Created 7/1/1996

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**http://www.j-bradford-delong.net/Intro_Finance/BAonethirty4.html**

**Rules of thumb from last time:**

- Present value of a perpetuity: C/r
- Present value of a growing (or shrinking) perpetuity: C/(r-g)
- Present value of C dollars t years from now: C/[(1+r)
^{t}] - Present value of a C-dollar t-year annuity: C[(1/r)-(1/[r(1+r)
^{t}])

If these rules by themselves don't give you enough to solve almost *any
*problem in this course, you haven't been ingenious enough.

**This time: valueing common stocks**

Investors will not invest their money in stocks--which are more risky than U.S. Treasury notes, bills, and bonds, unless they are offered a required rate of return "commensurate with the risk." So this chapter presupposes part 2--or rather makes full sense only with part 2 already assimilated.

- A deep reason why you need to understand what creates stock market value: even if you are trying to act in the interest of your shareholders--to maximize shareholder value--it is very hard to do so if you are clueless about what maximizes shareholder value.

Common stocks are traded; NYSE; AMEX; NASDAQ

Brealey and Myers use Ford as an example (from February 15, 1995):

- 52 week high: 33 7/16
- 52 week low: 24 1/4
- Dividend per share: $1.04
- Yield (%): 4.0(%)
- P/E: 5
- Volume: 4,014,300
- Daily high 26 5/8
- Daily low 26
- Daily close 26 1/4
- Net change + 1/8

Note that with a billion shares outstanding, annual trading in Ford stock
is equal to its *entire* outstanding capitalization. This is a highly
"liquid" market: on average, each share is sold (for some reason
or another) once a year.

The NYSE is a *secondary market .* The primary markets are the IPO
market, or the new-issues markets. But almost all stock trades are *secondary
market *trades: Trades unrelated to raising new capital for Ford Motor
Company.

**What is the present value of a stock?**

PV(Stock) = PV(Expected Future Dividends)

But don't people expect capital gains?

Yes, but...

Expected rate of return=required rate of return=market capitalization rate

r = (D + P(1))/P(0)

You can flip this formula around: given expectations of P(1), the dividend, and r, you can deduce P(0). How do we know that that is the right P(0)? Because it the price were higher, people would have to be really dumb to buy the stock; if the price were lower, everyone would already be trying to buy it.

But what determines next year's price?

r = (D(1) + P(2))/P(1)

Forward induction...

P(0) = sum{D(i)/[(1+r)^i]} + P(T)/[(1+r)^T]

Does the last term approach zero? It must--unless something truly weird is going on.

Is something truly weird ever going on? Think about gold (but perhaps it has a "convenience" dividend in some states of the world). If it doesn't have such a convenience dividend, then the last term is the only thing out there...

Discounted-Cash-Flow formula

A much easier formula to work with than "price equals the present value of expected future dividends" is:

- "market capitalization rate equals dividend yield plus expected rate of dividend growth"

**Duke Power Example**

5.2% dividend yield; 4.1% rate of dividend growth projected; seems to imply a 9.3% required rate-of-return on equity for Duke Power.

Danger: your estimate of the required rate-of-return is only as good as your estimate of dividend growth.

Do *not* use the simple constant-growth formula to test whether
the market is correct in its assessment of stock value. If your estimate
is different, it is more likely that you are wrong than that the marekt
is wrong.

**Earnings**

Suppose a business is earning $10 a share (expected to continue forever), the market capitalization rate is 8%, and the firm pays out some of its earnings as dividends and invests the rest in projects that yield the market capitalization rate--and suppose we know that the company is going to be able to continue this policy forever.

What is its price?

You might say that you need to know the dividend in order to calculate its price. Actually, you don't.

Suppose it pays a dividend of zero. Then next year it is earning $10.80--and if it then starts paying out all of its earnings as dividends, it will be worth (

with dividend) $135+$10.80=$145.80 per share. $145.80 per share next year has a P.V. of $135 this year--the with dividend price of the stock.Suppose it pays a dividend of $10 this year. Then its with-dividend value is the same $135.

Only if the firm has

the opportunity to invest at above-market rates of return(because of market position, monopoly power, some special edge, whatever) does its dividend policy matter.P(0) = EarningsPerShare/r + PresentValueofGrowthOpportunities

or EPS/P(0) =r{1- PVGO/P(0)}

If EPS/P(0) is less than r, then the firm had better have super-market return investment opportunities...

**Fledgling Electronics:**

Market capitalization rate r of 15% per year

$5 first-year dividend

Thereafter dividend grows by 10% per year

Market price of $100 a share

Now suppose Fledgling has earnings per share of $8.33, so that it is plowing back into its business 40% of its earnings. The growth rate of earnings (and of dividends, and of the stock price) is equal to the return on equity investments times the plowback ratio--which for a growth rate of 10% and a plowback ratio of 40%, must imply that Fledgling has open to it investment opportunities that pay 25% rates of return.

What if Fledgling didn't invest? $8.33/.15 = $55.56 as its stock market value. The other $44.44 must come from the "present value of growth opportunities".

What are its growth opportunities? Well, this year it is the opportunity to invest $3.33 in earnings in investments that pay 25% rates of return (rather than the market's 15% rate of return). This is an above-market profit of $0.3333 per year forever--and discounting that above market return at 15% gives us a figure of $2.22 for the "value of the growth opportunity" this year.

Next year we will have another growth opportunity--10% bigger--and so on for the year after that...

So if we calculate the value of all growth opportunities: PVGO(0)/r-g we get $44.44

Which checks

A growth stock: one in which the net present value of its opportunities to make above-market rate-of-return investments accounts for a large chunk of its stock price.

Notice that it is *not* true to say that a share's value is equal
to the discounted stream of future earnings per shares.

Should we pay attention to P/E ratios? They depend on PVGO, and on r for firms of that risk characteristic