Proper valuation of perpetuities in an inflationary environment without real growth

We examine the proper valuation of perpetuities without real growth. The case of a 'pure' non growing perpetuity (zero real growth and zero inflation) is of academic interest but in practice it might be difficult to find. The findings contradict what is generally accepted in the literature. In particular we examine the textbook formula for calculating the value of a perpetuity. When working with perpetuities we are in presence of a Chinese box: we have found that when working with perpetuities in a scenario of non zero inflation and zero real growth value increases with inflation. On the other hand, the textbook formula for calculating a non growing perpetuity in the same scenario under values the value of the perpetuity by relevant amounts.