Computing Horizon Yield Using IRR & MOD

How to calculate the horizon yield in the most efficient and fastest way using approved CFA calculator?

Look at the example below:

An investor purchased an option-free bond with 6 years to maturity, the par value equal to USD 100 and both an annual coupon and a yield to maturity equal to 10%. What is the realized rate of return, if the investor holds the bond till maturity and reinvests all coupons at 11%?

Before we begin our calculations, we should notice that the purchase price of the bond has to be USD 100 (bond is selling at par), because the coupon rate is equal to yield to maturity.
Let's solve this example using two different approaches. First, we will calculate the horizon yield in 'algebraic way'. Then, we will use TIBA Professional CF and IRR worksheets.

Algebraic way

First we have to calculate the future value of coupon payments:

\(\text{FV of coupons}=10\times1.11^5+10\times1.11^4+10\times1.11^3+\\+10\times1.11^2+10\times1.11+10=\text{USD }79.1286\)

and then we solve the following equation:

\(100=\frac{100+79.1286}{(1+r)^6}\)

So:

\(100\times(1+r)^6=100+79.1286\)

\((1+r)^6=\frac{100+79.1286}{100}\)

\((1+r)^6=1.7913\)

\((1+r)=1.7913^{1/6}\)

\(r=1.7913^{1/6}-1\)

Calculator keystroke sequence (calculator set in chain mode) for the last part is:

\(1.7913\) \(1.1020 - 1 = 10.20\%\)

\(r = 10.20\%\)

Using CF and IRR worksheets

Press to enter CF worksheet

Press to clear the CF worksheet


\(CF0=-100\)

\(C01=10\)\(F01=5\) [first five coupons]

\(C02=110\)[= last coupon (10) + face value (100)] \(F02=1\)


Press to enter IRR worksheet

\(IRR\)[calculate the internal rate of return]

\(RI=11\)[set the reinvestment rate]

\(MOD=10.20\%\)

MOD stands for the modified rate of return and is equal to the horizon yield.

Summary

As you can see both approaches give us the same result, which is definitely good news;) But you should also notice that the second one is much quicker. Usually, the Curriculum doesn't teach you how to solve exam problems the fastest way, but WE DO. Get access to one of our premium accounts and see by yourself.

Are you interested in pros and cons of CFA Institute approved calculators? Read this blog post.

Posted in: