A lumberjack was the first to answer
the ad. He offered to pay $50. "That's what it would
fetch if I cut it down for firewood." The old man moaned,
"You are foolish. You see only the tree's salvage value.
Perhaps, your price would be good for a pine tree or
perhaps even an apple tree no longer bearing fruit.
Or perhaps if apple wood had become prized, more than
apples. But my tree is worth much more than $50. No,
thank you."
Current
production A grocer was next.
She offered $100. "I will harvest and sell this year's
crop." The old man smiled, "You are not quite so foolish
as the first one. You see this tree has more value as
a producer of apples than as a source of firewood. But
$100 is not the right price. What of next year's crop?
And the many crops after? Your price will not do."
Future
(undiscounted) production A
marketer then answered the ad. He lived by the adage,
"Buy low, sell high." So he offered $1499. "I figure
the tree should live for at least another fifteen years.
If I sell the apples for $100 a year, that will total
$1,500." The old man wrinkled his nose, "You think ahead,
but not carefully enough. Will the $100 you earn by
selling apples fifteen years from now be worth $100
to you today? Stop and consider that if you placed $41.73
today in a bank account paying 6% interest, compounded
annually, you would have $100 at the end of fifteen
years. The present value of $100 worth of apples fifteen
years from now, assuming an interest rate of 6%, is
only $41.73, not $100. I'm afraid that you will
buy high and have to sell low. I cannot take your money."
Market
price A wealthy physician
was next. "You get what you pay for," she announced.
"I'll pay the market price  whatever your last serious
offer." The old man laughed, "You can't be serious,
doctor. Now if there were truly a market in which apple
trees were traded with some regularity, the prices at
which they traded would be an indicator of their value.
But there is no such market. The isolated offer I just
received tells very little. If you had only heard the
last offer I received today!! You should seek advice
before you invest."
Book
value An accountant soon answered
the ad, demanding first to see the old man's books.
The old man had kept careful records and gladly shared
them. After examining them, the accountant declared,
"You paid $75 for this tree ten years ago. You have
made no deductions for depreciation. Assuming this conforms
with generally accepted accounting principles, the book
value of your tree if $75. I will pay that." The old
man chided the accountant, "It is true the tree has
a book value of $75, but is that its worth? Why, in
just one year I can sell more than $75 in apples. Your
accounting numbers look to the past, not the future."
Capitalized
earnings A young stock broker
was next. She too asked to examine the books and after
several hours announced she was prepared to offer. "I
will value the tree on the basis of the capitalization
of its earnings." The old man's interest was piqued.
The broker continued, "While the apples sold for $100
last year, those weren't your profits from the tree.
You had expenses. There was the cost of fertilizer and
tools. You paid for others to prune the tree, to pick
the apples, to cart them to market, to sell them. These
costs and expenses should be charged against the revenues
from the tree. Moreover, the purchase price of the tree
was an expense, a portion of which should be taken into
account each year of the tree's useful life. Finally,
there were taxes. Your profit from the tree was a mere
$50 last year." The old man exclaimed, "Wow. I thought
I made $100 off that tree."
"You should have matched expenses with
revenues, in accordance with generally accepted accounting
principles," she explained. "And you don't actually
have to write a check to be charged with an expense.
For example, you bought a station wagon some time ago
and you sometimes used it to cart apples to market.
Some of the wagon's original cost has to be matched
against revenues. A portion of the amount has to be
deducted each year even though you expended it all at
one time. Accountants call that depreciation. I'll bet
you never figured that in your calculation of profits."
The old man said, "No, I didn't. Tell me more."
"I also noticed in your books that in
some years the tree produced less apples than in other
years, and the prices varied and the costs were not
exactly the same each year. Taking an average of only
the last three years, I came up with a figure of $45
as a fair sample of the tree's earnings. But we're only
halfway to figuring the value." The old man asked, "What's
the other half?"
"The tricky part," she told him. "We
now have to figure how much I value owning something
that produces $45 in earnings every year. If I believed
the tree were a oneyear wonder, I would say 100% of
its value  as a going business  was represented
by one year's earnings. But if I believe, as we both
do, that the tree is like a corporation that will keep
producing earnings year after year. What am I willing
to pay to receive $45 in earnings every year into the
future. That will be the capitalized value of the tree."
The old man was ready to hear an offer, "Do you have
something in mind?" he asked.
