The Importance of Bond Calculations

Although the vast majority of finance professionals do not deal with bonds on a daily basis, the principles involved with calculating bond values go to the very foundation of finance. If you do not have a good working knowledge of what sets bond values, you are incompetent! Any business student with a basic finance course under his/her belt ought to be able to immediately give the right answers when confronted by a Finance or Economics professor about bonds or the bond market.

All that it takes to master this subject is a firm grasp of present value principles, bond terminology definitions, and supply and demand relationships.

• Present Value Principle--An amount to be received in the future is always worth less than the same amount today! The method used is compound interest in reverse.
• Bond Terminology--You have to know it cold-memorize it!
  • Face Value--printed on the bond, never changes, the amount you get at maturity.
  • Maturity--printed on the bond, never changes , the date at which you get the face value paid
  • Coupon rate--printed on the bond, never changes, the percentage of Face Value that is paid as interest each year [actually one half of the interest is paid every six months]
  • Yield or market yield--not on the bond, changes every day, determined by supply and demand of bonds in the bond market
  • Market value or price of the bond--not on the bond, changes every day, calculated by figuring the present value of the coupon payments and the present value of the face value at maturity at the discount rate set equal to the market yield.
• Supply and Demand relationships--Funds flow into and out of the bond market and the level is not constant. Treasury actions to fund the deficit and monetary policy by the Federal Reserve profoundly affect the price [yield] in the market.

Examples

The following table show the present value calculations for a $1000 Face Value bond with a 9% coupon in both a 6% and a 13% market. Look through the table a see if you can explain where all of the numbers come from.

		Market=	Market=
Period	Cash Flow	0.06	0.13	Face Value		1000
1	45	43.69	42.25	Coupon Rate		0.09
2	45	42.42	39.67
3	45	41.18	37.25	Interest Payment		45
4	45	39.98	34.98	Life		5	years
5	45	38.82	32.84
6	45	37.69	30.84
7	45	36.59	28.96
8	45	35.52	27.19
9	45	34.49	25.53
10	1045	777.58	556.7
Total Present Value of Bond		1127.95	856.22

The chart below depicts the magnitude of the present values of the cash flow coming from interest and face value under the 6% and the 13% market conditions. Notice the magnitude of the present value of the face value compared to the present value of all the interest payments. The largest proportion of present value comes from the face value at maturity because the maturity is relatively near [ 5years]. Notice a 9% coupon bond is worth more than face value when rates decline to 6% and it is worth less than face value if rates go up to 13%!. Why? Because a market yield of 6% means that new bonds are coming into the market at that rate and this 9% bond is more attractive than them. So investors bid up the price of the 9% bond until it yields 6% also.

The next example show similar calculation for a 9% coupon with a twenty year life. This is a different bond from the one above because maturity dates are printed on the bond and never change!

		Market=	Market=
Period	Cash Flow	0.06	0.13	Face Value		1000
1	45	43.69	42.25	Coupon Rate		0.09
2	45	42.42	39.67
3	45	41.18	37.25	Interest Payment		45
4	45	39.98	34.98	Life		20	years
5	45	38.82	32.84
6	45	37.69	30.84
7	45	36.59	28.96
8	45	35.52	27.19
9	45	34.49	25.53
10	45	33.48	23.97
11	45	32.51	22.51
12	45	31.56	21.14
13	45	30.64	19.85
14	45	29.75	18.63
15	45	28.88	17.5
16	45	28.04	16.43
17	45	27.23	15.43
18	45	26.43	14.49
19	45	25.66	13.6
20	45	24.92	12.77
21	45	24.19	11.99
22	45	23.49	11.26
23	45	22.8	10.57
24	45	22.14	9.93
25	45	21.49	9.32
26	45	20.87	8.75
27	45	20.26	8.22
28	45	19.67	7.72
29	45	19.1	7.25
30	45	18.54	6.8
31	45	18	6.39
32	45	17.48	6
33	45	16.97	5.63
34	45	16.47	5.29
35	45	15.99	4.97
36	45	15.53	4.66
37	45	15.07	4.38
38	45	14.64	4.11
39	45	14.21	3.86
40	1045	320.35	84.17
Total Present Value of Bond		1346.72	717.09

 

Notice that the present value of the face value is now a much smaller proportion of the total value. It is the face value that provides the stability for a bond price when the maturity is nearby. In very long term bonds this stability is lost and they are very volatile as they react to daily yield changes.

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