Stocks Valuation
Bonds Valuation
Mortgage
Present Value
Present Value (Uneven CFs)
Future Value
Future Value (Uneven CFs)
Internal Rate of Return
Modified IRR
Net Present Value
Yield to Maturity
PVIF
PVIFA
FVIF
FVIFA

A bond is a security that pays a given amount of interest to the investor, time after time, until it is finally retired by the issuing body. A bond has a face value, this value is usually $1,000 per bond in the U.S. The bond almost always has a stated maturity, which is the time company or issuing body is obligated to pay the bondholder the face value of the instrument. Then there is the coupon rate or nominal annual rate of interest which is stated on the bond's face. For example, if the coupon rate is 14% on a $1,000 face value bondm the company or issuing body pays the holder $140 each year until the bond matures.

In valuing a bond or any other security, we are mainly concerned with discounting, or capitalizing, the cash flow stream that the security holder would receive over the life of the instrument. The terms of a bond establish a legally binding payment pattern at the time the bond is originally issued. This pattern consists of the payment of a stated amount of interest over a given number of years coupled with final payment, when the bond matures, equal to the bond's face value.

Perpetual Bonds
This type of bond is a unique class of bonds that never matures. These are indeed rare but they help illustrate the valuation technique in its simplest form. The present value of the perpetual bond would simply be equal to the capitalized value of an infinite stream if interest payments. If a bond promises a fixed annual payment INT forever, its present value V at the investor's required rate of return for this debt issue is K_d.

Thus the present value of a perpetual bond is simply the periodic interest payment divided by the appropriate discount rate per period. Suppose you could buy a bond that paid $75 a year forever. Assuming that your required rate of return for this type of bond is 10%, then the present value of this security would be

V=$75/0.10=$750.00

Non Zero Coupon Bonds

If a bond has a finite maturity , then we must consider not only the interest stream but also the terminal value or maturity value (face value) in valuing the bond. The valuation equation for such a bond that pays interest at the end of each year is

We might want to determine the value of a $1000 par value bond with a 10% coupon and 10 years to maturity. The coupon rate corresponds to the interest payments of $100 a year. If our required rate of return on the bond is 14%, then

V=$100(PVIFA_14%,10)+$1,000(PVIF_14%,10)

V=$100(5.216)+$1,000(0.270)

V=$791.6

Zero Coupon Bonds

A zero coupon bond makes no periodic interest payment but instead is sold at a steep discount from its face value. The valuation equation for zero coupon bond is a truncated version of that used for a normal interest paying bond. The present value of interest payments component is looped off, and we are left with value being determined solely by the present value of the principal payment at maturity or

V=MV(PVIF_kd,n)

Suppose that Tequilla Corp. issues a zero coupon bond having a 12 year maturity and a $1,000 face value, If your required rate of return is 11%, then

V=$1,000(PVIF_11%,12)

V=$1000(0.286)

V=$286

Semiannual Compounding of interest

Although some bonds (typically those issued in the Euro markets) make interest payments once a year, most bonds issued in the U.S. pay interest twice a year. As a result, it is necessary to modify the bond valuation equations to account for compounding twice a year.

where k_d us the nominal annual required rate of return, I/ 2 is the semiannual coupon payment, and 2n is the number of semiannual periods until maturity.