Maturity value

Example 4 Determination of present worth and discount. A bond has a maturity value of 1000 and is paying discrete compound interest at an effective annual rate of 3 percent. Determine the following at a time four years before the bond reaches maturity value ... 

An NBD-PC fluorescence polarization value of less than 260 mP is considered mature, values between 260 and 290 mP are considered transitional, and values greater than... 

Repair materials. Repair materials to be used in areas where current is flowing should have similar electrical resistivity as the parent concrete in order not to disturb uniform current flow. Repair mortars should be tested for resistivity for several months to obtain mature values, preferably in a cHmate that simulates the exposure of the structure [7,8]. A difference of a factor two between mortar and concrete resistivity is considered acceptable [13]. It appears that most cementitious... 

The rate r is compounded using e and an initial investment M earning r(t, T) over the period T—t, initial investment at time t and for maturity at T, where T>t, would have a value of Me " on maturity. If we denote the initial value and the maturity value Mj, then we can state and... 

A short-rate model can be used to derive a complete term structure. We can illustrate this by showing how the model can be used to price discount bonds of any maturity. The derivation is not shown here. Let P t, T) be the price of a risk-free zero-coupon bond at time t maturing at time T that has a maturity value of 1. This price is a random process, although we know that the price at time T will be 1. Assume that an investor holds this bond, which has been financed by borrowing funds of value C,. Therefore, at any time t the value of the short cash position must be C,= —P(t, T) otherwise, there would be an arbitrage position. The value of the short cash position is growing at a rate dictated by the short-term risk-free rate r, and this rate is given by... 

A bond, like any security, can be thought of as a package of cash flows. A bond s cash flows come in two forms—coupon interest payments and the maturity value or par value. In European markets, many bonds deliver annual cash flows. As an illustration, consider a 6% coupon... 

An index-linked bond has its coupon or maturity value or sometimes both linked to a specific index. When governments issue index-linked bonds, the cash flows are linked to a price index such as consumer or commodity prices. Corporations have also issued index-linked bonds that are connected to either an inflation index or a stock market index. For example, Kredit Fuer Wiederaufbau, a special purpose bank in Denmark, issued a floating-rate note in March 2003 whose coupon rate will be linked to the Eurozone CPI (excluding tobacco) beginning in September 2004. Inflation-indexed bonds are detailed in Chapter 8. 

The cash flows of a fixed-income security can be denominated in any currency. For bonds issued by countries within the European Union, the issuer typically makes both coupon payments and maturity value payments in euros. However, there is nothing that prohibits the issuer from making payments in other currencies. The bond s indenture can specify that the issuer may make payments in some other specified currency. There are some issues whose coupon payments are in one currency and whose maturity value is in another currency. An issue with this feature is called a dual-currency issue. 

To illustrate the process, let s value a 4-year, 6% coupon bond with a maturity value of 100. The coupon payments are 6 for the next four years. In addition, on the maturity date, the investor receives the repayment of principal ( 100). The value of a nonamortizing bond can be divided in two components (1) the present value of the coupon payments (i.e., an annuity) and (2) the present value of the maturity value (i.e., a lump sum). Therefore, when a single discount rate is employed, a bond s value can be thought of as the sum of two presents values—an annuity and a lump sum. 

The present value of the maturity value is just the present valne of a lump sum and is equal to... 

Simply put, this number tells us how much the coupon payments contribute to the bond s valne. In addition, the bondholder receives the maturity value when the bond matures so the present value of the maturity value must be added to the present value of the coupon payments. The present value of the maturity value is... 

This number ( 79.21) tells us how much the bond s maturity value contributes to the bond s value. The bond s value is the sum of these two present values which in this case is 100 ( 20.79 + 79.21). 

At the maturity date, the bond s value is equal to its par or maturity value. So, as a bond s maturity approaches, the price of a discount bond will rise to its par value and a premium bond will fall to its par value— a characteristic sometimes referred to as pull to par value. ... 

