The Present Value of Growth Opportunities

To grow or not to grow, that is the question. And whether it is nobler to reinvest earnings or not depends on the opportunities available.

Everything has an opportunity cost. When the company has earnings, it better do some good things with it, like investing in new projects that will offer returns in excess of those opportunity costs—in other words, the required rate of return. If it can't do that, then it gives the money to shareholders either in a cash dividend or with share repurchases. All of it. If this is the case, do you expect that the company will grow?

You're right.

No, it won't.

Growth requires reinvestment. If the company doesn't have promising opportunities, then there's no reason to keep earnings, or to ask shareholders for any more. It should just distribute it so that they can find better opportunities elsewhere. In this case, earnings will just remain flat, so this 100% distribution each year will be a perpetuity and can be valued just like a perpetuity: earnings divided by the required rate of return. $$\displaystyle V_0 = \frac{E_1}{r} $$ Simple enough.

$$\displaystyle V_0 = \frac{E_1}{r} + PVGO $$ What do you think is the minimum PVGO needed for a company to justify reinvesting earnings?

No. That's far too large for a minimum. It doesn't have to be that much.

No. The cash flows from projects must at least cover the initial outlay, but that's separate from the present value concept. Keep in mind that this value includes all cash outflows and inflows, all discounted to the present.

Exactly! This should sound familiar; it's basically the NPV again, just looking at all feasible opportunities together instead of separate projects. So the money will chase anything positive, since that means a rate of return in excess of _r_.

But if there _are_ some interesting opportunities out there, then the company is worth more. Not only can it provide the present value of that perpetuity, but there are excess returns to be made by reinvesting those earnings. So those future excess returns, discounted to the present, sum to the __present value of growth opportunities (PVGO)__. Add that on to the end of the equation.

For example, suppose that a company has expected earnings of EUR 10 per share, and investors require a 10% return. If the stock is priced at EUR 140, then the PVGO has to be EUR 40. $$\displaystyle 140 = \frac{E_1}{r} + PVGO = \frac{10}{0.10} + 40 $$ Using this same example, consider that the P/E ratio would be 14, since you'd just divide the price of 140 by earnings of 10, each on a per-share basis. What would the P/E have to be if there were no more attractive growth opportunities?

No. The price would fall if the PVGO went to zero.

No. Consider just the no-growth price per share and the earnings.

Yes! Using that same equation for value, or price, just divide everything by earnings to get the P/E. $$\displaystyle \frac{V_0}{E_1} \, or \, \frac{P_0}{E_1} \, or \, P/E = \frac{1}{r} + \frac{PVGO}{E_1} $$ Without any growth opportunities, the P/E is just the inverse of the required rate of return, which is 10 in this case. Lower required rate of return, higher P/E. But with growth, the P/E ratio can even be decomposed into no-growth and growth components.

As a final note here, the PVGO is tough to measure. It's hard to see through combinations of opportunities, and anything in the distant future is impossible to see as technology marches forward. But these should also include the __real options__ available to management. Recall that this is the extra option available when projects are ongoing. Sure, cash flows are forecast, but if things don't work out, there is usually a Plan B available. Those real options can be very valuable in unchartered waters.

To summarize: [[summary]]

No

Yes

Anything positive

At least the initial outlay

At least the current firm value

10

12

14

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