Question

How could a growing annuity be used to value a corporation that has growth opportunities?

Answer 1

A growing annuity refers to equal cash flows growing at equal rate. For example, if company has cash flow of $100 p in year 1 and the cash flows grows at 10% rate then it shall receieve cash flows of $110 and $121 in year 2 and 3 respectively.

There are formulas to calculate growing annuity's present value and future value. These can be used inorder to find the net present value or net future value. We shall understand the concept of valuation from the following example.

Suppose a company finds out that there are various growing opportunities and decides to engage in a project with initial investment of $500. The company researches and finds out that the cash inflows in the coming year will $100 and this cash flow will grow by 10% annually. The required rate of return for the company is 15%. The company wants to value this project for 10 years. With the help of growing annuity we shall find the net present value and decide whether the project is viable for growth or not.

$Present Value of Growing Annuity = \frac{P}{r-g}*\left [ 1- (\frac{1+g}{1+r})^{n} \right ]$

Where P = starting cash flow, r = required rate, g = growth rate and n = number of years

Now in our example starting cash flow is 100, required rate is 15%, growth rate is 10% and number of the year = 10.

$Present Value of Growing Annuity = \frac{100}{.15-.10}*\left [ 1- (\frac{1+.10}{1+.15})^{10} \right ]$

Solving this we get,

Present Value of Growing Annuity = 717.733

Hence the present value is 717.733 and the initial cash outflow is $500. Therefore, the project should be accepted.

Hence, in this manner growining annuity can be used to value a corporation that has growth opportunity.

If you have any doubt, ask me in the comment section.