09	4.96	0.22
								2012-12	1.72	12/1/12	6.28	12/1/12	0.30947	12/1/12	0.07	4.56	0.24
								2013-01	1.91	1/1/13	5.98	1/1/13	0.30261	1/1/13	0.07	4.07	0.23
								2013-02	1.98	2/1/13	6.1	2/1/13	0.2905	2/1/13	0.1	4.12	0.19
								2013-03	1.96	3/1/13	5.89	3/1/13	0.2819	3/1/13	0.09	3.93	0.19
								2013-04	1.76	4/1/13	5.72	4/1/13	0.27714	4/1/13	0.06	3.96	0.22
								2013-05	1.93	5/1/13	5.48	5/1/13	0.27417	5/1/13	0.04	3.55	0.23
								2013-06	2.30	6/1/13	6.49	6/1/13	0.27374	6/1/13	0.05	4.19	0.22
								2013-07	2.58	7/1/13	6.45	7/1/13	0.26758	7/1/13	0.04	3.87	0.23
								2013-08	2.74	8/1/13	6.48	8/1/13	0.2634	8/1/13	0.04	3.74	0.22
								2013-09	2.81	9/1/13	6.45	9/1/13	0.25318	9/1/13	0.02	3.64	0.23
								2013-10	2.62	10/1/13	6.17	10/1/13	0.24177	10/1/13	0.05	3.55	0.19
								2013-11	2.72	11/1/13	5.96	11/1/13	0.23825	11/1/13	0.07	3.24	0.17
								2013-12	2.90	12/1/13	5.88	12/1/13	0.2439	12/1/13	0.07	2.98	0.17
								2014-01	2.86	1/1/14	5.79	1/1/14	0.23823	1/1/14	0.04	2.93	0.20
								2014-02	2.71	2/1/14	5.73	2/1/14	0.2352	2/1/14	0.05	3.02	0.19
								2014-03	2.72	3/1/14	5.6	3/1/14	0.2341	3/1/14	0.05	2.88	0.18
								2014-04	2.71	4/1/14	5.53	4/1/14	0.2275	4/1/14	0.03	2.82	0.20
								2014-05	2.56	5/1/14	5.45	5/1/14	0.22609	5/1/14	0.03	2.89	0.20
								2014-06	2.60	6/1/14	5.26	6/1/14	0.23095	6/1/14	0.04	2.66	0.19
								2014-07	2.54	7/1/14	5.45	7/1/14	0.23417	7/1/14	0.03	2.91	0.20
								2014-08	2.42	8/1/14	5.7	8/1/14	0.23465	8/1/14	0.03	3.28	0.20
								2014-09	2.53	9/1/14	5.9	9/1/14	0.23403	9/1/14	0.02	3.37	0.21
								2014-10	2.30	10/1/14	6.15	10/1/14	0.23138	10/1/14	0.02	3.85	0.21
								2014-11	2.33	11/1/14	6.14	11/1/14	0.23286	11/1/14	0.02	3.81	0.21
								2014-12	2.21	12/1/14	6.75	12/1/14	0.24461	12/1/14	0.03	4.54	0.21
								2015-01	1.88	1/1/15	6.7	1/1/15	0.25432	1/1/15	0.03	4.82	0.22

Interest Rate Sensitivity

0 0.04 0.09 0.14000000000000001 0.2 0.3 2350 1555.9193716084067 1000 692.89160073898529 485.6980093353809 313.67564300982889

Market interest rate, rd

Bond Value, VB

Price of Bond Over Time

rd Falls and Stays at 4% (Premium Bond) 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 1555.9193716084067 1528.1561464727429 1499.2823923316523 1469.2536880249186 1438.0238355459153 1405.5447889677519 1371.7665805264619 1336.6372437475204 1300.102733497421 1262.1068428373178 1222.5911165508105 1181.4947612128428 1138.7545516613566 1094.3047337278108 1048.0769230769231 1000 rd = Coupon Rate = 9% (Par Bond) 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 1000 999.99999999999989 1000.0000000000001 1000 1000 999.99999999999989 1000.0000000000001 1000 1000 999.99999999999989 1000.0000000000001 999.99999999999989 1000 1000 999.99999999999989 1000 rd Rises and Stays at 14% (Discount Bond) 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 692.89160073898529 699.89642484244303 707.88192432038522 716.98539372523919 727.36334884677262 739.19421768532084 752.68140816126572 768.05680530384302 785.5847580463809 805.56662417287441 828.34595155707689 854.31438477506754 883.91839864357723 917.66697445367799 956.14035087719287 1000

