6. Summary

This section has taken a closer look at so-called perpetuities. These are projects or investment proposals that deliver a constant stream of cash flows and run indefinitely. Hence the name "perpetuity."

  

Perpetuities differ along two main dimensions:

  • Timing of cash flows: Does the cash flow occur at the beginning or at the end of each investment period?
  • Growth of cash flows: Does the perpetuity deliver a constant cash flow or a cash flow that grows at a constant rate?

   

Based on these two dimensions, there are 4 basic types of perpetuities:

   

Type Timing Growth Formula
Ordinary Perpetuity End of investment period Constant Cash Flow \( PV = \frac{C}{R} \)
Perpetuity Due Beginning of investment period Constant Cash Flow \( PV = C+ \frac{C}{R} \)
General Formula for Level Perpetuity In n investment periods Constant Cash Flow \( \bf{PV = \frac{C}{R} \times (1+R)^{(1-n)}} \)
Growing Perpetuity End of investment period Constant Growth Rate \( PV = \frac{C_1}{R-g} \)
Growing Perpetuity Due Beginning of investment period Constant Growth Rate \( PV = C_0 \times \frac{1+R}{R-g} \)
General Formula for Growing Perpetuity In n investment periods Constant Growth Rate \( \bf{PV = \frac{C_{n}}{R-g} \times (1+R)^{(1-n)}} \)

 

   

Properly applied, perpetuities are an extremely useful and powerful valuation tool. Especially in the context of equity or firm valuation, financial analysts and managers often rely on perpetuities to model (parts of) the firm's future. As it turns out, the model of a growing perpetuity often does a very good job at valuing mature firms or their stocks. These topics will be discussed extensively in other modules.