## Internal Rate of Return Analysis

The social internal rate of return (SIRR) is the interest or discount rate that equates the present value of future receipts to the initial cost or outlay. The equation for calculating the social internal rate of return is simply the SNPV formula set equal to zero:

SNPV. = 0 = £ MSBit - £ MSCit 1 t = 1 (1 + k*)t t = 1 (1 + k*)t

This equation is solved for the discount rate, k*, that produces a zero net present value by setting discounted future marginal social benefits equal to marginal social costs. That discount rate is the social internal rate of return earned by the program, that is, SIRR{ = k*.

Because the social net present-value equation is complex, it is difficult to solve for the actual social internal rate of return on an investment without a computer spreadsheet. For this reason, trial and error is sometimes employed. One begins by arbitrarily selecting a social discount rate, such as 10 percent. If it yields a positive SNPV, the social internal rate of return must be greater than the 10 percent interest or discount rate used, and another higher rate is tried. If the chosen rate yields a negative SNPV, the internal rate of return on the program is lower than the 10 percent social discount rate, and the SNPV calculation must be repeated using a lower social discount rate. This process of changing the social discount rate and recalculating the net present value continues until the discounted present value of future marginal social benefits equals the present value of marginal social costs. The interest rate that brings about this equality is the yield, or social internal rate of return on the program.

Using trial and error, an electronic financial calculator, or a spreadsheet software program, the internal rate of return for program A is SIRRA = 6.79%. Similarly, SIRRB = 15.78% and SIRRC = 14.81%. Because SIRRB and SIRRC exceed the cost of capital, program B and program C are attractive and should be undertaken. Because SIRRA is less than the cost of capital, program A is unattractive and should not be undertaken. In general, social internal rate of return analysis suggests that programs should be accepted when the SIRR > k and rejected when the SIRR < k.