As the bond moves toward maturity with no change in the discount rate, the price has declined from 103.546 to 102.7278. What are the mechanics of this result The value of a coupon bond can thought of as the sum of two present values—the present value of the coupon payments and the present value of the maturity value. What happens to each of these present values as the bond moves toward maturity with no change in the discount rate The present value of the coupon payments falls for the simple reason that there are fewer coupon payments remaining. Correspondingly, the present value of the maturity value rises because it is one year closer to the present. What is the net effect The present value of the coupon payments fall by more than the present value of the maturity value rises so the bond s value declines or is pulled down to par. 

The intuition for the result reveals a great deal about bond valuation. Why does the present value of the coupon payments fall by more than the present value of the maturity value rises Recall why a coupon... 

Why does the present value of the maturity value rise by more than the present value of the coupon payments falls A coupon bond sells at a discount because it offers a lower coupon rate (6%) than new comparable bonds issued at par (7%). So, relative to a bond selling at par, the repayment of the principal at maturity is a relatively more important cash flow. To be sure, it is the capital gain we obtain from this payment... 

The final cash flow represents the last coupon payment and the maturity value of 100. Also assume the following ... 

The cash flow is found by multiplying the coupon rate and the maturity value (assumed to be 100). However, the coupon rate (the forward rate in the previous period plus the quoted margin) must be adjusted for the number of days in the quarterly payment period. The formula to do so is... 

In addition to the projected cash flow, in period 16 the investor receives the maturity value of 100. The projected cash flows four our hypothetical 4-year floater are shown in Column (5). 

The investor s tenure as a bond s owner ends as a result of one of the following circumstances. First, the investor may simply sell the bond and will receive the bond s prevailing market price plus accrued interest. Next, the issuer may call the bond in which case the investor receives the call price plus accrued interest or the investor may put the bond and receive the put price plus accrued interest. Lastly, if the bond matures, the investor will receive the maturity value plus the final coupon payment. Regardless of the reason, if the proceeds received are greater than the investor s initial purchase price, a capital gain is generated, which is an additional source of dollar return. Similarly, if the proceeds received are less than the investor s initial purchase price, a capital loss is gener-... 

Consider a hypothetical 10-year bond selling at par ( 100) with a coupon rate of 7%. Assume the bond delivers coupon payments aimually. The yield to maturity for this bond is 7%. Suppose an investor buys this bond, holds it to maturity, and receives the maturity value of 100. In addition, the investor receives 10 annual coupon payments of 7 and can reinvest them every year that they received at an annual rate of 7%. What are the total future euros assuming a 7% reinvestment rate As demonstrated above, an investment of 100 must generate 196.72 in order to generate a yield of 7% compounded semiannually. Alternatively, the bond investment of 100 must deliver a total euro return of 96.72. 

EXHIBIT 3.16 Calculation of the Discount Margin for a Floater Floater Maturity = 6 years Coupon rate = Reference rate + 80 basis points Resets every 6 months Maturity value = 100 ... 

Exhibit 3.16 presents the calculation of the discount margin for this security. Each period in the security s life is enumerated in Column (1), while the Column (2) shows the current value of the reference rate. Column (3) sets forth the security s cash flows. For the first 11 periods, the cash flow is equal to the reference rate (10%) plus the quoted margin of 80 basis points multiplied by 100 and then divided by 2. In last 6-month period, the cash flow is 105.40—the final coupon payment of 5.40 plus the maturity value of 100. Different assumed margins appear at the top of the last five columns. The rows below the assumed margin indicate the present value of each period s cash flow for that particular... 

The third and final step is to calculate the percentage change in the bond s portfolio value when each key rate and neighboring spot rates are changed. There will be as many key rate durations as there are preselected key rates. Let s illustrate this process by calculating the key rate duration for a coupon bond. Our hypothetical 6% coupon bond has a maturity value of 100 and matures in five years. The bond delivers coupon payments semiannually. Valuation is accomplished by discounting each cash flow using the appropriate spot rate. The bond s current value is 107.32 and the process is illustrated in Exhibit 4.27. The initial hypothetical (and short) spot curve is contained in column (3). The present values of each of the bond s cash flows is presented in the last column. 

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