# How to calculate internal rate of return [beginner]

I am an informatics student who was given an assignment to do with finance and we're not very financially literate.

We are asked to theoretically build a platform to mimic bond exchanges. As part of this platform, we are told we need to calculate an internal rate of return.

You can see the rate of return formula we were provided here:

Now, assuming we have a bond whose details are as follows: the bond is priced at \$100 with a term of 5 years. The coupon/interest rate is 5%, and the frequency of payments is annual.

Using the assumptions above, we can infer that the payout would be \$125 (paid in four instalments of \$5 and a final instalment of \$105).

From what I understand and what we were told (and please do correct me if I'm wrong), the internal rate of return represents the point at which inflation becomes too high for an investor to make a profit on the bond.

I have a function that already calculates the payout assuming inflation (for example, assuming an inflation of 5% using the bond described above, the payout would be \$99.99).

We are told that the internal rate of return for this bond is 0.0432 (i.e. 4.32%). What I do not understand is how to get to that number.

So, in summary:

I have the details at Point A (price = \$100, term = 5 years, coupon = 5%, frequency = annual) and I have the number I want to get to at Point B (internal rate of return = 4.32%).

I just want to know how to get from point A to point B.

• The price at any given moment and the redemption value, the value paid at maturity, are almost never the same. Nov 23, 2017 at 5:19

Either there is some more information you have not given us or the answer you have been provided is incorrect. The internal rate of return based on this information is 5%.

The internal rate of return is the rate which, when used to discount the payments of a bond, makes the present value of the bond payments equal to its price. Therefore in your case, it's the r that solves

0 = -100 + 5/(1+r) + 5/(1+r)^2 + 5/(1+r)^3 + 5/(1+r)^4 + 105/(1+r)^5

In the context of a default-free bond the IRR is the same as the Yield to Maturity. You will need to use an optimizer in general, but for an annual bond that has just paid a coupon and is priced at par, the IRR or YTM will be equal to the coupon rate.

Is there perhaps a chance that the bond will default? Does the first payment come a year from today? Is today's price really 100? Any other complications you have not mentioned?