NPV and IRR

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NPV and IRR
An Optional Impromptu Discussion of Net Present
Value and Internal Rate of Return
Here is an example of what you will have in store
for you if you take investments and finance at
the university level. NOTE This material is not
going to be on the exam.
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Recall Present Value Valuation

• Present Value and Valuation
• Recall A fundamental assertion of finance holds
  that the value of a stock is based on the present
  value of its future cash flows
• Examples Dividends, stock prices, interest
  payments, principal repayments
• But present value is not limited to stocks and
  bonds
• We can calculate the present value of a future
  stream of income from any source
• Real estate, factories, bridges, water projects,
  nuclear reactors, etc.

You already know how to compute the present value
of any stream of income.
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Calculating Present Value

• Do your remember the formula for calculating
  Present Value? (The one we never used?)
• Using the Present Value tables, we used

Value Dividend1PVM1 Dividend2PVM2
Dividend3PVM3 etc
In this version, the cash flows were dividends
and the price of the stock when we forecast we
were ready to sell, but they could be any cash
flow rent, bridge tolls, electricity
generation, etc.
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Discounted Cash Flow Model
(continued)

• Example 1
• Assume it is January 1, 2015. Pretzels Unlimited
  is currently selling for 22 per share and will
  pay 2.00 per share in dividends in 2015. PU
  expects to increase their dividends to 2.20 in
  2016, 2.30 in 2017, and 2.30 in 2018. We will
  be selling the stock at the end of 2018 and we
  expect the price to be 27 per share at that
  time. Our required rate of return is 12.
• Value of stock present value of future
  dividends
• present value of price of stock when you
  plan to sell
• Value (2.000.893)(2.200.797)(2.300.712
  )(2.300.636)
• (27.000.636)
• 1.786 1.7534 1.6376 1.4628
  17.172
• 6.6398 17.172 23.8118 ? 23.81

If our required rate of return is 12, this is a
pretty good stock to buy.
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Example Pretzels Unlimited
(continued)

• Recall Example 1
• Pretzels Unlimited in Spreadsheet Format

Years Cash Flows PVM12 Discounted Cash Flows
2015 2.00 0.893 1.786
2016 2.20 0.797 1.7534
2017 2.30 0.712 1.6376
2018 2.30 27 0.636 17.172
Total Present Value Total Present Value Total Present Value 23.8118 ? 23.81
Since 23.81 is greater than the current market
price of 22, then we would consider this a good
investment for our Required Rate of Return of
12.
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How Was Present Value Useful?

• The Present Value told us what we thought the
  future stream of income was worth today
• And if it were roughly equal to or greater than
  the current market price
• (What we had to pay today for that future stream
  of income)
• Then we predicted that it was a good investment
• For our desired Required Rate of Return

Recall that the Required Rate of Return was very
important because as you changed the Required
Rate of Return, the Present Value changed,
sometimes greatly!
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Present Value versus Net Present Value

• Okay, so what is Net Present Value (NPV)?
• Net Present Value takes into account all cash
  flows (called inflows) and all cash outflows
• And if Net Present Value is positive, then it is
  a good investment
• For our Required Rate of Return
• And if Net Present Value is negative, then it is
  not a good investment
• For our desired Required Rate of Return

Net Present Value is much more popular when you
get to upper division and graduate level finance
classes at the university.
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Calculating Net Present Value
(continued)

• Example 1

Years Cash Flows PVM12 Discounted Cash Flows
(22.00) 1.000 (22.00)
2015 2.00 0.893 1.786
2016 2.20 0.797 1.7534
2017 2.30 0.712 1.6376
2018 2.30 27 0.636 18.6207
Net Present Value Net Present Value Net Present Value 1.6047
The Net Present Value is positive because the
Present Value was greater than the market price
(Initial Cash Outflow).
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Calculating Present Value NPV

• Are you sick and tired of calculating Present
  Value using the Present Value tables?
• Good! That means you know how to calculate and
  understand what it means to discount a stream of
  future cash flows. And I have done my job.
• Hey! It is easier than using the formula with
  the exponents, right?
• But you also know how to use the easy way!
• Spreadsheets calculate Present Value and Net
  Present Value without breaking a sweat
• Lets take another look, this time adding NPV

Someday, I want to add a lab component to this
class or create a one-unit class that is done
completely in the computer lab.
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Internal Rate of Return (IRR)

• This brings us back to Internal Rate of Return
• The very popular measure that business people and
  investors use when measuring the rate of return
  from a stream of future income
• You will also learn how to compute the Internal
  Rate of Return manually if you go on to an upper
  division or graduate level finance class at the
  university
• Specifically, the Internal Rate of Return is the
  desired Required Rate of Return where the Net
  Present Value equals zero
• Huh? What?

It is easier to show you how to calculate IRR
than it is to explain it to you. Lets go back
to the spreadsheet.
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Calculating IRR w/o a Spreadsheet

• w/o a spreadsheet, taint easy to compute!
• In fact, it is a real PITA
• I have not done it manually since I left graduate
  school
• Uh, that is why they made computers
• Plus, as we saw on the spreadsheet, Internal Rate
  of Return can give you some very bizarre and
  unreliable results
• Sometimes there can be more than one Internal
  Rate of Return (!?)

With odd or unusual streams of cash outflows and
inflows, you really should create a Net Present
Value graph like the one we saw in the
spreadsheet to check if your Internal Rate of
Return is reasonable.
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So Whats the Bottom Line?

• So how does having a spreadsheet change the way
  we do our calculations?
• The quick answer is, Not much! But
• It makes calculating Present Value or Net Present
  Value (whichever you prefer) much, much easier
• But the tables are not that hard, are they?
• And it gives you an extremely precise result when
  calculating your rate of return from a stream of
  future income
• Which is exactly what I do not want you to rely
  on!

Uh, why not? Because unless you are
calculating the return from a very predictable
source (example bonds), precision is your
enemy! Never forget that you are predicting the
future and as the old saying goes, Prediction is
difficult, especially about the future!
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NPV and IRR
Thank you for your time.