If Stream B really is negative, my solution can still work. The token explanation is he is borrowing the net present value of Stream B which he will pay back accordingly to help fund Stream A from which she will get the future cash flows.

Row 4 will still be the total but because the signs of Stream A and B are opposites, the result will be the difference.

I repeat she has to extend the years until the resulting IRR is the same from one year to the next.

quote:

Originally posted by trapper189:
Seems like a poorly worded question. How does one receive negative cash flow?

I read it as with A you get $11,600 at the end of year 3 and then the amount grows at 4% in each of the following years. So $11,600*1.04 in year 4, $11,600*1.04^2 in year 5, $11,600*1.04^3 in year 6, and so on.

For B you pay out a fixed $13,000 a year starting at the end of year 2.

If you add the two streams together it would be:

Today: 0+0
Year 1: 0+0
Year 2: 0-$13,000
Year 3: $11,600-$13,000
Year 4 and subsequent years: $11,600*1.04^(Year-3)-$13,000

But again, the question doesn't seem right.

I believe this is set up right.

This looks like a project that would start debt service (the B negative cash flows) in two years and start generating earnings (the A positive cash flows) a year later. The combined project would be cash flow negative for an initial period, starting in year 2 and would take take a few years (till year 6) for the growth factor to turn the combined annual cash flow positive.

The IRR is the interest rate that would make the sum of the year's numbers set up above, after each is discounted back to the present by the 12% discount rate, equal zero. I suspect the prof is looking for an algebraic answer.

For a rough approximation I put it into Excel for 50 years and got an IRR of 8.6%.

Thank you all!

Rey HRH, you had it set up right. I set up a spreadsheet using your instructions, and came up with an IRR of 16.84% going out 100 years. The answer they were looking for was 16.9%, and it may have gotten there if I had taken it out past 100 years.

Good to hear. There’s most likely a formula to address the ever increasing payout into perpetuity but it would be in the textbook your friend is using for class.

You probably would have seen the IRR still not being constant if you displayed more decimal places. But I don’t know how many places it would take and I didn’t think of that angle when I was considering the problem. I don’t know if I would have caught it myself.