Bond Calculator

Bond Valuation Concept

Definitions of Bond Valuation

Bond Valuation

The determination of a bond's fair price is defined as bond valuation [1].

Face Value

The printed amount on the bond is called as face value [2].

Coupon Rate

Coupon rate is the rate at which the bond pays interest on its face value at regular time intervals until the redemption date [2].

Bond Value Formula - How to Calculate Bond

Let

$F$ = Face Value
$R_c$ = Coupon Rate
$R$ = Yield to Maturity
$N$ = Number of Years
$Q$ = Payment Frequency

$C$ = Cash Flow
$c$ = Coupon Payment
$B$ = Bond Value
$D$ = Maculay Duration
$D_m$ = Modified Duration
$K$ = Convexity

Coupon Payment can be calculated as the following:

We can calculate Bond Value by using the following formula:

Then, Maculay duration can be calculated as follows:

We can also calculate Modified Duration:

Then, convexity can be calculated as the following:

where

$C=c$, if $i=N\times Q$
$C=F+c$, otherwise.

and $PV$ is the present value function.

Examples

Example 1

Input

Face Value = 1000
Coupon Rate = 8%
Yield to Maturity = 8%
Years = 6
Frequency = Semiannually

Output

Bond Value = 1000
Maculay Duration = 4.88
Modified Duration = 4.69
Convexity = 27.227

Example 2

Input

Face Value = 1000
Coupon Rate = 14
Yield to Maturity = 16
Years = 7
Frequency = Quarterly

Output

Bond Value = 916.685
Maculay Duration = 4.454
Modified Duration = 4.282
Convexity = 25.057

References

1. Bond valuation (n.d.). Retrieved August 18, 2016, from https://en.wikipedia.org/wiki/ Bond_valuation

2. Bonds and Bond Pricing. (n.d.). Retrieved from http://www.mysmu.edu/faculty/ yktse/FMA/S_FMA_6.pdf