I have a question for one of the practice problems in the back of Reading 34. Question 14 states that Wilson Flannery is concerned that this project has multiple IRRs and provides the cash flows as -50 in year 0, 100 in year 1, and -50 in year 3. No cash flow in year 2. It asks how many discount rates produce a zero NPV for this project?

Then the options are:

A) One a discount rate of 0%.

B) Two, discount rates of 0 and 32%.

C) Two, discount rates of 0 and 62%.

Now I computed this and I found that NPV is zero only at 0%. It also happens at approximately 61.8%, but that isn’t one of the options, so I chose A. But the answer key says C because 61.8% is close enough to 62%.

My question is why is this so? Almost everywhere that I have read, it always says to select the exact answer. At 62% the NPV wasn’t 0, so then why are the answers saying that 61.8% is close enough to 62% to be selected. The question didn’t say anywhere approximately 62% either.

Can someone help out? Is this a mistake or is this how we should be looking at the questions on CFA?

You think that 61.8% is not exact enough to be 62%?

What about 62.000000000000000000000000001?

Put 61.8 in Excel and round to nearest integer.

If 61.8% is an IRR then answer A is clearly _ wrong _; it says that there’s _ only one _ IRR.

On the real exam the questions always include hedging words, such as “closest to”, to account for rounding.

Okay thank you S2000magician. That helps! :slight_smile:

My pleasure.

Also, the cumulative cash flow changed sign more than once, so there will be multiple IRRs.

That’s better.

Calculating an IRR is essentially determining the zeros (roots) of a polynomial.

If you have, say, a 3rd-degree polynomial with two sign changes, it might have three roots, but it might have only one. Or two. It definitely has at least one.