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Finance

 levelcoupon
 Present value of a level coupon bond

 Calling Sequence levelcoupon(face, rate, couponrate, maturity)

Parameters

 face - face value of the bond rate - interest rate couponrate - interest rate indicated by the bond maturity - number of periods to maturity

Description

 • The function levelcoupon calculates the present value at interest rate rate of a bond with face value face maturing in maturity period and paying at a rate couponrate per period.
 • The coupon rate is the rate that determines the payments that the bond gives. The rate is the interest rate used in calculating the present value of the bond.
 • If the bond never matures, one has a perpetuity. See Finance[perpetuity].
 • The present value of a bond that pays only its face value at maturity, but no coupon payments (pure discount bonds or zero level bonds), is calculated using the Finance[presentvalue] function.
 • Since levelcoupon used to be part of the (now deprecated) finance package, for compatibility with older worksheets, this command can also be called using finance[levelcoupon]. However, it is recommended that you use the superseding package name, Finance, instead: Finance[levelcoupon].

Examples

I hold a bond with face value of 1000 units with an annual coupon rate of 12%. The coupon is paid twice yearly. The maturity is in 3 years. What is the present value of the bond given that the interest rate is presently 10% compounded semi-annually.

 > $\mathrm{with}\left(\mathrm{Finance}\right):$

There are 6 periods of half a year until maturity.

 > $\mathrm{levelcoupon}\left(1000,\frac{0.10}{2},\frac{0.12}{2},6\right)$
 ${1050.756921}$ (1)

If the interest rate is the same as the coupon rate.

 > $\mathrm{levelcoupon}\left(1000,\frac{0.12}{2},\frac{0.12}{2},6\right)$
 ${999.9999998}$ (2)

In other words, the bond is valued at par when the interest rate is equal to the coupon rate.

Now let the interest rate rise to 14%, compounded semi-annually.

 > $\mathrm{levelcoupon}\left(1000,\frac{0.14}{2},\frac{0.12}{2},6\right)$
 ${952.3346034}$ (3)

This example shows that the value of the bond declines with rising interest rate.

Compatibility

 • The Finance[levelcoupon] command was introduced in Maple 15.