# IRR vs Interest rate v loan

Probably a simple answer, but I don't seem to get it. I've always been taught the IRR is the equivalent of the rate i'd get if I invest the same amount at a bank. (Or the % I need to compare my investment to a loan).

Now, calculating it in Excel gives me results I don't understand. Let's assume (i'm working on energy saving projects) I install solar panels: Investment: 8000 € Yearly income 1500 €

That's a Payback Time of 5,3 yrs

Now, over a period of 10, Excel calculates an IRR of 13% Cashflow wise, i have 15000 € in hand at the end of the 10 yrs....Which is nowhere close to the 13% of course, but rather around 6,5 % interest rate If I had invested the 8000 € @ 13% in a bank I'd have 27157 € in hand. As seen in my Excel

Now, if i take a loan for the 8000 € investment, I could will always make profit as long as I don't exceed the rate of the IRR. I guess this is the "cost of capital" which I've heard about.

Is there a financial tool/concept which calculates or compares my investment in solar panels to an investment in a bank. I guess the main difference is you don't keep you capital which you have invested when you pay for something like solar panels.

Any help welcome, thanks.

You're forgetting to value the intermediate cash flows separately. Yes if you saved 8,000 and it grew to 15,000 in 10 years that would be an IRR of about 6% (you can confirm this in Excel by setting the intermediate flows to 0 and the last flow to 15,000).

But, you don't just have a final balance- you are taking out 1,500 each year!

I think about IRR this way:

At what interest rate could I save the 8,000 so that I could withdraw 1,500 each year and end up with 0 after 10 years?

If I save 8,000 at 13.4%, after one year I'll have 9,075 after interest. If I take out 1,500, I'll have 7,575. After year two, I'll have 8,592 saved (earning slightly less interest since I took out more than I earned in interest), and 7,092 after taking out 1,500. If I continue for 10 years, I'll have exactly 1,500 left, leaving zero after I withdraw it.

The full "amortization table" is as follows That's the reason the loan interest rate must be lower to make it profitable overall. If you pay more in loan interest than you're "making" on the solar panels, then you're losing out overall.

• Thanks, D Stanley, I thought the IRR takes into account the reinvestment of the profit (1500 in this example), which it doesn't apparently. So IRR is a good tool to compare it to a loan, not to compare it to a bank investment. Is there a tool to do this? Thanks again!
– JoF
Dec 21, 2021 at 21:11
• Reinvestment only makes sense if you think about a bond with coupons that you have to reinvest. That's not really a proper analogy here since you have an initial outflow, periodic inflows, and no "final" outflow. For this type of project a loan is a more appropriate structure (which is the same as what I have above with the cash flows reversed) Dec 21, 2021 at 21:47
• Thanks D Stanley!
– JoF
Dec 21, 2021 at 22:37