GEK2507

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Compound Prosper!

• GEK2507

Frederick H. Willeboordse frederik_at_chaos.nus.edu.s
g
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Values

• Lecture 8

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Todays Lecture

• What kinds of values are there?

Art
Religion
Politics
In business, this is not really how we categorize
value.
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Value
These are the most common types of value in
business

• General Value
• Book Value
• Intrinsic Value
• Market Value
• Liquidation Value
• Time Value of Money

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General Value
In very general terms one could call the value of
a business the amount a purchaser and a seller
agree upon during the sale of the
business. In this sense, the value of the
asset is equal to its price. This is, however,
not always the case. The price of an asset can
also be higher than its (or one of its types of)
value(s) or lower than its (or one of its types
of) value(s).
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Book Value

• Book value of an asset This is simply the
  purchase price of an asset minus its accumulated
  depreciation.
• This is important for accounting but often a poor
  reflection of the true value of an asset.

• Book value of a stock This is the amount of
  owners equity per share.
• Be aware that this is very different from Market
  Value.

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Intrinsic Value
Intrinsic value is the value an investor assigns
to an asset. This is a highly individual matter
and hence the intrinsic value of an asset is
different for each investor. Generally, an
investor would look at the cash flows of an
investment (e.g. the dividends plus the proceeds
of the sale of the stock at the end of the
expected holding period), discount them with an
expected rate of return and thus determine its
intrinsic value. The differences in perception
are an importantingredient for the functioning
of the financialmarkets.
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Market Value
The market value of an asset is the price one
would pay for that asset in a competitive market
place. The same, of course, is true for a stock
with the market place being the stock market.
Boom or Gloom?
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Liquidation Value
This is how much a business would fetch in a
fire-sale. The liquidation value of certain
assets can be extremely low since those assets
may not be of any use to other parties.
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Examples

• Pokemon Card
• General Value 12 dollars. The price you just
  bought it for from a friend.
• Book Value 12 dollars. Not much depreciation
  in a Pokemon card.
• Intrinsic Value 30 dollars. It was the only
  card you were missing!
• Market Value 8 dollars. Actually, at the
  fair, many people turned out to have this
  card.
• Liquidation Value 0.01 cents. The paper isnt
  worth much

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Examples
Pokemon Card You dont agree with my reasoning
here?Excellent! Thats exactly the point.
Opinions on what constitutes value are diverse.
Always keep that in mind when considering value
statements.
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Examples

• Coffee Shop
• General Value 500K. The price someone has just
  offered.
• Book Value 200K. Your 250K investment minus
  50K depreciation.
• Intrinsic Value 250K. You didnt like the idea
  of running a shop and you just want your
  money back.
• Market Value 100K. Enough Starbucks already!
• Liquidation Value 20K. Wont get anything back
  for the renovation Only little for the rest.

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Examples
Coffee Shop Again much to debate. Numbers
themselves do not lie but the question is of
course What do they mean?
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Time Value
The core of this lecture is actually quite
similar to what we will do for bonds. We say
that money has a Time Value because it can be
invested and thus become more. In other words, if
we have a dollar today, we expect/hope that we
will have more than a dollar in the
future. The Time Value of money is an
essential concept when deciding on an investment.
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Time Value

• The are a few terms important to know as with
  regards to the time value of money
• Present Value This is just the monetary value
  of the investments we have right now
• Future Value This is the value of our
  investment in the future
• Compounding Reinvesting the interest received,
  in other words, receiving
  interest on interest

