CFA® Exam: Computing Horizon Yield Using IRR & MOD

CFA Exam: Level 1 / Fixed Income / Horizon Yield



Level 1 CFA Exam: Computing Horizon Yield Using IRR & MOD

This blog post was created as a part of the CFA exam review series to help you in your level 1 exam revision, whether done regularly or shortly before your CFA exam.


How to calculate the horizon yield in the most efficient and fastest way using an approved CFA exam 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 an 'algebraic way'. Then, we will use the TIBA Professional CF and IRR worksheets.


Horizon Yield: 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 to Compute Horizon Yield

Here's how to compute the horizon yield using the CF and IRR worksheets in your CFA exam approved calculator (TIBA Plus Professional):

Press to enter the 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 the 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. Set up your study plan and and get all the CFA exam materials and tools that we have prepared for you.


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Are you interested in the pros and cons of CFA exam approved calculators?
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LAST UPDATE: 19 Sept 2022

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