Years Remaining Until Maturity

Bond Value

($)

Mar-80 0.5 1 5 10 30 0.15 0.14000000000000001 0.13500000000000001 0.128 0.123 Feb-00 0.5 1 5 10 30 6.9999999999999999E-4 2.3E-3 1.52E-2 2.1100000000000001E-2 2.7300000000000001E-2 Feb-05 0.5 1 5 10 30 5.979999999999999 9E-2 6.1899999999999997E-2 6.7400000000000002E-2 6.6799999999999998E-2 6.3100000000000003E-2

Years to Maturity

Interest Rate (%)

1-Year 0.05 0.1 0.15 0.2 0.25 1047.6190476190475 999.99999999999989 956.52173913043487 916.66666666666674 880 25-Year 0.05 0.1 0.15 0.2 0.25 1704.6972283022378 999.99999999999989 676.79254573649303 505.24129800519802 402.26673591177746

Interest Rate, rd

Bond Value ($)

36892 36923 36951 36982 37012 37043 37073 37104 37135 37165 37196 37226 37257 37288 37316 37347 37377 37408 37438 37469 37500 37530 37561 37591 37622 37653 37681 37712 37742 37773 37803 37834 37865 37895 37926 37956 37987 38018 38047 38078 38108 38139 38169 38200 38231 38261 38292 38322 38353 38384 38412 38443 38473 38504 38534 38565 38596 38626 38657 38687 38718 38749 38777 38808 38838 38869 38899 38930 38961 38991 39022 39052 39083 39114 391 42 39173 39203 39234 39264 39295 39326 39356 39387 39417 39448 39479 39508 39539 39569 39600 39630 39661 39692 39722 39753 39783 39814 39845 39873 39904 39934 39965 39995 40026 40057 40087 40118 40148 40179 40210 40238 40269 40299 40330 40360 40391 40422 40452 40483 40513 40544 40575 40603 40634 40664 40695 40725 40756 40787 40817 40848 40878 40909 40940 40969 41000 41030 41061 41091 41122 41153 41183 41214 41244 41275 41306 41334 41365 41395 41426 41456 41487 41518 41548 41579 41609 41640 41671 41699 41730 41760 41791 41821 41852 41883 41913 41944 41974 42005 1.9900000000000002 2 2.0900000000000007 2.0600000000000005 1.9000000000000004 1.8999999999999995 1.8899999999999997 2.0499999999999998 2.4399999999999995 2.46 2.3199999999999994 1.6799999999999997 1.5099999999999998 1.5999999999999996 1.5299999999999994 1.5499999999999998 1.5899999999999999 1.7000000000000002 1.88 2.1100000000000003 2.2800000000000002 2.3800000000000003 2.2599999999999998 2.1799999999999997 2.12 2.0500000000000003 2.0799999999999996 1.7800000000000002 1.65 1.6399999999999997 1.5100000000000002 1.4299999999999997 1.4500000000000002 1.4100000000000001 1.3500000000000005 1.3500000000000005 1.3899999999999997 1.42 1.5 1.3800000000000008 1.3200000000000003 1.2799999999999994 1.3200000000000003 1.37 1.33 1.37 1.3299999999999992 1.2399999999999993 1.1400000000000006 1.0300000000000002 0.90000000000000036 0.99000000000000021 1.0100000000000007 0.96 0.87999999999999989 0.83000000000000007 0.92999999999999972 0.88999999999999968 0.87999999999999989 0.90000000000000036 0.87000000000000011 0.77999999999999936 0.8100000000000005 0.84999999999999964 0.83999999999999986 0.77999999999999936 0.75999999999999979 0.79999999999999982 0.79 0.77999999999999936 0.73000000000000043 0.76000000000000068 0.64000000000000057 0.66999999999999993 0.74000000000000021 0.77999999999999936 0.71999999999999975 0.69000000000000039 0.73000000000000043 1.1200000000000001 1.2200000000000006 1.1299999999999999 1.29 1.3900000000000006 1.5899999999999999 1.79 2 1.8699999999999997 1.6900000000000004 1.58 1.6600000000000001 1.7499999999999996 1.9600000000000004 2.4700000000000002 2.5900000000000003 2.63 2.5299999999999998 2.3999999999999995 2.68 2.4599999999999995 2.25 1.8900000000000001 1.85 1.67 1.73 1.7600000000000002 1.7900000000000005 1.67 1.5299999999999998 1.6599999999999997 1.5399999999999996 1.44 1.54 1.6799999999999997 1.71 1.79 1.8800000000000003 2.1399999999999997 2.1100000000000003 1.7299999999999995 1.65 1.6399999999999997 1.7199999999999998 1.7000000000000002 1.79 1.9900000000000002 1.9299999999999997 2.0700000000000003 2.11 1.83 1.8600000000000003 1.9500000000000002 1.8800000000000001 1.8800000000000001 1.8200000000000003 