Financial Management
Professor Jaime F Zender
A Good Place To Start
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What is finance?
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Finance is a hybrid of economics, statistics, and
accounting.
It is the science of capital.
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In other words, it considers the allocation of money
across investment opportunities.
Necessarily draws on these underlying disciplines in
making such decisions.
We will concentrate on corporate finance rather than
personal finance but the issues and concepts are
fundamentally the same and I will often draw parallels.
Typical Question
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Three years ago your cousin Ralph opened a
brew-pub in downtown Boulder.
While it has been operating fairly successfully
its survival depends upon some expansion
and upgrades in its production equipment.
Ralph has come to you as a potential equity
investor.
The expansion requires $100,000 and the two
of you are discussing the ownership stake this
would imply for you.
Ralph’s Position
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Ralph argues that three years ago he
invested $30,000 of his own capital.
He also argues that for three years he has
been working at a less than competitive wage
(in order to reinvest the generated cash).
He estimates this amounts to $40,000 in
“sweat equity” for each of the three years.
Ralph suggests these facts imply your
$100,000 will purchase 40% of the equity.
Is this argument valid?
Valuation Basics – Where We Are Headed
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Assets have value due to the payoffs they
generate for those that purchase them.
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What does past investment have to do with this?
The price you should be willing to pay for an
asset depends upon the future value you will
receive from owning that asset.
Another piece of the puzzle is that cash today
is more valuable than cash tomorrow – a
concept we call the “time value of money.”
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Most business decisions come down to an
evaluation of money today versus money tomorrow.
Valuation
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The present value formula is a way to express
today’s value of a stream of cash payments to
be received in the future.
Suppose you expect to receive cash payments
of $100, $150, $180, and $210 respectively at
year end for the next 4 years if you purchase
a particular security.
Today’s value of this security can be
expressed using a simple formula.
Valuation
Value  $100  $150 180  210
Rather
$100
$150
$180
$210
Value 

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
(1  r0,1 ) (1  r0, 2 ) (1  r0,3 ) (1  r0, 4 )
or
C3
C1
C2
C4
Value 



