Question

Explain why we can use the present value of a no-growth perpetuity to quickly estimate the value of a relatively long-lived, no-growth financial asset. Make sure you provide a mathematical example.

Answer 1

A perpetuity involves the financial system where a stream of cash flow payments is determined on continues indefinite means or and is an annuity which has no end. In valuation analysis, perpetuities are used to find the present value of a company’s future projected cash flow stream and the company’s terminal value. Essentially, perpetuity is a series of cash flows that keep paying out forever. A growing perpetuity is a series of periodic payments that grow at a proportionate rate and are received for an infinite amount of time.
We can use the present value of a no-growth perpetuity to quickly estimate the value of a relatively long-lived, no-growth financial asset supported by following arguments:
-   No growth perpetuity calculation is less complex process as compared to the growth perpetuity calculation for investments made for long term.
-   The discounting factor or the Present value factor in case of relatively long-lived, no-growth financial assets is larger than the growth factor to the extent that we may skip the growth factor for present value perpetuity calculation.
-   We can use the simple perpetuity calculation method to determine the Present value perpetuity of long term investments or assets with least or no growth to increase the chances of the accuracy of results ignoring the explicit growth conditions.
-   The long term market timeline would offer exponentially higher inflation rates, so that the real growth factor becomes nil or slightly negative.
-   Using the no-growth perpetuity calculation in case of long term investments would give an absolute present value of cash flows even if the investment grows at a considerable rate.

For instance, the present value of a growing perpetuity formula would be an annual cash flow of $600,000 that will continue indefinitely for the investment in real estate bonds. The cash flow is expected to grow at 1.5% per year and the required return used for the discount rate is 10%. The equation for this example of the present value of a growing perpetuity formula would be:

= $600,000/0.10-0.015 = $7,058,823.52,

$600,000 would be the return a present value of $7,058,823.52.