1.9100000000000001 1.9999999999999998 2.02 1.8699999999999999 1.8 1.7700000000000002 1.7200000000000002 1.85 1.93 1.89 1.92 1.9700000000000002 1.97 1.9600000000000002 1.9699999999999998 1.7599999999999998 1.7999999999999998 1.8299999999999996 1.9100000000000001 1.9099999999999997 1.7200000000000002 1.6300000000000003 1.7400000000000002 1.6599999999999997 1.5300000000000002 1.6 1.65 1.62 1.6600000000000001 1.5800000000000005 1.62 1.5899999999999999 1.58 1.58 36 892 36923 36951 36982 37012 37043 37073 37104 37135 37165 37196 37226 37257 37288 37316 37347 37377 37408 37438 37469 37500 37530 37561 37591 37622 37653 37681 37712 37742 37773 37803 37834 37865 37895 37926 37956 37987 38018 38047 38078 38108 38139 38169 38200 38231 38261 38292 38322 38353 38384 38412 38443 38473 38504 38534 38565 38596 38626 38657 38687 38718 38749 38777 38808 38838 38869 38899 38930 38961 38991 39022 39052 39083 39114 39142 39173 39203 39234 39264 39295 39326 39356 39387 39417 39448 39479 39508 39539 39569 39600 39630 39661 39692 39722 39753 39783 39814 39845 39873 39904 39934 39965 39995 40026 40057 40087 40118 40148 40179 40210 40238 40269 40299 40330 40360 40391 40422 40452 40483 40513 40544 40575 40603 40634 40664 40695 40725 40756 40787 40817 40848 40878 40909 40940 40969 41000 41030 41061 41091 41122 41153 41183 41214 41244 41275 41306 41334 41365 41395 41426 41456 41487 41518 41548 41579 41609 41640 41671 41699 41730 41760 41791 41821 41852 41883 41913 41944 41974 42005 2.7699999999999996 2.7700000000000005 2.95 2.9300000000000006 2.6800000000000006 2.6899999999999995 2.7299999999999995 2.88 3.2999999999999989 3.34 3.1599999999999993 2.9600000000000009 2.83 2.9799999999999995 2.8299999999999992 2.8199999999999994 2.9299999999999997 3.0200000000000005 3.25 3.3200000000000003 3.5300000000000002 3.7900000000000005 3.5700000000000003 3.42 3.3 3.1599999999999997 3.14 2.8899999999999997 2.81 2.8600000000000003 2.64 2.5599999999999996 2.5200000000000005 2.4400000000000004 2.3600000000000003 2.33 2.29 2.1899999999999995 2.2800000000000002 2.1100000000000003 2.0300000000000002 2.0499999999999998 2.12 2.1799999999999997 2.1399999999999997 2.1100000000000003 2.0099999999999998 1.92 1.7999999999999998 1.6500000000000004 1.5599999999999996 1.71 1.87 1.8600000000000003 1.7700000000000005 1.7000000000000002 1.83 1.8399999999999999 1.8499999999999996 1.8500000000000005 1.8200000000000003 1.6999999999999993 1.6900000000000004 1.6899999999999995 1.6399999999999997 1.67 1.67 1.71 1.71 1.6899999999999995 1.6000000000000005 1.6600000000000001 1.58 1.5600000000000005 1.71 1.6999999999999993 1.6399999999999997 1.6000000000 000005 1.6500000000000004 1.9800000000000004 2.0700000000000003 1.9500000000000002 2.25 2.5500000000000007 2.8 3.08 3.38 3.2899999999999996 3.05 2.9700000000000006 3.1500000000000004 3.2600000000000002 3.6199999999999997 5.07 5.6800000000000015 6.01 5.620000000000001 5.21 5.6 5.4600000000000009 4.7700000000000005 3.78 3.53 2.99 2.9099999999999997 2.9 2.9200000000000004 2.7800000000000002 2.52 2.65 2.5399999999999996 2.4 2.63 3.0300000000000002 3 2.96 3.0100000000000002 3.1799999999999997 3.16 2.8099999999999996 2.6999999999999997 2.5700000000000003 2.62 2.5599999999999996 2.6100000000000003 2.75 2.76 3.0600000000000005 3.2899999999999996 3.22 3.13 3.27 3.2600000000000007 3.17 3.0600000000000005 3.1400000000000006 3.2700000000000005 3.3999999999999995 3.34 3.2300000000000004 3.12 2.83 2.86 2.91 2.8200000000000003 2.8699999999999997 2.8899999999999997 2.83 2.8000000000000007 2.8900000000000006 2.74 2.6799999999999997 2.6599999999999997 2.6899999999999995 2.6599999999999997 2.48 2.3300000000000005 2.3899999999999997 2.3399999999999994 2.1900000000000004 2.1999999999999997 2.1999999999999997 2.1900000000000004 2.2700000000000005 2.27 2.3900000000000006 2.46 2.5300000000000002 2.5700000000000003

