IRR/ Yield Calculation on Bonds

[student]

Can someone please show me how the Yield to Maturity has been calculated:

Bond - Irish Gov.
Coupon - 4%
Redemption Date - 11 November 2011
Price - 102.50
Yield to Maturity - 3.03%

An investor buys €1million nominal of bonds on 12th Feb 2009 at a clean price of 102.50.

1 million x 102.50 = 1,025,000

+ 93 days accrued interest = 10,191.78

Total = 1,035,191.78

Cashflow
11/11/2009 - 40,000
11/11/2010 - 40,000
11/11/2011 - 1,040,000

Question - How is the 3.03% YTM calculated?

 

[jpd]

A quick way to estimate the YTM is as follows:-

Nominal interest rate is 4%
Purchase price is € 102.50

Gross yield if 4 / 102.50 * 100 = 3.90%

Bond is paid back at par ie € 100 so there will be a capital loss of 102.50 - 100.00 = € 2.50

This will occur in 2 years 9 months ie Feb 2009 - Nov 2011 or 2.75 years

Average loss per year = 2.50 / 2.75 = 0.91%

So estimate of net yield to maturity = 3.90 - 0.91 = 2.99%

The actual calculation is more complicated. See here http://thismatter.com/money/bonds/bond-yields.htm or here http://en.wikipedia.org/wiki/Yield_to_maturity