We have been asked a number of times now about how precisely the internal rate of return is calculated in the NetActuary Property Calculator. Take (for example) the 3.56% on page 8 of the Technical Note.

The logic is that the internal rate of return equates the present value of the periodic inflows and the net sale proceeds with the initial outflow. This is from the perspective of the individual.

The initial outflow is sale price plus establishment costs less amount borrowed i.e. $500,000 + $15,000 - $300,000 equals $215,000.

The net proceeds for a sale at the end of year four is sale amount less loan outstanding at that point less sale costs less CGT payable i.e. $584,929 - $300,000 - $11,846 - $8,608 equals $264,475. The sale price takes four years of capital appreciation into account. The realised gain is 10% for the CGT (a super fund has a third of the 15% discount after the first year).

The periodic inflows are in fact negative because costs are larger than the rent. This net reduction in take home pay (to take tax effects into account) is adjusted for the value of the non cashflows (depreciation) i.e. 15% x $7,000 equals $1,050. The net inflows for the four years are -$4,362; -$4,128; -$3,889; and -$3,643.

Consequently:

Net Sale Proceeds 264,475 x 1.035551^{-4} = 229,985

Year 1 -4,362 x 1.035551^{-0.5} = -4,286

Year 2 -4,128 x 1.035551^{-1.5} = -3,917

Year 3 -3,889 x 1.035551^{-2.5} = -3,564

Year 4 -3,643 x 1.035551^{-3.5} = -3,224

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**Equals Initial Outlay $215,000**

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The $6 difference is rounding. It will be necessary to make this more complex if the cashflows are positive from rent; where the pension mode is reached; and where there are adjustments for principal payments off the loan.

The calculator uses code to seek through the possible rates of return by interaction to find the appropriate result.

**The NetActuary Team**

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