Spread (%)

Hi-Yield Spread 36892 36923 36951 36982 37012 37043 37073 37104 37135 37165 37196 37226 37257 37288 37316 37347 37377 37408 37438 37469 37500 37530 37561 37591 37622 37653 37681 37712 37742 37773 37803 37834 37865 37895 37926 37956 37987 38018 38047 38078 38108 38139 38169 38200 38231 38261 38292 38322 38353 38384 38412 38443 38473 38504 38534 38565 38596 38626 38657 38687 38718 38749 38777 38808 38838 38869 38899 38930 38961 38991 39022 39052 39083 39114 39142 39173 39203 39234 39264 39295 39326 39356 39387 39417 39448 39479 39508 39539 39569 39600 39630 39661 39692 39722 39753 39783 39814 39845 39873 39904 39934 39965 39995 40026 40057 40087 40118 40148 40179 40210 40238 40269 40299 40330 40360 40391 40422 40452 40483 40513 40544 40575 40603 40634 40664 40695 40725 40756 40787 40817 40848 40878 40909 40940 40969 41000 41030 41061 41091 41122 41153 41183 41214 41244 41275 41306 41334 41365 41395 41426 41456 41487 41518 41548 41579 41609 41640 41671 41699 41730 41760 41791 41821 41852 41883 41913 41944 41974 42005 8.4 7.5600000000000005 7.8500000000000005 8.23 7.39 7.7499999999999991 7.93 7.7400000000000011 8.7799999999999994 9.24 8.27 7.76 7.5900000000000007 7.5500000000000007 6.87 6.64 6.42 7.3000000000000007 8.65 9.0400000000000009 9.2100000000000009 9.92 8.82 8.16 7.36 7.6 7.24 6.2 5.82 5.57 4.9800000000000004 4.95 4.5199999999999996 4.0599999999999996 3.830000000000001 3.5100000000000007 3.1599999999999993 3.4699999999999998 3.6399999999999997 3.25 3.580000000000001 3.4499999999999993 3.42 3.51 3.3600000000000003 3.24 2.8699999999999992 2.7199999999999998 2.8900000000000006 2.8 2.7699999999999996 3.5700000000000003 4.05999999999 99996 3.7699999999999996 3.3900000000000006 3.3 3.54 3.54 3.6000000000000005 3.6499999999999995 3.54 3.3899999999999997 3.3099999999999996 3.0499999999999989 2.9799999999999995 3.29 3.3800000000000008 3.4200000000000008 3.4300000000000006 3.26 3.16 3.0300000000000002 2.79 2.6500000000000004 2.87 2.7199999999999998 2.5700000000000003 2.58 3.3000000000000007 4.2100000000000009 4.24 3.95 5 5.3000000000000007 6.2799999999999994 6.57 7.3100000000000005 6.73 6.14 6.24 7.17 7.57 8.49 13.979999999999999 16.79 19.399999999999999 15.84 15.599999999999998 16.899999999999999 14.57 11.39 9.6999999999999993 9.15 7.92 7.3699999999999992 6.6499999999999986 6.43 5.74 4.99 5.4500000000000011 4.9000000000000004 4.3800000000000008 5.3699999999999992 5.9300000000000006 5.6300000000000008 5.63 5.3599999999999994 4.91 4.71 4.38 3.9199999999999995 3.4799999999999995 3.71 3.5300000000000002 3.7199999999999998 4.33 4.26 5.96 6.7899999999999991 7 6.6899999999999995 6.6099999999999994 5.9300000000000006 5.34 5.03 5.22 5.5 6.08 5.66 5.17 4.8100000000000005 4.6900000000000004 4.9600000000000009 4.5600000000000005 4.07 4.1199999999999992 3.9299999999999997 3.96 3.5500000000000007 4.1900000000000004 3.87 3.74 3.64 3.55 3.2399999999999998 2.98 2.93 3.0200000000000005 2.8799999999999994 2.8200000000000003 2.89 2.6599999999999997 2.91 3.2800000000000002 3.3700000000000006 3.8500000000000005 3.8099999999999996 4.54 4.82 TED Spread: 3-month LIBOR - 3-month T-Bill 36892 36923 36951 36982 37012 37043 37073 37104 37135 37165 37196 37226 37257 37288 37316 37347 37377 37408 37438 37469 37500 37530 37561 37591 37622 37653 37681 37712 37742 37773 37803 37834 37865 37895 37926 37956 37987 38018 38047 38078 38108 38139 38169 38200 38231 38261 38292 38322 38353 38384 38412 38443 38473 38504 38534 38565 38596 38626 38657 38687 38718 38749 38777 38808 38838 38869 38899 38930 38961 38991 39022 39052 39083 39114 39142 39173 39203 39234 39264 39295 39326 39356 39387 39417 39448 39479 39508 39539 