Bonds With Difficult Expected Cash Flow Estimation
The bonds for which it is difficult to estimate expected cash flows fall into three categories:

1. Bonds for which the issuer or investor has an option or right to change the contract due date for the payment of the principal. These include callable bonds, puttable bonds, MBSs and ABSs.
2. Bonds for which coupon payment rate is reset occasionally based on a formula with values that change, such as reference rates, prices or exchange rates. A floating-rate bond would be an example of this type of category.
3. Bonds for which investor has the option to convert or exchange the security for common stock.

The problems when estimating the cash flows of these types of bonds include:

1. In the case of bonds for which the issuer or investor has the option/right to change the contract due date for the payment of principal, the bonds can be affect by future interest rates. If rates decline, a corporation may issue new bonds at a lower cost and call the older bonds. The same thing happens with MBSs and ABSs. As rates decline, borrowers have the right to refinance their loans at cheaper rates. This causes the bond to be paid off earlier than the stated maturity date.
2. When rates increase, a puttable bond will be sold back to the issuing corporation at the put price once the increase in rates drives the price of the security below the put price.
3. For bonds in which the coupon payment rate is reset occasionally based on a formula with changing values, because the rate is always changing based on other variables it is hard to estimate the cash flows. Also, for bonds that give the investor the option to convert or exchange the security for common stock, the cash flows will stop altogether once the investor decides that it would be more profitable to exchange the fixed income security for equity. The investor will have no certain idea as to when this may occur, making it difficult to value the cash flows until the maturity of the bond.
4. Because the value of the bond rests on the performance of the securities that back the bond, it is hard to determine whether the bonds may be converted into those securities.

Determining Appropriate Interest Rates
The minimum interest rate that an investor should accept is the yield that is available in the market place for a risk-free bond, or the Treasury market for a U.S. investor. The Treasury security that is most often used is the on-the-run issues because they reflect the latest yields and are the most liquid securities.

For non-treasury bonds such as corporate bonds, the rate or yield that would be required would be the on-the-run government security plus a premium that takes up the additional risks that come with non-treasury bonds.

As for the maturity, an investor could just use the final maturity date of the issue compared to the Treasury security. However, because each cash flow is unique in its timing, it would be better to use the maturity that matches each of the individual cash flows.

Computing a Bond's Value
First of all, we need to find the present value (PV) of the future cash flows in order to value the bond. The present value is the amount that would be needed to be invested today to generate that future cash flow. PV is dependent on the timing of the cash flow and the interest rate used to calculate the present value. To figure out the value the PV of each individual cash flow must be found. Then, just add the figures together to determine the bonds price.

Formula 14.7

 PV at time T = expected cash flows in period T / (1 + I) to the T power

After you develop the expected cash flows, you will need to add the individual cash flows:

Formula 14.8

 Value = present value @ T1 + present value @ T2 + present value @Tn

Let's throw some numbers around to further illustrate this concept.

Example: The Value of a Bond
Bond GHJ matures in five years with a coupon rate of 7% and a maturity value of \$1,000. For simplicity's sake, the bond pays annually and the discount rate is 5%.

Answer:
The cash flow for each of the years is:
Year one = \$70 Year Two = \$70 Year Three = \$70, Year Four is \$70 and Year Five is \$1,070.

PV of the cash flows is: Year one = 70 / (1.05) to the 1st power = \$66.67
Year two = 70 / (1.05) to the 2nd power = \$ 63.49
Year three = 70 / (1.05) to the 3rd power = \$ 60.47
Year four = 70 / (1.05) to the 4th power = \$ 57.59
Year five = 1070 / (1.05) to the 5th power = \$ 838.37

Now to find the value of the bond:
Value = 66.67 + 63.49 + 60.47 + 57.59 + 838.37
Value = 1, 086.59

Bond Value and Price

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