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Financial methods in environmental decisions
Financial methods in environmental decisions

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Average net annual rate of return

The average net annual rate of return method is a variation on the average gross annual rate of return method. It assumes full recovery of the whole project investment, including fixed asset costs (such as buildings and machinery), out of net cash flows before calculating the rate of return on the investment. Because of this, the average annual rate of return is expressed as a percentage of the average capital employed instead of as a percentage of the original investment.

This can be illustrated with the same two examples that I used previously.

The variables in the equations stand for the following:

  • PI is initial project investment
  • NCF is positive net cash flow
  • L is project life
  • ANCF is average net cash flow.

Project A

equation left hand side cap p times cap i equals right hand side prefix pound of 100 000
multiline equation line 1 total cap n times cap c times cap f over the five years line 2 of the project life equation left hand side equals right hand side prefix pound of 135 000
multiline equation line 1 surplus total cap n times cap c times cap f after line 2 recovery of initial investment equation left hand side equals right hand side pound 35 000
multiline equation line 1 cap a times cap n times cap c times cap f per year equation left hand side equals right hand side cap n times cap c times cap f minus cap p times cap i divided by cap l line 2 equation left hand side equals right hand side pound 35 000 divided by five line 3 equation left hand side equals right hand side prefix pound of 7000

This is then divided by the average capital employed (ACE), which in this case is calculated on the basis of the initial outlay of £100 000, and a final outlay of zero, that is

equation left hand side cap a times cap c times cap e equals right hand side prefix pound of 50 000
multiline equation line 1 average net annual rate of return equation left hand side equals right hand side cap a times cap n times cap c times cap f divided by cap a times cap c times cap e multiplication 100 line 2 equation left hand side equals right hand side prefix pound of 7000 divided by prefix pound of 50 000 multiplication 100 line 3 equals 14 percent

Project B

equation left hand side cap p times cap i equals right hand side pound 100 000
equation left hand side cap n times cap c times cap f equals right hand side pound 160 000
cap l equals five
equation left hand side multiline equation line 1 surplus total net cash flow line 2 after recovery of cap p times cap i equals right hand side prefix pound of 60 000
multiline equation line 1 cap a times cap n times cap c times cap f per year equation left hand side equals right hand side prefix pound of 60 000 divided by five line 2 equation left hand side equals right hand side prefix pound of 12 000
multiline equation line 1 average net annual rate of return equation left hand side equals right hand side prefix pound of 12 000 divided by prefix pound of 50 000 multiplication 100 line 2 equals 24 percent

So the overall result from the net method identifies project B as the better option, the same as from the gross method.