# Yield On A Coupon Date

You can calculate the yield to maturity on a coupon date by:

1) Using the __RATE__ function.

2) Using the Goal Seek Iterative technique.

### Assumptions

The following assumptions are made to simplify the calculation:

* The calculation can only be performed on a coupon date.

* It is assumed that the bond is held to maturity

* Every cash flow is discounted at the same discount factor or rate. (flat yield curve)

There are plenty of problems in finance that require solving for a single parameter in a function where it is difficult (or impossible) to isolate a parameter exactly.

Lets imagine we have the following bond:

2 year treasury bond

Coupon rate of 6% (paid semi-annually)

Principal of $1,000

Current price is $950

What is the yield to maturity (or bond yield) ?

The following equation needs to be solved, where r represents the yield to maturity.

### RATE Function

RATE(nper, pmt, pv [,fv] [,type] [,guess])

__RATE__ - Returns the interest rate for a series of equal cash flows at regular intervals.

This function can only be used to calculate the yield to maturity **on an coupon date** (or interest payment date).

The yield returned by this function is actually the semi-annual yield so we need to multiple our answer by 2.

ammend the formula in SS and include all the arguments in this screen shot.

This returns the BEY

above - rows 22 and 23 - remove the (*2) - these are semi-annual IRR

The equivalent annualised IRR would be (1 + C22)^2 - 1

### Goal Seek - Iterative Approach

An iterative approach can be used by using Goal Seek

The yield returned here is the 'periodic yield. (or semi-yield)

We can annualise this periodic yield by multiplying by 2.

The annualised semi-annual periodic yield is (A * 2)

This gives us the semi-annual bond equivalent yield (BEY)

We can cross reference our answer:

### Important

When the price of a bond is equal to par, then the yield equals the coupon rate.

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