### bondXL v1.0

(1 Dimension)

Analyze a single **bond**

- Price & Coupon rate
- Yield to maturity & Yield to horizon
- Modified and Macaulay Duration
- Convexity

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The price of bond is determined by summing the discounted periodic interest payments and the maturity value. These discounted payments are discounted using an interest rate that sets equal the market price of the bond to the present value (the sum of discounted interest payments and par value). This interest rate is called the YTM - yield to maturity, a YTM is also referred to as the promised yield as this is return the lender is promised to be paid by the borrower. That all fine but how do you find the YTM - no easy task mind you as there are no closed form mathematical formulas to my knowledge that can determine the yield. On zero coupon bonds one can easily calculate the YTM as there are only two money amounts the price and the maturity value. For coupon paying bonds the series of discounted cash flows make it virtually impossible to isolate or to separate the variable of interest rate from the equation.

This means as an analyst you would have to resort to applying numerical methods also termed iterative methods to find the yield to maturity. There are a very large number of iterative methods that you can apply when determining the interest rate on bonds. Such methods have their pros and cons where some are easy to implement in a programming language yet the results are not as precise and require a large number of iteration before closing in on the rate. Others are more complex yet offer results that are near accurate, one of these methods that is commonly used is the Newton-Raphson method or simply the Newton's method of finding roots of a polynomial. In our case the sum of discounted cash flows represents the polynomial and finds its roots is akin to finding the interest rate at which the functions yields a value of zero.

Using tadXL function such as tadBYTM finding yield to maturity in Excel 2007, 2010 and 2013 becomes really easy. Let us now briefly look at the financial functions in tadXL to find YTM using Excel:

=tadBYTM( years_to_maturity, coupon_rate, bond_price, par_value, compounding )

%

Nominal YTM =

Annual effective yield =