39569 39600 39630 39661 39692 39722 39753 39783 39814 39845 39873 39904 39934 39965 39995 40026 40057 40087 40118 40148 40179 40210 40238 40269 40299 40330 40360 40391 40422 40452 40483 40513 4054 4 40575 40603 40634 40664 40695 40725 40756 40787 40817 40848 40878 40909 40940 40969 41000 41030 41061 41091 41122 41153 41183 41214 41244 41275 41306 41334 41365 41395 41426 41456 41487 41518 41548 41579 41609 41640 41671 41699 41730 41760 41791 41821 41852 41883 41913 41944 41974 42005 0.54817999999999945 0.46816000000000013 0.54398000000000035 0.74387999999999987 0.48365999999999953 0.34407999999999994 0.24114000000000013 0.20602000000000009 0.3945599999999998 0.24004999999999965 0.23297999999999996 0.23431000000000002 0.17060000000000008 0.17318999999999996 0.19788000000000006 0.24696000000000007 0.17454999999999998 0.17761000000000005 0.16844999999999999 0.15484999999999993 0.17461000000000015 0.20453999999999994 0.22588000000000008 0.21724999999999994 0.19605000000000006 0.17334000000000005 0.15624000000000016 0.17047000000000012 0.21449999999999991 0.20252999999999999 0.20953999999999995 0.18484000000000012 0.20246000000000008 0.23836999999999986 0.24233999999999989 0.27033000000000007 0.24814999999999998 0.19408999999999998 0.17217000000000016 0.21194000000000002 0.23331999999999997 0.23059999999999992 0.29803999999999986 0.24917000000000011 0.25389000000000017 0.32250000000000001 0.23611000000000004 0.30914000000000019 0.33674999999999988 0.27950000000000008 0.28350999999999971 0.37326000000000015 0.43402000000000029 0.45624999999999982 0.39301999999999992 0.35902000000000012 0.48572000000000015 0.45739999999999981 0.47222999999999971 0.60099999999999953 0.36526999999999976 0.32555000000000067 0.41028999999999982 0.47115000000000062 0.46551000000000009 0.59480000000000022 0.54532999999999987 0.46070000000000011 0.57366000000000028 0.45333999999999985 0.43208000000000002 0.50997000000000003 0.38000999999999951 0.32940999999999931 0.40714999999999968 0.48475999999999964 0.62890999999999941 0.75 0.53965999999999958 1.282709 9999999998 1.6039400000000001 1.2465199999999999 1.6920800000000003 1.9794099999999997 1.16764 0.96758999999999995 1.5225000000000002 1.5046599999999999 0.96238000000000001 0.90538999999999992 1.1623399999999999 1.0862499999999999 1.9916800000000001 3.3885899999999998 2.0890599999999999 1.79935 1.08081 0.94262999999999986 1.05674 0.94621999999999995 0.63502999999999998 0.44070999999999999 0.33532999999999996 0.25451999999999997 0.17795 0.21307999999999999 0.21814 0.20305000000000001 0.19012000000000001 0.14052000000000003 0.11842 0.15160999999999999 0.29850999999999994 0.41690000000000005 0.35032999999999992 0.20254999999999998 0.14137000000000002 0.15883999999999998 0.14711999999999997 0.16271999999999998 0.15341000000000002 0.18190000000000001 0.20842999999999998 0.22138000000000002 0.22070999999999999 0.20782 0.20990999999999999 0.27323999999999998 0.34022999999999998 0.38647999999999999 0.46528999999999998 0.54574 0.53589999999999993 0.41324000000000005 0.39328999999999997 0.38680999999999999 0.37653000000000003 0.37558999999999998 0.35355000000000003 0.33260000000000001 0.27562999999999999 0.23049 0.22102000000000002 0.23947000000000002 0.23260999999999998 0.19049999999999997 0.19189999999999999 0.21714 0.23417000000000002 0.22373999999999999 0.22757999999999998 0.22340000000000002 0.23318000000000003 0.19177 0.16824999999999998 0.1739 0.19822999999999999 0.18519999999999998 0.18409999999999999 0.19750000000000001 0.19609000000000001 0.19094999999999998 0.20416999999999999 0.20465 0.21403 0.21138000000000001 0.21286000000000002 0.21461 0.22431999999999999

