Great question, thanks for reaching out!
First, let's agree what we mean by ROI and why we want to calculate it. In this simplest case ROI is the same as IRR (because it’s a project with a fixed timeline), it's an annualized rate of return that we're going to get on our investment. We usually want to calculate it to compare with our Cost of Capital or “WACC” (which is the time value of money for the investor). In conclusion, if our return exceeds our cost of capital, that means we're creating value for our shareholders. So you don’t use time value of money when calculation ROI, you rather use it as a comparable value.
Using the above logic, if the return exactly equals cost of capital we’re not creating and not destroying value, so the NPV is exactly 0. And that’s the equation you use to calculate the IRR (you discount your cashflows by exactly IRR and solve for NPV=0):
For the case interviews no one expects you to be able to nail an IRR number in your head. But if you can get pretty close, you're fine. There are some simple IRRs that you can remember, such as:
- Double your money in 1 year, IRR = 100%
- Double your money in 2 years, IRR = 41%; about 40%
- Double your money in 3 years, IRR = 26%; about 25%
- Double your money in 4 years, IRR = 19%; about 20%
- Double your money in 5 years, IRR = 15%; about 15%
For more than 5 years, there's also a "Rule of 72", which says that if you divide 72 by your rate of return, the resulting number is roughly how many years it will take your money to double. For example, if I expect returns of 7 percent a year, I would expect my money to double in about 10 years (72 / 7 = 10.3 years).
Let's look at your case. We invest 100 and get 15 every year, so it takes around 7 years to "double our money" (in this case of a fixed project - to return our 100 back). By the rule of 72, we can say that the IRR is 72/7 ~= 10%, which is pretty close if you want to double-check it in Excel:
Now, on the second part you are absolutely right. If the projects have the same IRR and require the same investment, you want your cashflows as soon as possible, so you are comparing your Payback periods (how long it takes to return the initial investment).
Hope this helps, feel free to reach out if you have any further questions.