Fixed-Income Features: Bond Cash Flow Diagram
Nothing can illustrate the anatomy of a bond quite like an illustration.
A bond is defined by its cash flows. These are given by the three main features of a bond:
* Face value, or par value, or principal
* Coupon rate
* Maturity or term
With these three pieces of information (which by the way are printed on the bond, so they don't change) every cash flow is known and can be shown in a cash-flow diagram.
Consider a bond with a face value of $4,000, an annual-pay coupon rate of 3.5%, and a maturity in five years. The investor will pay some price for this bond today, depending on market interest rates and the relative risk of this bond issue. If the investor demands a return of 4%, then the investor will pay less than face value for this bond that only offers a 3.5% coupon, buying at a discount to par.
That's really the end of the ambiguity. From there, every cash flow is determined by the bond's features. An annual coupon payment with a maturity of five years means five coupon payments, the fifth one being with the principal. The 3.5% coupon combined with the face value of $4,000 means that the size of the coupon payments will be 3.5% x $4,000 = $140 per year. These cash flows are more easily seen in a __cash-flow diagram__:
How would you summarize the cash flows of a bond in terms of their direction between the investor and the issuer?
That's right!
The investor purchases the bond, and that price goes from the investor to the issuer. This investment is then repaid by the remaining cash flows made from the issuer back to the investor.
No.
Consider that a bond is essentially a loan to raise capital for a firm, and so the initial cash flow is the price paid by the investor to the firm.
No.
The initial cash flow and the final cash flow go in opposite directions.
In this diagram, the time periods are annual, labeled as time zero through time five. Time zero, or $$T_0$$, denotes the sale of the bond, with subsequent times as the years of the bond's term.
How do you imagine this cash-flow diagram would change if the bond offered semiannual coupon payments instead of annual coupon payments?
No.
The time periods are in terms of years, but the bond would still have a five-year term.
Correct!
A semiannual 3.5% coupon bond, also with a five-year term and a $4,000 face value, will have time increments of 0.5 years and coupon payments half the size of an annual pay bond:
No.
There would be no $140 payments in this case. The coupon payments would each be $70.
Now suppose that this bond is designed as a zero-coupon bond, with the same maturity and face value. How will this cash-flow diagram simplify?
No.
This indicates the principal payment of the bond without any consideration from the investor.
No.
There will be no cash flow in year one. Recall that the bond is purchased in time zero.
To summarize this discussion:
[[summary]]
Correct!
This cash-flow diagram is the simplest of the three, but still involves two cash flows in total. The intermediate years don't really need to be listed here, but they were left to highlight the fact that the principal payment remains in year five.
Of course this is far from an exhaustive listing of bond cash-flow structures, but thinking in terms of a timeline cash-flow diagram such as this can help to mentally organize the cash flows of other, perhaps more exotic bonds you may encounter.
The initial cash flow is from the investor to the issuer, and the remainder are from the issuer to the investor
The initial cash flow is from the issuer to the investor, and the remainder are from the investors to the issuer
The initial cash flow and final cash flow are from the investor to the issuer, and the intermediate cash flows are from the issuer to the investor
The diagram would range from $$T_0$$ to $$T_{10}$$
The diagram would include $$T_{0.5}$$
The diagram would have more $140 payments
To a single cash flow of $4,000 in year five
To two cash flows in years one and five
To two cash flows in years zero and five
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