Growing Perpetuity

Definition

A growing perpetuity is a financial concept that refers to a stream of cash flows that continues indefinitely, increasing at a constant rate over time. This idea connects closely to the present value calculations, as it helps determine the current worth of future cash flows that will grow forever. Understanding growing perpetuities is crucial for evaluating investments or assets that generate returns that are expected to rise consistently in the future.

5 Must Know Facts For Your Next Test

1. The formula for calculating the present value of a growing perpetuity is given by $$PV = \frac{C}{r - g}$$, where C is the cash flow in the first period, r is the discount rate, and g is the growth rate.
2. For a growing perpetuity to be valid, the growth rate must be less than the discount rate (g < r). If not, the present value would be infinite.
3. Growing perpetuities are often used in business valuations, particularly when assessing companies with predictable growth in dividends or cash flows.
4. Common applications include stocks with dividend growth models, where dividends are expected to grow at a constant rate indefinitely.
5. Investors use growing perpetuity concepts to evaluate projects and investments by assessing their long-term profitability based on expected growth rates.

Review Questions

• How does understanding growing perpetuities enhance the evaluation of long-term investments?
  • Understanding growing perpetuities allows investors to assess the value of investments that provide cash flows expected to increase over time. By using the present value formula for growing perpetuities, investors can estimate how much future cash flows are worth today, enabling more informed decisions about whether to invest. This perspective is particularly relevant for businesses or assets that have reliable growth patterns in their earnings or dividends.
• Discuss how the discount rate and growth rate interact in determining the present value of a growing perpetuity.
  • The interaction between the discount rate and growth rate is critical when calculating the present value of a growing perpetuity. The formula highlights that if the growth rate exceeds the discount rate, it leads to an undefined present value because it implies an ever-increasing cash flow without bounds. Therefore, for meaningful valuations, it's essential that the discount rate is greater than the growth rate. This relationship helps investors gauge risk and potential returns when forecasting future cash flows.
• Evaluate a hypothetical scenario where an investment has a cash flow starting at $100, with a growth rate of 5% and a discount rate of 8%. What implications does this have for its valuation as a growing perpetuity?
  • In this scenario, we can apply the formula for the present value of a growing perpetuity: $$PV = \frac{C}{r - g}$$. Substituting in our values gives us $$PV = \frac{100}{0.08 - 0.05} = \frac{100}{0.03} = 3333.33$$. This means that today's worth of receiving $100 per year, growing at 5%, while being discounted at 8%, is $3,333.33. This valuation indicates that despite a modest initial cash flow, consistent growth over time creates significant value for investors. Thus, it highlights how growing perpetuities can lead to attractive investment opportunities even with low starting cash flows.

Related terms

Present Value: The current value of a future sum of money or stream of cash flows, discounted at a specific interest rate.

Perpetuity: A financial instrument that pays a constant amount indefinitely without an end date.

Discount Rate: The interest rate used to determine the present value of future cash flows, reflecting the opportunity cost of capital.