Perpetuities

The Perpetuity

A perpetuity is the closed form for a level cash flow forever.

highlighted = computed this step

Level cash flow forever

A level perpetuity is a projected cash flow that continues forever at the same amount.

level perpetuity: C,C,C,…\text{level perpetuity: } C,C,C,\ldots

Closed form

The closed form present value is cash flow divided by discount rate.

PV=Cr\text{PV}=\frac{C}{r}

Level perpetuity value

With projected cash flow of $100.00 per year and discount rate 10%, the DCF value under these assumptions is $1,000.00.

PV=$100.0010%=$1,000.00\text{PV}=\frac{\$100.00}{10\%}=\$1,000.00