Perpetuities

The Growing Perpetuity (Gordon)

A growing perpetuity adds a constant growth assumption.

highlighted = computed this step

Growth forever

A growing perpetuity assumes the projected cash flow grows at a constant rate forever.

PV=C(1+g)r−g\text{PV}=\frac{C(1+g)}{r-g}

Gordon-growth value

With projected cash flow of $100.00, growth of 4%, and discount rate 10%, the DCF value under these assumptions displays as $1,733.33. The exact fraction is 520000/3 cents.

PV=$100.00(1+4%)10%−4%=520000/3 cents≈$1,733.33\text{PV}=\frac{\$100.00(1+4\%)}{10\% - 4\%}=520000/3\text{ cents}\approx \$1,733.33

Growth constraint

This formula requires the discount rate to be greater than the growth rate. If growth is greater than or equal to the discount rate, the infinite value diverges and the formula is not meaningful.

r>gr>g