Spread

(%)

Yield Curve for March 1980

Yield Curve for February 2000

Yield Curve for February 2015

Web 5A

Tool Kit			Web 5A				2/27/15
			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%. 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.
This example analyzes the after-tax cost of issuing zero coupon debt.
Figure 5A-1
Analysis of a Zero Coupon Bond from Issuer’s Perspective
Input Data
Amount needed =			$50,000,000
Maturity value=				$1,000
Pre-tax market interest rate, rd =				6%
Maturity (in years) =				5
Corporate tax rate =				40%
Coupon rate =				0%
Coupon payment (assuming annual payments) =				$0
Analysis:
Issue Price =	PV of payments at rd =			$747.26
	Years	0	1	2	3	4	5
(1) Remaining years		5	4	3	2	1	0
(2) Year-end accrued value		$747.26	$792.09	$839.62	$890.00	$943.40	$1,000.00
(3) Interest payment			$0.00	$0.00	$0.00	$0.00	$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		$747.26	$17.93	$19.01	$20.15	$21.36	($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		bonds
Face amount of bonds = # bonds x $1,000			=	$66,911,279
Figure 5A-2
Analysis of an OID Bond from Issuer’s Perspective
Input Data
Amount needed =			$50,000,000
Maturity value=				$1,000
Pre-tax market interest rate, rd =				6%
Maturity (in years) =				5
Corporate tax rate =				40%
Coupon rate =				5%
Coupon payment (assuming annual payments) =				$50
Analysis:
Issue Price =	PV of payments at rd =			$957.88
	Years	0	1	2	3	4	5
(1) Remaining years		5	4	3	2	1	0
(2) Year-end accrued value		$957.88	$965.35	$973.27	$981.67	$990.57	$1,000.00
(3) Interest payment			$50.00	$50.00	$50.00	$50.00	$50.00
(4) Implied interest
deduction on discount			$7.47	$7.92	$8.40	$8.90	$9.43
(5) Tax savings			$22.99	$23.17	$23.36	$23.56	$23.77
(6) Cash flow		$957.88	($27.01)	($26.83)	($26.64)	($26.44)	($1,026.23)
After-tax cost of debt =		3.60%
Number of $1,000 OID bonds the company must issue to raise $50 million
			=	(Amount needed)/(Price per bond)
			=	52,198.803		bonds
Face amount of bonds = # bonds x $1,000			=	$52,198,803

