# Link between Present Value of Growth Opportunities (PVGO) and Dividend Valuation

Valuing a corporation is a complex exercise. This is partly because there are multiple ways of looking at the same information. One such example is mentioned in this article. Dividend discount valuation and present value of growth opportunities may seem to be two completely different topics. However, there exists a link between them. In fact if the dividend discount valuation is known, we can point out with some degree of precision what is the amount of money that the acquirer is paying anticipating growth opportunities in the target firm.

### A Different Perspective:

Let’s say that we have used the dividend discount model and come to the conclusion that a certain company is worth \$100. We done this by adding the present value derived from the horizon periods to the terminal value which could have been derived using the Gordon growth model.

Hence, Value (Firm) = Present Value (Horizon Period) +Terminal Value

Now, a different way to look at this would be to consider the value of the company in two parts again. One part would be the value that the firm would have if it simply continued its current level of operations and paid out all its earnings as dividend i.e. the no growth scenario

The residual part would therefore be the present value of the anticipated gains from growth in the firm’s business. To put it in the form of a formula:

Value (Firm) = Value (No Growth Assumption) + Value (Growth Opportunities)

Now, if we just rearrange the components of the formula, we get

Present Value (Growth Opportunities) = Value (Firm) – Value (No Growth Assumption)

In this case, we already know the value of the firm i.e. \$100. So, if we can find the value of the firm without the growth, we can obtain the present value of growth opportunities.

### Finding the Value of a Firm with No Growth Assumption

To answer this question, we need to think about how does a firm which is not aiming for any growth functions. Well, it gives out 100% of its earnings as dividend and does not invest anything in growth. Hence, the earnings will be the same every year and there will be no growth.

Value (No Growth Assumption) = Earnings/Required Rate of Return

Usually, earnings and dividends mean two very different things. However, in this case, they mean the exact same thing because the firm is paying 100% of its earnings out as dividends.

Since, we know the present dividend, we can solve for the value of the firm with no growth assumption. Let’s say this value is \$45

Hence, the present value of growth opportunity being paid by the firm is \$100 - \$45 i.e. \$55

### Use of this Analysis:

This analysis is widely used within to industry to double check whether the price being paid for the target firm is rational. For instance, let’s say if in this case, the target firm is a market leader with 60% market share. We are paying over two times the amount that the firm is worth considering its current operations and assets.

However, since the firm already has 60% market share, it is highly unlikely that the firm will able to grow twice as big unless the market itself is growing rapidly and the firm is expected to get a large share of that growth.

Thus, we must acquire this firm at \$100 only if we are sure that it is worth \$55 in terms of future opportunities i.e. the assets or the operations which are not present as of now.

### Conclusion:

The job of an analyst is to check multiple times using different relationships amongst the financial statements and common sense whether the price being paid is fair.

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