Title: NPV and IRR
1NPV 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.
2Recall 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.
3Calculating 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.
4Discounted 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.
5Example 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.
6How 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!
7Present 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.
8Calculating Net Present Value
(continued)
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).
9Calculating 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.
10Internal 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.
11Calculating 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.
12So 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!
13NPV and IRR
Thank you for your time.