Editing Present value (section)

====PV of a bond====
:''See: [[Bond valuation#Present value approach]]''
A corporation issues a [[Bond (finance)|bond]], an interest earning debt security, to an investor to raise funds.<ref name=Ross/> The bond has a face value, <math> F </math>, coupon rate, <math> r </math>, and maturity date which in turn yields the number of periods until the debt matures and must be repaid. A bondholder will receive coupon payments semiannually (unless otherwise specified) in the amount of <math> Fr </math>, until the bond matures, at which point the bondholder will receive the final coupon payment and the face value of a bond, <math> F(1+r) </math>.

The present value of a bond is the purchase price.<ref name="Broverman"/>
The purchase price can be computed as:
:<math>PV = \left[\sum_{k=1}^{n} Fr(1+i)^{-k}\right]</math> <math> + F(1+i)^{-n} </math>

The purchase price is equal to the bond's face value if the coupon rate is equal to the current interest rate of the market, and in this case, the bond is said to be sold 'at par'. If the coupon rate is less than the market interest rate, the purchase price will be less than the bond's face value, and the bond is said to have been sold 'at a discount', or below par. Finally, if the coupon rate is greater than the market interest rate, the purchase price will be greater than the bond's face value, and the bond is said to have been sold 'at a premium', or above par.<ref name="Ross"/>

=====Technical details=====
Present value is [[Additive inverse|additive]]. The present value of a bundle of [[cash flow]]s is the sum of each one's present value. See [[time value of money]] for further discussion.
These calculations must be applied carefully, as there are underlying assumptions:
* That it is not necessary to account for price [[inflation]], or alternatively, that the cost of inflation is incorporated into the interest rate; see [[Inflation-indexed bond]].
* That the likelihood of receiving the payments is high — or, alternatively, that the [[default risk]] is incorporated into the interest rate; see [[Corporate bond#Risk analysis]].
(In fact, the present value of a cashflow at a constant interest rate is mathematically one point in the [[Laplace transform]] of that cashflow, evaluated with the transform variable (usually denoted "s") equal to the interest rate. The full Laplace transform is the curve of all present values, plotted as a function of interest rate. For discrete time, where payments are separated by large time periods, the transform reduces to a sum, but when payments are ongoing on an almost continual basis, the [[Compound interest#Continuous compounding|mathematics of continuous functions]] can be used as an approximation.)