# Rate of Return Analysis (IRR)

Basically, we are solving for an unknown interest rate $i_{∗}$.

- The idea when we solve is to set the Net Present Worth to 0, and solve for $i_{∗}$

#### Internal Rate of Return Analysis (IRR)

The example below was so confusing to me, but I finally get it. They probably should have shown example 2 first though.

- The idea is that we are trying to solve for $i_{∗}$. Below, they show a table with different values of $i_{∗}$, and the values that they return for the RHS.

#### Incremental Rate of Return (ΔIRR)

ummm so do we always just use the incremental rate of return, or do we do the other things too?

IMPORTANT: To compare two mutually exclusive projects ($A$ and $B$), we will write the cash flow of $B$ as $B=A+(B−A)$.

This part seems way to complicated?

- This diagram seems like a good explanation?

##### Examples

They use a pretty drawn out explanation for this first example.

So I think the template is just to set project 1 as the one with the cheaper initial cost. Then, you calculate 3 different IRR, and see which one surpasses the MARR to make your decision.

- Actually, you only need to calculate the third one:

“If the rate of return of the incremental investment is larger than the MARR, then alternative 2 should be selected; otherwise, alternative 1 must be chosen.”

#### Multiple IRR

Make sure to wrap your head around this: