Question

show and explain why the formula for growing perpetuity holds only when r > g.

Answer 1

The present value of growing perpetuity can be calculated as Cash flow/(R-g)

The formula holds true only when R>g. For example if the expected cash flow = $100 and R=8% while g=6%

The PV of perpetuity will be 100/(8%-6%) = $5000

If R=g, or R< g the formula will fai; because the stream of payments will no longer be an infinitely decreasing series of numbers that have a finite sum. For example in the above problem if g=r=8%

The PV of perpetuity cannot be ascertained since the divisor is zero

If g= 8% while R=6%

Pv will be 100/(6%-8%) = -$5000 which is a negative figure. This is not true since there are only receipts occurring and hence its present value cannot be negative.