Contents
Time Value of Money
Annuities
Perpetuities
Kinds of Interest Rates
Future Value of an Uneven Cash flow
Probability Distribution
Standard Deviation
CAPM
Security Market Line
Bond Valuation
Stock Valuation
Cost of Capital
The Balance Sheet
Capital Budgeting
Hall of Fame
Credit Report
Forex
401K
ETFs
Futures
Inflation
IPOs
Mergers
Online Scams
Calculators
Financial Terms
Scientific Terms
Military Terms
Financial Charts
Unemployment
Fuel Mileage
Sports Finance
Energy Efficiency
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Disclaimer

Capital Budgeting
Payback, Discounted Payback, NPV, Profitability Index,
IRR and MIRR are all capital budgeting decision methods.
Cash Flow We are going to assume that the project we
are considering approving has the following cash flow.
Right now, in year zero we will spend 15,000 dollars on
the project. Then for 5 years we will get money back as
shown below.
Year 
Cash flow 
0 
15,000 
1 
+7,000 
2 
+6,000 
3 
+3,000 
4 
+2,000 
5 
+1,000 
Payback  When
exactly do we get our money back, when does our project
break even. Figuring this is easy. Take your calculator.
Year 
Cash flow 
Running Total 

0 
15,000 
15,000 

1 
+7,000 
8,000 
(so after the 1st year, the project has not
yet broken even) 
2 
+6,000 
2,000 
(so after the 2nd year, the project has not
yet broken even) 
3 
+3,000 
+1,000 
(so the project breaks even sometime in the
3rd year) 
But when, exactly? Well, at the
beginning of the year we had still had a 2,000 balance,
right? So do this.
Negative Balance / Cash flow
from the Break Even Year 
= 
When in the final year we break even 
2,000 / 3,000 
= 
.666 
So we broke even 2/3 of the way through the 3rd year.
So the total time required to payback the money we
borrowed was 2.66 years.
Discounted Payback  is
almost the same as payback, but before you figure it, you
first discount your cash flows. You reduce the future
payments by your cost
of capital. Why? Because it is
money you will get in the future, and will be less
valuable than money today. (See Time Value of
Money if you don't understand).
For this example, let's say the cost of capital is 10%.
Year 
Cash flow 
Discounted Cash flow 
Running Total 
0 
15,000 
15,000 
15,000 
1 
7,000 
6,363 
8,637 
2 
6,000 
4,959 
3,678 
3 
3,000 
2,254 
1,424 
4 
2,000 
1,366 
58 
5 
1,000 
621 
563 
So we break even
sometime in the 5th year. When?
Negative Balance / Cash flow
from the Break Even Year 
= 
When in the final year we break even 
58 / 621 
= 
.093 
So using the Discounted
Payback Method we break even after 4.093 years.
Net Present Value (NPV)  Once
you understand discounted payback, NPV is so easy! NPV is
the final running total number. That's it. In the example
above the NPV is 563. That's all. You're done, baby.
Basically NPV and Discounted Payback are the same idea,
with slightly different answers. Discounted Payback is a
period of time, and NPV is the final dollar amount you
get by adding all the discounted cash flows together. If
the NPV is positive, then approve the project. It shows
that you are making more money on the investment than you
are spending on your cost of capital. If NPV is negative,
then do not approve the project because you are paying
more in interest on the borrowed money than you are
making from the project.
Profitability Index
Profitability Index 
equals 
NPV 
divided by 
Total Investment 
plus 
1 
PI 
= 
563 
/ 
15,000 
+ 
1 
So in our example, the
PI = 1.0375. For every dollar borrowed and invested we
get back $1.0375, or one dollar and 3 and one third
cents. This profit is above and beyond our cost of
capital.
Internal Rate of Return
 IRR is the amount of profit you get by investing in a
certain project. It is a percentage. An IRR of 10% means
you make 10% profit per year on the money invested in the
project. To determine the IRR, you need your good buddy,
the financial calculator.
Year 
Cash flow 
0 
15,000 
1 
+7,000 
2 
+6,000 
3 
+3,000 
4 
+2,000 
5 
+1,000 
Enter these numbers and press these
buttons.
15000 
g 
CFo 
7000 
g 
CFj 
6000 
g 
CFj 
3000 
g 
CFj 
2000 
g 
CFj 
1000 
g 
CFj 
f 
IRR 
After you enter these
numbers the calculator will entertain you by blinking for
a few seconds as it determines the IRR, in this case
12.02%. It's fun, isn't it!
Ah, yes, but there are problems.
 Sometimes it gets confusing
putting all the numbers in, especially if you
have alternate between a lot of negative and
positive numbers.
 IRR assumes that the all cash
flows from the project are invested back into the
project. Sometimes, that simply isn't possible.
Let's say you have a sailboat that you give rides
on, and you charge people money for it. Well you
have a large initial expense (the cost of the
boat) but after that, you have almost no
expenses, so there is no way to reinvest the
money back into the project. Fortunately for you,
there is the MIRR.
Modified Internal Rate of
Return  MIRR  Is basically the same as the
IRR, except it assumes that the revenue (cash flows) from
the project are reinvested back into the company, and are
compounded by the company's cost of capital, but are not
directly invested back into the project from which they
came.
WHAT?
OK, MIRR assumes that the revenue is
not invested back into the same project, but is put back
into the general "money fund" for the company,
where it earns interest. We don't know exactly how much
interest it will earn, so we use the company's cost of
capital as a good guess.
Why use the Cost of Capital?
Because we know the company wouldn't do
a project which earned profits below the cost of capital.
That would be stupid. The company would lose money.
Hopefully the company would do projects which earn much
more than the cost of capital, but, to play it safe, we
just use the cost of capital instead. (We also use this
number because sometimes the cash flows in some years
might be negative, and we would need to 'borrow'. That
would be done at our cost of capital.)
How to get MIRR  OK, we've got these
cash flows coming in, right? The money is going to be
invested back into the company, and we assume it will then get
at least the company'scostofcapital's interest on it.
So we have to figure out the future value (not the present value) of the sum of all the
cash flows. This, by the way is called the Terminal
Value. Assume, again, that the company's cost of capital
is 10%. Here goes...
Cash Flow 
Times 

= 
Future Value of that years
cash flow.

Note 
7000 
X 
(1+.1)^{ 4} 
= 
10249 
compounded for 4 years 
6000 
X 
(1+.1)^{ 3} 
= 
7986 
compounded for 3 years 
3000 
X 
(1+.1)^{ 2} 
= 
3630 
compounded for 2 years 
2000 
X 
(1+.1)^{ 1} 
= 
2200 
compounded for 1 years 
1000 
X 
(1+.1)^{0} 
= 
1000 
not compounded at all because this is the
final cash flow

TOTAL 


= 
25065 
this is the Terminal Value 
OK, now get our your financial
calculator again. Do this.
15000 
g 
CFo 
0 
g 
CFj 
0 
g 
CFj 
0 
g 
CFj 
0 
g 
CFj 
25065 
g 
CFj 
f 
IRR 
Why all those zeros?
Because the calculator needs to know how many years go
by. But you don't enter the money from the sum of the
cash flows until the end, until the last year. Is MIRR
kind of weird? Yep. You have to understand that the
cash flows are received from the project, and then get
used by the company, and increase because the company
makes profit on them, and then, in the end, all that
money gets 'credited' back to the project. Anyhow, the
final MIRR is 10.81%.
Decision Time Do we
approve the project? Well, let's review.