"I'm getting there. If this tree's earnings
were steady and predictable, like a U.S. Treasury bond,
it would be easy. But its earnings are not guaranteed.
So we have to take into account risk and uncertainty.
If the risk of its ruin is high, I would insist that
a single year's earnings represent a higher percentage
of the value of the tree. After all, apples could glut
on the market one day and you would have to cut the
price and increase the costs of selling them. Or some
doctor could discover that eating an apple a day is
linked to heart disease. A drought could cut the yield
of the tree. Or the tree could become diseased and die.
These are all risks. And, on top of this, we don't know
what will happen to costs related to the tree." The
old man sought to brighten her perspective, "There are
treatments, you know, that could be applied to increase
the yield of the tree. In fact, this tree could spawn
a whole orchard."
"I know," she assured him. "We will include
that in the calculus. The fact is, we are talking about
risk, and investment analysis is a cold business. We
don't know with certainty what's going to happen. You
want your money now and I'm supposed to live with the
risk. Your tree isn't the only game in town. I have
to choose between your tree and the strawberry patch
down the road. I cannot do both and the purchase of
your tree will deprive me of alternative investments.
That means I have to compare the opportunities and the
risks."
"To determine the proper rate at which
we should capitalize earnings, I have looked at investment
opportunities that are comparable to the apple tree,
particularly in the agribusiness industry where these
factors have been taken into account. I have concluded
that an appropriate rate of return is 20%. In other
words, assuming the average earnings over the last three
years are representative, I am willing to pay a price
that will earn me a 20% return on my investment. If
you say I should take a lower rate of return, I'll simply
go buy the strawberry patch instead. Now, to figure
the price, we simply divide $45 by .20."
The old man hesitated, "Long division
was never my long suit. Is there a simpler way of doing
the figuring?"
"There is," she assured him. "The reciprocal
of .20 is 5. If you don't want to divide by the capitalization
rate, you can multiply by its reciprocal, which we Wall
Street types prefer. We call that reciprocal the priceearnings
(or PE) ratio. To compute the ratio, we divide
100 by the percentage rate of return we are seeking.
If I was willing to take an 8% return, the PE ratio
would be 12.5 to 1. Since I want to earn 20%, by PE
ratio is 5:1. I'm willing to pay five times the tree's
estimated annual earnings or $225  $45 times 5. The
old man sat back. "I appreciate the lesson. Let me think
about your offer. Can we meet again tomorrow?"
Discounted
cash flows.
The next day when the young woman returned
she found the old man emerging from a sea of work sheets,
small print columns of numbers and a calculator. "Glad
to see you," he said. Perhaps we can do business. It's
easy to see how you Wall Street types make money, buying
people's property for a fraction of its value. But I
think you'll agree my tree is worth more than you figured."
The broker was willing to listen, "I'm open minded."
"You worked so hard over my books to
come up with something you called profits, or earnings.
I'm not so sure it tells you anything that important."
She protested, "Yes, it does. Profits measure efficiency
and economic utility."
"Maybe," he mused, "but it sure doesn't
tell you how much money you've got. Yesterday I looked
in my safe and found some stocks that hadn't ever paid
much of a dividend. The company sent me reports telling
me how great earnings were, but I couldn't spend them.
It's just the opposite with the tree. You figured the
earnings were lower because of some amounts you called
depreciation that I never had to spend. It seems to
me these earnings, after depreciation, are an idea worked
up by the accountants. Now ideas are useful, but you
can't fold them and put them in your pocket." The broker
was surprised, "What's important, then?"
"Cash flow," the old man declared. "I'm
talking about dollars you can spend, or save or give
to your children. This tree will go on for years yielding
revenues after costs." She sputtered, "what about the
risks, the uncertainties?"
"Ah, yes," the old man observed, "I think
we can deal with that. Chances are that you and I could
agree, after some thought, on the possible range of
revenues and costs. I suspect we would estimate that
for the next five years, there is a 25% chance that
the cash flow will be $40, a 50% chance it will be $50
and a 25% chance it will be $60. That makes $50 our
best guess, if you average it out. Then let us figure
that for the next ten years that the average will be
$40. And that's it. The tree doctor tells me the tree
won't last longer than 15 years. Now all we have to
do is figure out what you pay today to get $50 each
year for the next five years, and $40 each year for
ten more years. Then, throw in the $50 we can sell the
tree for firewood at the end of 15 years."