Web 5C

Tool Kit			Web 5C			10/27/15
			Duration
Duration is a measure of risk for bonds. The following example illustrates its calculation.
Figure 5C-1
Duration
Inputs
Years to maturity =	20
Coupon rate =	9.00%
Annual payment =	$90.0
Par value = FV =	$1,000
Going rate, r =	9.00%
Analysis:
t (1)	CFt (2)	PV of CFt (3)		t x (PV of CFt) (4)
1	$90	$82.57		82.57
2	$90	$75.75		151.50
3	$90	$69.50		208.49
4	$90	$63.76		255.03
5	$90	$58.49		292.47
6	$90	$53.66		321.98
7	$90	$49.23		344.63
8	$90	$45.17		361.34
9	$90	$41.44		372.95
10	$90	$38.02		380.17
11	$90	$34.88		383.66
12	$90	$32.00		383.98
13	$90	$29.36		381.63
14	$90	$26.93		377.05
15	$90	$24.71		370.63
16	$90	$22.67		362.69
17	$90	$20.80		353.54
18	$90	$19.08		343.43
19	$90	$17.50		332.58
20	$1,090	$194.49		3,889.79
		↓		↓
	VB =	$1,000.00	Sum of (t x PV of CFt ) =	$9,950.11
	Duration =	[Sum of (t x PV of CFt)] / VB =		9.95
Finding Duration with the Excel Formula
Settlement date =	1/1/14
Maturity	12/31/33
Coupon =	9%
Yield =	9%
Frequency =	1
Duration =	9.95
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 =				$1,000.00
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 =	9.00%
FV at year 10 =	$5,775.89
PV of payments beyond year 10 discounted back to year 10 =				$4,224.11
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:		$5,775.89
Current value of bond:		$4,224.11
	Total value of position =	$10,000.00
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
	$5,775.89	$4,224.11	$10,000.00
1%	$3,977.42	$7,424.73	$11,402.15	$1,402.15
2%	$4,162.75	$6,880.15	$11,042.90	$1,042.90
3%	$4,358.22	$6,386.06	$10,744.28	$744.28
4%	$4,564.36	$5,937.17	$10,501.53	$501.53
5%	$4,781.73	$5,528.81	$10,310.54	$310.54
6%	$5,010.94	$5,156.80	$10,167.74	$167.74
7%	$5,252.60	$4,817.48	$10,070.07	$70.07
8%	$5,507.35	$4,507.55	$10,014.90	$14.90
9%	$5,775.89	$4,224.11	$10,000.00	$0.00
10%	$6,058.93	$3,964.55	$10,023.48	$23.48
11%	$6,357.20	$3,726.57	$10,083.77	$83.77
12%	$6,671.50	$3,508.09	$10,179.59	$179.59
13%	$7,002.63	$3,307.27	$10,309.90	$309.90
14%	$7,351.45	$3,122.44	$10,473.89	$473.89
15%	$7,718.86	$2,952.12	$10,670.98	$670.98
16%	$8,105.78	$2,794.98	$10,900.76	$900.76
Using Duration to Measure Risk
If the term structure is flat and the change in r is fairly small, then the change in the bond’s price (∆VB) is:
∆VB = (−Duration)(Percentage change in 1 + r)(VB)
Suppose r changes to:	9.10%
		−Duration before change in r =	-9.95
		Percentage change in 1 + r =	0.0917%
		∆VB before change in r=	$1,000.00
		Predicted change in VB =	-$9.13
		Actual VB after change in r=	$990.94
		Actual change in VB after change in r=	-$9.06