# Not exam-related: Help with interesting IRR problem

I’m actually working on this problem and thought I could use some feedback from all of you well-energized folks over here… Project A: Initial investment= \$50k. It has 60 payments of \$1k each. No other CF’s. Project B: Initial investment= \$50k. It has 60 payments of \$1k each. No other CF’s. They are alike, but project A’s payments occur every 20 days, while project B’s payments occur every 30 days. What’s the IRR of each project?

Off the top of my head IRR A > IRR B (as would NPV A > NPV B) since you’d be getting your payments faster.

11.9% for A and 7.8% for B?

plus them into excel and use formula “XIRR”

I might try the Excel, but I’m interested in finding out how this is usually done. Welcome to the real world CFAI.

It is usually done in a computer software, like excel

It’s just increasing the annualized return - take 1k/3 for one and 1k/2 for the other, adjust the rate and number of periods, and you’ll be able to calculate the IRR.

With project B, you’re extending the life of the project, which will result in a higher discount factor [(1+r)^(t/365)] for every cash flow at a given rate of interest. So you know that with all else equal, the project with the longer life and the higher discount factor is going to have a lower NPV and IRR. What’s your hurdle rate?

The IRR is 7.42% per year assuming 360 days /year, because you just enter initial amount -\$50k, plus 60 payments of \$1000 each. At least that’s what we assume when we say an IRR of x%. If we divide that by 12, we should get the monthly rate, or the period rate. In project A, the period is 30 days, but in project B, the period is 20 days. Therefore, 7.42%/12= 0.6183. Project A : Annualizing the 0.6183 rate, you get 0.6183 * (360/30) = 7.42%. Project B : Annualizing the 0.6183 rate, you get 0.6183 * (360/20) = 11.13% Does that make sense? Does anyone know if the effective APR uses 360 or 365 days?