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September 29th, 2012, 09:41 AM   #1
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internal rate of return specific for this exercise

Hi,
I am revising for a final test from introduction into finance that I am taking at coursera. Today I came accross a problem with internal rate of return, but let me explain all from the beginning.

The exercise I am looking at is this:
Question 9
(15 points) Reggie has just taken over management of a family business. He wants to make sure
that it makes financial sense to keep the business going. He could sell the building today for
$520,000. Keeping the business going will require a $50,000 renovation now and will yield an
annual profit of $72,000 for the next 20 years (for simplicity assume these occur at year end,
beginning one year from now). The discount/interest rate is 10%? What are the NPV and IRR of
this decision?

When I was first doing the test, I was able to calculate that the Net Present Value = 42,976.59 (difference between present value of the first option and of the second option). This question was a multiple choice, where one answer contained both NPV and IRR values. I was getting funny results for Internal Rate of Return, none of them was listed in the options, so I went for the answer which I knew was right (because of NPV) and chose it, even if I had no idea of how to get the result reported, which was 11.09%. I kind of thought that the things would eventually click somewhere in my head and I would understand how to get through the problem... anyway, now I am one week from the final test and still donīt get it.

Do you think you could explain me how to come to that number? What should I take into account? What cash flows are the important ones? I really would be very thankful.

Bye, Laura
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October 2nd, 2012, 02:29 PM   #2
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Re: internal rate of return specific for this exercise

You arrive at the 11.09% IRR very similarly to how you calc'd the present value of the cash flow stream using a 10% discount rate.

For the first part of the question you hit the cash flow sequence (-570,000; +72,000; +72,000; ??? ; +72,000) with a discount rate of 10% and determined the NPV to be 42,976.59.

Getting to the IRR is similar, although involving a more drawn out trial-and-error approach. Just keep hitting that same cash flow sequence with different discount rates until you land on one that gives a NPV of zero (or close enuf for practical purposes). The fact that the cash flows have a positive NPV when discounted at 10% at least tells you that whatever rate (the IRR) produces a zero NPV, it'll be some rate north of 10%. Thus you at least know what direction from 10% you need to proceed in, to get started.

Financial calculators and spreadsheets also have built-in IRR functions which knock out those trial-and-error iterations for you in a blink, but such method might not be permissible in your homework / test context. Besides, it's good to understand the concept of IRR as being that rate that make's a project's NPV equal to zero, and knocking out a few trial-and-error exercises the long way helps to illuminate that for you.

Good luck on the final.
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