"Simple," she said, again on familiar
ground. "You want to discount to the present value of
future receipts. Of course, you need to determine the
rate at which you discount."
"Precisely," he noted. "That's what all
these charts and the calculator are doing." She nodded
knowingly as he showed her discount tables that revealed
what a dollar received at a later time is worth today,
under different assumptions of the discount rate. It
showed, for example, that at a 8% discount rate, a dollar
delivered a year from now is worth $.93 today, simply
because $.93 today, invested at 8%, will produce $1
a year from now.
"You could put your money in a bank and
receive 5% interest, insured. But you could also put
your money into obligations of the U.S. Government and
earn 8% interest. That looks like the risk free rate
of interest to me. Anywhere else you put your money
deprives you of the opportunity to earn 8% risk free.
Discounting by 8% will only compensate you for the time
value of the money you invest in the tree rather than
in government securities. But I concede that the cash
flow from the apple tree is not riskless, sad to say,
so we can use a higher discount rate to compensate you
for the risk in your investment. Let us agree that we
discount the receipt of $50 a year from now by 15%,
and so on with the other deferred receipts. That is
about the rate that is applied to investments with this
magnitude of risk. You can check with my cousin who
sold his strawberry patch yesterday. According to my
figures, the present value is 


Present value 
Year 
Cash flow 
(8% discount rate) 
(15% discount rate) 
1 
50 
$ 46.30 
$ 43.48 
2 
50 
$ 42.87 
$ 37.81 
3 
50 
$ 39.69 
$ 32.88 
4 
50 
$ 36.75 
$ 28.59 
5 
50 
$ 34.03 
$ 24.86 
6 
40 
$ 25.21 
$ 17.29 
7 
40 
$ 23.34 
$ 15.04 
8 
40 
$ 21.61 
$ 13.08 
9 
40 
$ 20.01 
$ 11.37 
10 
40 
$ 18.53 
$ 9.89 
11 
40 
$ 17.16 
$ 8.60 
12 
40 
$ 15.88 
$ 7.48 
13 
40 
$ 14.71 
$ 6.50 
14 
40 
$ 13.62 
$ 5.65 
15 
40 
$ 12.61 
$ 4.92 
Salvage 
50 
$ 15.76 
$ 6.14 

Total 
$ 398.07 
$ 273.56 
That is, the total present value of all
the net cash flows is $273.56, assuming a discount rate
of 15%. You can see how much I'm allowing for risk because
if I discounted the stream at a riskfree 8%, it would
come to $398.07. So I'll take $270  to round
it off."
After a few minutes reflection, the young
broker said to the old man. "It was a bit foxy of you
yesterday to let me appear to be teaching you something.
Where did you learn so much about finance as an apple
grower?" He counseled her softly, "Don't be foolish,
my young friend. Wisdom comes from experience."
The young woman smiled. "I have enjoyed
this lesson. But I'll tell you something that some financial
whiz kids say whether you figure value on the basis
of the discounted cash flow method or the capitalization
of earnings, so long as we apply both methods perfectly
we should come out at exactly the same point."
"Of course," the old man exclaimed. "But
which method is more likely to be misused? I prefer
my method because I don't have to monkey around with
depreciation. You have to make assumptions about useful
life and how fast you're going to depreciate. That's
where you went wrong in your figuring."
"You are crafty," she rejoined. "But
your calculations aren't perfect, either. It's easy
to discount cash flows when they are nice and steady,
but what if you have some lumpy expenses? For example,
several years from now that tree will need pruning and
spraying that you didn't include in your cash flow.
The costs of that will throw off your calculations.
Tell you what. "I'll offer $250. My cold analysis says
I'm overpaying, but I've come to like that tree. Maybe
I'll sit in its shade."
"It's a deal," said the old man. "I never
said I was looking for the perfect offer, but
only the best offer."

Moral
of the story
There are several morals. First,
you should have noticed that the prospective buyers
used essentially three methods to value productive
assets 
 asset approach
 income (cash flow) approach
 market (comparables) approach
Second, asset valuation methods are
useful tools, but valuation is an art that combines
methods, good judgment and experience. And experience
comes from mistakes. Third,
you should listen closely to the experts  focus
not only on what they say, but on what they don't
say. Behind their elegance, there is much discordance
and uncertainty. One wrong assumption can carry
you off track.
Finally, you're never too young
or too old to learn. 
