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Calculating the Fair Price of a Bond

The fair price of a bond is a sum of the present value of its principal and the present value of its income stream (the coupons).

Present value of the principal

Formula

PV = FV / (1 + r)n

Calculation

Future value (FV)
$
Future value of the bond
Discount rate (r)
 
Discount rate or yield to maturity depends on the risk of a particular bond. It can be estimated by the yields currently applicable to bonds with similar coupon, term and credit quality.
Number of periods
 
Number of compounding periods from the present to the date on which the coupon is calculated.
Present value
$

Example

Example: a 4.50% five-year bond with a par value of $100 would have ten remaining semi-annual coupon payments of $2.25 each. The present value of each of these coupons added together is the present value of the bond's income stream of $1.38.

Now you will have to repeat these steps for each coupon payment. However, there is an easier way.

Present value of the income stream

Formula

APV = C (1 - 1/(1+r)n)/r

Calculation

Coupon payment (C)
$
The coupon payment amount.
Discount rate (r)
 
Discount rate or yield to maturity depends on the risk of a particular bond. It can be estimated by the yields currently applicable to bonds with similar coupon, term and credit quality.
Number of coupon payments (n)
 
Present Value of Coupon Payment Series (APV)
$