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##### Subject 4. The Present Value of Growth Opportunities
If a company does not reinvest its earnings and pays out each period's income to the shareholders, its growth rate will be zero, provided that return on equity is constant. Income in each period equals the product of ROE and the company's equity balance. When both of these two components are constant, dividends are essentially a perpetuity, with each period's dividend equal to the company's earnings. Consequently, the value of a company that distributes all its earnings can be calculated as:

V = E/r

Positive NPV projects earn more than other projects with similar risk. For that reason, companies that reinvest a part of earnings in positive-NPV projects should have a premium to the no-growth base value. Such premium is called the present value of growth opportunities (PVGO). Consequently, the total value of a company that reinvests its earnings equals the base no-growth value plus the PVGO:

V = E/r + PVGO

If the projects available to the company have negative NPV, retention of earnings would be detrimental to the company's value, as PVGO would be negative.

Assuming that the markets are efficient (price of a company equals its value), we can always calculate the PVGO as PVGO = P - E/r

Dividing this value by P, the company's price, we can estimate what part of a company's value depends on its expected growth opportunities.

Example

An analyst has gathered the following data to analyze a stock.

• Current stock price: \$20.
• Expected price at the end of the next period: \$22.
• Current period earnings: \$2.
• Expected next period's earnings: \$2.2.
• Stable earnings growth rate to infinity: 6%.
• Beta: 1.2.
• Required rate of return: 12%.

The present value of the growth opportunities of this stock is 20 - 2/0.12 = 3.33.

User Comment
danlan2 PVGO=FF*G*E
weiw when calculating the PVGO in example, we should use the next period earnings instead of current period earnings in numerator, right?
tbg091789 Yes, the E should be E1 instead.
connor15 No. The E should be a non-growth E, which means E = E1 = E2 = \$2.
davidt876 yea they do say that the current period earnings = 2, and the current price = 20. so they really should ask for the *current* present value of PVGO. if they had asked for the *next period's expected value* of PVGO, you'd be right to say 22-2.2/0.12=3.67, and if they asked for the *present value of the next period's expected PVGO*, it'd be 3.67/1.12=3.27 