## Are Faster Growing Firms Better Bargains

A similar question to that posed in the previous subsection is "Would it make more sense to The price should invest in companies that grow quickly rather than slowly"? If you wish, you can think of this at^bute^ofthe firms question as asking whether you should buy stocks in a fast-growing company like Microsoft '

or in a slow-growing company like Exxon. The answer is that it does not matter in a perfect market. Whether a company is growing fast or growing slow is already incorporated in the firm's price today, which is just the discounted net present value of the firm's cash flows that will accrue to the owners. Therefore, neither is the better deal.

For example, consider company "Grow" (G) that will produce Should you invest in a fast grower or a slow

and company "Shrink" (5) that will produce

Is G not a better company to buy than 5?

There is no uncertainty involved, and both firms face the same cost of capital of 10% per annum. Let's find out: Then the price of G today is C°mpute the va|ues.

PVt=°(G) = (1 + 10%)1 + (1 + 10%)2 + (1 + 10%)3 ~ $402"71 (35)

and the price of 5 today is

PVt=°(5) = (1 + 10%) 1 + (1 + 10%)2 + (1 + 10%)3 ^ $225"39 (36)

If you invest in G, then next year you will have $100 cash, and own a company with $150 and Your investment dollar

$250 cash flows coming up. G's value at time 1 (so PV now has subscript 1) will thus be grows at the same rate, disconnected from the

$150 $250 cash flow rate.

Your investment will have earned arate of return of $442.98/$402.71-1 = 10%. Ifyouinstead invest in 5, then next year you will receive $100 cash, and own a company with "only" $90 and $80 cash flows coming up. 5's value will thus be

38" Chapter 3 MORE TIME VALUE OF MONEY

Your investment will have earned a rate of return of $247.39/5225.39 - 1 = 10%. In either case, you will earn the fair rate of return of 10%. Whether cash flows are growing at a rate of +50%, -10%, +237.5%, or -92% is irrelevant: the firms' market prices today already reflect their future growth rates. There is no necessary connection between the growth rate of the underlying project cash flows or earnings, and the growth rate of your investment money (i.e., your expected rate of return). Make sure you understand the thought experiment here: This statement that higher-growth firms do not necessarily earn a higher rate of return does not mean that a firm in which managers succeed in increasing the future cash flows at no extra investment cost will not be worth more. Such firms will indeed be worth more, and the current owners will benefit from the rise in future cash flows, but this will also be reflected immediately in the price at which you can purchase this firm.

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