internal rate of return vs. "simple rate of return"

Hi there,

I'm a practitioner (not in Ibanking) and am cosidering the following (real world) potential investment: Up-front purchase price of investment (a used machine): 14,000 Euros Annual profit of the machine: 1,802 Euros (for 11 years) no residual value after 11 years.

Now I want to calculate the annual rate of return of this investment.

My first simple approach only considers one period as follows: Gross profit: 1,802 Euros Depreciation: (1,273 Euros) net Profit: 503 Euros (Of course, the depreciation is not a cash flow, but it shall take account of the 14,000 Euros purchase price and therefore I think it can be thought of as a cash flow. If you don't like this, let's assume I take out a loan to finance the 14,000 Euros; At a 0% interest rate, the annuity over 11 periods is 1,273 Euros. Then it is a cash flow).

Rate of return: 530 Euros / 14.000 Euros = 3.8% (which I intuitively understand; I put in 14,000 Euros, get out 530 Euros, so the rate of return is 530 / 14,000 = 3,8%)

Second, it put the cash flows for each period into Excel (t0 = -14,000 Euros, t1 to t11 = +1,802 Euros). Using the IRR-function, I get an IRR of 6,3%

Could somebody explain to me, why these two qpproaches (whih seem equivalent to me) yield different rates of return?

Many thanks!