(1  r0,1 ) (1  r0, 2 ) (1  r0,3 ) (1  r0, 4 )
Payoffs and Rates of Return
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For a given investment, the dollar payoff of
that investment is simply the amount of cash
it returns to the investor (in one period).
The rate of return of the investment is the
future payoff net of the initial investment (or
the net payoff) expressed as a percentage of
the initial cash outlay.
It’s the net payoff, per dollar invested, for a
given period of time.
Example
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An investment project that costs $10 to establish
today will provide a cash payment of $12 in one year
has:
time 1 payoff = $12
time 1 payoff = C1
time 1 net payoff = $12 - $10 = $2
time 1 net payoff = C1 – C0
rate of return = ($12 - $10)/$10 = .20 = 20%
r0,1 = (C1 – C0)/C0 = C1/C0 -1
Future Value
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We can turn this formula around to answer
the question: “How much money will I receive
in the future if the rate of return is 20% and I
invest $100 today?”
The answer of course is:
or
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$100(1+20%) = $120
r1 = (C1 – C0)/C0  C0(1+r1) = C1 = FV1(C0)
This is referred to as the future value of $100
if the relevant rate of return is 20%.
Future Value
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We can use this idea to compute all sorts of
future payoffs.
For example: an investment requiring $212
today and earning a holding period return
(or total return) of 60% from now (time 0) till
time 12 would provide a payoff of:
$212(1+60%) = $339.20
C0(1+r0,12) = C12 = FV12(C0)
Problems
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A project offers a payoff of $1,050 for an
investment of $1,000. What is the rate of
return?
A project has a rate of return of 30%. What
is the payoff if the initial investment is $250?
A project has a rate of return of 30%. What
is the initial investment if the final payoff is
$250? **This is called the present value of
the future $250.**
Compounding Rates of Return
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What is the two-year holding period rate of
return if you earn a one-year rate of return of
20% in both years?
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Note: It is not 20% + 20% = 40%.
Why isn’t it?
If you invest $100 at 20% for one year you have
$120 = $100(1+20%) at the end of the first year.
If you then invest the $120 for the second year at
20% you end up with $144 = $120(1+20%).
This is a two-year rate of return of:
44% = ($144 - $100)/$100 = r0,2
Compounding…
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This two-year rate of return of 44% is
more than 40% because you earned an
additional $4 in interest the second year
as compared to the first.
During the second year you earned
interest on the $20 of interest earned
during the first year.
Compounding…
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We can represent this more generally using
the compounding (or the “one plus”) formula.
(1  20%)(1  20%)  (1.2)(1.2)  1.44
(1  r0, 2 )  (1  r0,1 )(1  r1, 2 )
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This can be expanded to consider an arbitrary
number of periods:
(1  rt ,t  N )  (1  rt ,t 1 )(1  rt 1,t  2 )  (1  rt  N 1,t  N )
Problems
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If for the first year the one year interest rate
is 20% and for the second year the one year
interest rate is 30%, what is the two-year
total interest rate?
If the per-year interest rate for all years is
5%, what is the two-year interest rate?
If the per-year interest rate is 5%, what is
the 100-year interest rate?
The Yield Curve
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The term structure of interest rates.
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The important message here is that
investments of different maturities have
different rates of return.
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Today’s average annualized interest rate that
investments pay as a function of their maturity.
This is true even for Treasury securities.
The following graph and chart provide a view
of a recent yield curve.
The Yield Curve
The Yield Curve
Maturity Yield
Yesterday
Last Week
Last Month
3 Month
4.89
4.91
4.93
4.98
6 Month
4.92
4.93
4.93
4.97
2 Year
4.73
4.74
4.76
4.86
3 Year
4.60
4.62
4.65
4.78
5 Year
4.54
4.56
4.59
4.74
10 Year
4.54
4.56
4.60
4.76
30 Year
4.63
4.64
4.68
4.88
The Yield Curve
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On November 25th 2006 how much
money did an investment of $100,000
in a 2-year U.S. Treasury note promise
to payout in two years time?
r0,2 = (1+4.73%)(1+4.73%) – 1 = 9.68%*
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Thus in two years the $100,000 will
turn into:
(1.0968)  $100,000 = $109,680
*This isn’t exactly correct since semi-annual compounding is
always presumed in the bond market but lets keep it simple.
The Yield Curve
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On November 25th 2006 the 5 year rate
is quoted as 4.54%.
This means that if you had invested
$100 in a 5 year bond it would (at the
maturity of the bond) become:
$100×(1+r0,5) = $100×(1.0454)5 = $124.86
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These values must therefore be
equivalent.
Evaluating Investments
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Finance views all investments as if they were a series
of cash payments received at different times.
The actual costs or benefits may not be in cash,
however for a proper evaluation of an investment,
the costs and benefits must all be assigned a
monetary value.
Once all incremental cash flows for an investment are
listed, finance can take over and evaluate the
desirability of the project.
The decision of whether to make an investment will
always entail a comparison of that investment to an
alternative use of the required cash.
How do we make such a comparison?
Present Value and Net Present Value
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Recall our basic rate of return formula:
C1  C0 C1
r0,1 

1
C0
C0
Just as we can turn this around to determine
the future value of the current cash flow we
can also use it to determine the present value
of the future cash flow:
C1
C0 
 PV0 (C1 )
1  r0,1
Example
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A project has an annual rate of return of 30%. If we
invest $100 for one year what is the future value of
our investment?
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If a project has an annual rate of return of 30% and
will payoff $130 in one year, what is the initial
investment?
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Ans: $100(1 + 30%) = $100(1.3) = $130.
Ans: $130/(1+ 30%) = $100 = C1/(1 + r0,1)
$100 is the present value of $130 to be received in
one year if the relevant rate of return is 30%. This is
true because if you had $100 today it would become
$130 in one year investing at 30%. Alternatively, we
“charge” next year’s $130 the 30% rate of return we
could receive if we had money now.
Extension
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This technique can be used to find the
present value of cash at any future date.
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For example, suppose the annual interest rate is
15% (for years one and two) and you will receive
$300 in two years, what is the present value of
this future cash flow?
r0,2 = (1 + r0,1)(1 + r1,2) = 1.151.15 - 1 = 32.25%
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The present value of the $300 is:
PV(C2) = $300/(1.3225) = C2/(1 + r0,2) = $226.84
So What?
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How does this help us evaluate a project?
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Investment projects have lots of cash flows at
different points in time. To make an investment
decision we need a way to compare cash flows
received at different times.
We can’t compare $100 today with $120 next year
but we can compare $100 today with the present
value (today’s value) of $120 next year.
The present values of future cash flows are all in
terms of dollars today.
Investment decisions are all made by comparison
with a comparable alternative. Is it better than an
alternative use of the upfront investment?
Present Value
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Consider a project that will generate a payoff of $15
in one year’s time and $10 in two years. What is the
present value of these payments if the annual
interest rate on Treasury bills is 10% for both years?
The present value of the first payoff is:
r0,1 = 10% so PV0(C1) = C1/(1 + r0,1) = $15/1.1 = $13.64 ($, today)
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The present value of the second payoff is:
r0,2 = (1.1)(1.1) – 1 = 21% so PV0(C2) = $10/1.21 = $8.26 ($, today)
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Their sum is $13.64 + $8.26 = $21.90 ($, today)
Would you undertake this project if it cost $20?
Net Present Value
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This is just the net present value (NPV) rule.
If the sum of the present values of a project’s
future cash flows is greater than its initial
cost, then taking it is creating value.
This is just like being able to buy $10 bills for
$5 or $8 or $9.98.
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Alternatively, we can think of a positive NPV
project as providing a return higher than the
available alternative.
If the NPV of an investment is negative you
are paying $10.05 for the $10 bill.
Precision
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The Net Present Value formula is:
C3
C1
C2
NPV  C0 

