# What is ROA's relation to the IRR?

My question is that if you have 3 cash flows \$36,\$23,\$11 that respectively occur at the end of year 1 , year 2, and year 3 and you paid 60 dollars at the beginning of the year to generate these cash flows. And the cash flows represent the only assets that you have. Why is the internal rate of return the same thing as your return on assets? note that : Your return on assets is (net income)/total assets. note that:; The irr simply gives you the rate of return required to be equivalent to the amount of money that you initially invested. Qualitatively and perhaps quantitatively why must ROA=IRR ?

The 60 you paid may be a mix of expense, capital investment, and who knows what else. From the information given you can’t determine ROA; it could be 1000% as far as we know.

ROA does not equal to IRR. It just so happens to be the case in this example. Dreary

But if the 60\$ only went into assets, is ROA = IRR since the return is generated only from assets?

Again, no. IRR is a forward-looking time value of money concept; ROA is a backward-looking snapshot of an accounting metric.

Ok. That makes sense. Thanks. Then, say the only cash flow is generated from your asset and the rate of return is constant over thse three years. If the company maintains a constant rate of return, then shouldn’t IRR = ROA? Thanks.

I think that if all the cash flow is generated from the capital invested, that is all the assets of the company participate to creating those cashflows then the internal rate of return should be equal to return on assets. Are you guys sure that Irr can be just forward looked?

Again, no. “Return” is typically some accounting measure like net income. There’s a large difference between revenues (positive project cash flows) and net income, such as debt service, DD&A, fixed costs, taxes, etc.

Darien basically you are saying that return has to do with non cash item such as depreciation but irr is solely based on cash flows. That makes sense.

IRR isn’t necessarily based on cash flows. Its most common uses in finance include YTM for bonds and evaluating projects in project finance, which usually reference cash flows. IRR is simply a mathematical calculation that could be applied to any time series of flows, such as # of seeds you sow vs # you harvest. But is has nothing whatsoever to do with roa or roe or eps or dividend yield or any other ratio you can dream up. Even if “return” were exactly cash flows, roa would still have nothing to do with irr. If you dont’ understand this you need some fundamental remediation in accounting and finance.

Also, with IRR you assume the cash flows compound over the years, but not so in your assets example, I think. Dreary