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Future Value
The present and future values can easily be
calculated in Excel
Future value of 1000 dollars (in five years time).
We assume 10 interest
So we see that 1000 dollars now will be 1610
dollars in 5 years
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Future Value
Of course this can easily be expressed
mathematically, but lets do it step by step to
understand what we are doing
1st year Value after one year Present Value
Interest 2nd year Value after two years
Value after one year Interest
Or Value after two years (Present Value
Interest) Interest
Substitute Line 1
This interest needs to be on the entire Value
after one year
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Future Value
Or
1st year Value after one year PV PV r
PV(1 r) 2nd year Value after two years PV
(1 r) PV (1 r) r
Value after one year
Value after one year
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Future Value
And thus we obtain the formula
Lets check this for our example
And indeed this is equal to 1610 as before.
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Future Value
Surprise! Theres also an Excel function for
this FV
Unused parameters for this problem
FV(10,5,0,-1000,0)
The present valueNote the minus!
The interest rate
The number of years
As expected, the same as before!
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Compounding
Compounding Interest is powerful .
One thousand dollars becomes nearly 2600 after 10
years! That must be too good to be true.
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Compounding
Compounding Interest is powerful .
50-year Chart
One thousand dollars becomes nearly 120,000 after
50 years if the interest is 10. Note how the
curve bends Upwards!
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Discount
A closely related topic especially in the context
of the time value of money is that of
discount. When a business decides to invest a
certain sum, it needs to discount the expected
future cash flows in order to decide whether the
investment is worthwhile.After all, if your
return is too small, it would not be wise to make
the investment.
Let us start with the case of receiving a single
lump sum sometime in the future. What would the
present value of this sum be?
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Present Value
Surprise! Theres an Excel function for this PV
Unused parameters for this problem
PV(3,10,0,-1000,0)
The future valueNote the minus!
The interest rate
The number of years
Note the relationship to inflation (see later on)
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Discount
The problem is now that the cash flow is expected
to grow over the years (since the business is
hopefully getting better and better). As always,
it may be complicated to imagine at first, but if
we have an idea of how to get started we can take
it from there. The obvious starting point is
The Cash Flows
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Discounting uneven cash flows
Let us assume that we have the following cash
flows
What would they be worth?
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Discounting uneven cash flows
We can of course just sum them up
15,450.-
Is this a reasonable value for the cash flows?
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Discounting uneven cash flows
No! we need to have some return (namely 10 in
this case)
The sum of each years cash flows present values!
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Discounting uneven cash flows
Thus we obtain
Surprisingly little, isnt it!
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Discounting uneven cash flows
Naturally there also is an Excel function for
this NPV Presumably standing for Net Present
Value.
Discount Rate
Range of Cash Flows
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Excels NPV
We just used the function NPV with NPV presumably
standing for Net Present Value. It would seem
that what we have calculated is the Present
Value and that there is no need for the
Net.Indeed, usually one calls what we have
calculated Present Value. Generally, Net
Present Value is when we subtract from this the
cost of acquiring the cash flow in question.
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Rate of Return
Of course, often things work the other way
around. We bargain to get a certain stream of
cash flows and then we wonder what the compounded
yield on this asset is going to be.
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Calculating the Yield
The key thing to realize is that at the actual
yield, the purchase price equals the present
value. In other words, the net present value is
zero.
Hence we can use the solver.
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Calculating the Yield
D5-D3
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Calculating the Yield
There is also a built in Excel function
IRR Standing for Internal Rate of Return
IRR(C10C20)
This is investment in year 0.
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Calculating the Yield
Another useful built in Excel function XIRR It
gives the IRR for non-periodic cash flows.
XIRR(C10C17,B10B17)
This is investment at the beginning
A cash flow at a certain date
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Risk
Theres of course nothing wrong with this
calculation but the determined present value
assumes the stream of cash flows to be
certain. In real life, one can never be entirely
certain of future cash flows and one therefore
needs to take risk into account.
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Risk
Generally speaking, the expected rate of return
should increase when the risk increases and
decrease when the risk decreases. Hence, the
expected return on US government bonds (very
little risk) is lower than than that of stocks (a
company might go bankrupt).
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Key Points of the Day

• Money has Time Value
• Interest can compound
• Discount is an important concept

Compound or be poor!
Time is your friend! Be patient.