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
(1  r0,1 ) (1  r0, 2 ) (1  r0,3 )
 Ct 
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  

t  0  1  r0 ,t 

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The discount rate is the expected return from
a comparable alternative investment.
The net present value rule states that you
should accept projects with a positive NPV
and reject those with a negative NPV.
The NPV Decision Rule
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It is important to note that the timing of the
project’s cash flows are irrelevant once you
find that the NPV is positive.
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What if you are 90 years old and find a positive
NPV investment that provides payoffs only in 30
years?
What if you are saving for your child’s college
expenses and there is a positive NPV investment
that provides a payoff immediately?
All agents agree on the desirability of positive
NPV projects. Nice in the corporate world.
Problem
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For simplicity assume the relevant interest
rate is 5% annually for all years.
What is the present value of the future cash
flows of a project if it has payoffs of $150 in
one year, $200 in two years, $600 in three
years, and $100 in four years?
What is the most you would pay for such an
investment?
If it costs $800 to purchase this investment
what is its NPV? What is today’s value of
being able to invest in this project?
Incremental Cash Flow
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Incremental cash flow for a given period is the
cash flow we want to estimate for use in the
discounted cash flow analysis.
Some issues that arise:
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Sunk costs. Costs, perhaps related to the project, that
have already been incurred and cannot be recaptured.
Opportunity costs. What else could be done?
Side effects. Does the project affect current cash flow?
Taxes.
Capital expenditures versus depreciation expense.
Increased investment in working capital.
Sunk Costs vs. Opportunity
Costs
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A short time ago you purchased a plot of
land for $2.5 million.
Currently, its market value is $2.0 million.
You are considering placing a new retail
outlet on this land. How should the land
cost be evaluated for purposes of
projecting the cash flows that will be part
of the NPV analysis?
Sunk Costs vs. Opportunity Costs
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Sunk costs should never be evaluated as part of the
incremental cash flow.
These are costs faced by the firm, regardless of what
the firm may do. They are usually easy to measure as
they have already been incurred.
Opportunity costs should always be considered as part
of incremental cash flow.
The most valuable opportunity forgone due to a
decision is the lost opportunity. Often these are
difficult to measure and sometimes difficult to
recognize.
Side Effects
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A further difficulty in determining
project cash flow comes from affects the
proposed project may have on other
parts of the firm.
The most important side effect is called
erosion: cash flow transferred from
existing operations to the project.
Taxes
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Typically,
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Revenues are taxable when accrued.
Expenses are deductible when accrued.
Capital expenditures are not deductible, but
depreciation can be deducted as it is accrued.
 Tax depreciation can differ from that reported
on public financial statements.
Sale of an asset for a price other than its tax basis
(original price less accumulated tax depreciation)
leads to a capital gain/loss with tax implications.
Working Capital
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Increases in Net Working Capital should
typically be viewed as requiring a cash outflow.
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An increase in inventory (and/or the cash balance)
requires an actual use of cash.
An increase in receivables/payables means that
accrued revenues/expenses exceeded actual cash
collections/payments.
 If you are estimating accrued revenues and
expenses you need a correcting adjustment.
 If you estimate cash revenues/expenses no
adjustment is required.
Handy Short Cuts
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A growing perpetuity:
C1
PV 
rg
A growing annuity
T

C1   1  g  
PV 
1 
 

r  g   1 r  
Examples
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The interest rate is 10%. Your aunt Maude
just promised to give you $150 every year for
Christmas, forever. If it is now New Year’s
eve how generous is she being?
What if the promise is for the next 10 years?
What if the promise is for 10 years but the
amount will grow by 5% after the first year to
account for inflation?
What if the promise lasts forever and grows
by 5% after the first year’s payment?