What condition must hold for the growing perpetuity terminal value formula to yield a finite value?

What condition must hold for the growing perpetuity terminal value formula to yield a finite value?

• A. w < g
• B. w = g
• C. w > g
• D. g > 0

Answer: (C)

The key idea is convergence of the growing perpetuity's value. When cash flows grow at rate g forever and you discount them at rate w, the terminal value formula is TV = CF1 / (w − g). For this to yield a finite number, the denominator must be positive, which means w must be greater than g. If w equals g, the denominator is zero and the value blows up to infinity; if w is less than g, the cash flows grow faster than you discount, so the present value diverges and the formula no longer gives a finite result. So the condition for a finite terminal value is that the discount rate exceeds the growth rate.

The key idea is convergence of the growing perpetuity's value. When cash flows grow at rate g forever and you discount them at rate w, the terminal value formula is TV = CF1 / (w − g). For this to yield a finite number, the denominator must be positive, which means w must be greater than g. If w equals g, the denominator is zero and the value blows up to infinity; if w is less than g, the cash flows grow faster than you discount, so the present value diverges and the formula no longer gives a finite result. So the condition for a finite terminal value is that the discount rate exceeds the growth rate.