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7/29/2019 Corporate Finance Lecture Notes 1
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Lecture Notes 1: Net Present Value and Investment Decisions
Corporate Finance
Joao F. CoccoAssociate Professor of Finance at London Business School
MBA Programme
September 2012
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The Goal of the Firm
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The Goal of the Firm
The objective of a financial decision maker:
MAXIMIZE VALUE
Need to know:
(1) How to make investment decisions?
(2) How to finance the project? Which is the cost of thesources of finance?
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Flow of Cash Between Investorsand the Firms Operations
`
Firms
Operations
Financial
Decision Maker
Investors
(Financial
Institutions,
Individuals,
Other Firms)
(1)
(1) Cash raised from investors by selling financial assets.
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Flow of Cash Between Investorsand the Firms Operations
Firms
Operations
Financial
Decision Maker
Investors
(Financial
Institutions,
Individuals,
Other Firms)
(1)
(1) Cash raised from investors by selling financial assets.(2) Cash invested in real assets (some are intangible).
(2)
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Flow of Cash Between Investorsand the Firms Operations
Firms
Operations
Financial
Decision Maker
Investors
(Financial
Institutions,
Individuals,
Other Firms)
(1)
(1) Cash raised from investors by selling financial assets.(2) Cash invested in real assets (some are intangible).
(3) Cash generated by operations.
(2)
(3)
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Flow of Cash Between Investorsand the Firms Operations
Firms
Operations
Financial
Decision Maker
Investors
(Financial
Institutions,
Individuals,
Other Firms)
(1)
(1) Cash raised from investors by selling financial assets.(2) Cash invested in real assets (some are intangible).
(3) Cash generated by operations.(4) Cash reinvested in the firm (retained earnings).
(2)
(3)
(4)
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Flow of Cash Between Investorsand the Firms Operations
Firms
Operations
Financial
Decision Maker
Investors
(Financial
Institutions,
Individuals,
Other Firms)
(1)
(1) Cash raised from investors by selling financial assets.(2) Cash invested in real assets (some are intangible).
(3) Cash generated by operations.(4) Cash reinvested in the firm (retained earnings).(5) Cash repaid to investors (interest, dividends, etc).
(2)
(3)(5)
(4)
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Opportunity cost of capital: The firm canalways give cash back investors.
Projects Investors
Opportunities
for investmentavailable inthe capitalmarkets
The opportunity cost of capital is the expected rate of return
offered by equivalent investments in capital markets. It compensatesinvestors for: The time value of money. The risk of the investment.
Cash
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The Goal of the Firm
The Objective: Create Value How?
1. Investment Decisions: How to select projects that increase the valueof the firm?
Need to find projects which are worth more than their requiredinvestment (+ NPV).
2. Financing Decisions: How to finance an investment project? Whichtype of security to choose in order to maximize the value of the firm?
Need to know the cost of the different sources of finance (debt,equity).
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Only one goal can stand the test of time
In some instances maximizing the value of the firm may
not be the same as maximizing the wealth of theshareholders in the firm:
In that case firms should strive to maximize the wealth
of the shareholders In most cases this implies that the firm must be
concerned about the well being of all stakeholders
But what if there are conflicts of interest? Who comesfirst?
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The wrong goals
Size: is bigger necessarily better?
Market share: is a larger market share necessarily better?
Growth: only works if there is value
Profits: not cash and measured at a particular point in time
Most companies could report higher profits in aparticular year if they wanted to
How?
Maximizing cash flows / funds distributed to shareholders: It is OK not to distribute the funds if
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What about the other stakeholders in the firm?
Customers Suppliers Employees
The community Corporate Social Responsibility
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Discounting and Net Present Value
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Introduction
The key driver of the value of any business is making the
right investment decision
Implies: buying and combining assets, ideas, people, sothat they cost less than what they are worth
Goal of this part is to study the process of making theinvestment decision in more detail
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Present Value
Present Value
Value today of a
future cash flow.
Discount Rate
Interest rate used to
compute present
values of future
cash flows.
Discount Factor
Present value of a
$1 future
payment.
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Investment decisions without uncertainty:
Invest $1 today if and only if your return (call it $X) at time T is
worth more than that $1
How do we compare $1 at t = 0 and $X at t = T?
Time value of money: other things equal, having one dollar today is worth
more than having the same dollar next year.Assume, for now, that the interest rate (r) is 5% per year.
Putting $1 in the bank gets you $1 1.05 = $1.05 a year from now.
Present Value
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Future Value of $y in T years at an interest rate of r:
FV ($y, T, r) = $y (1 + r)T (e.g $15 (1.05)4 = $18.23)
How much is having $x at time t = T (say in 4 years) worth today?
Answer: How ever much I would have to invest today to get $x at time t =
T.
Present Value: PV ($x, T, r) = $x / (1 + r)T (e.g. $20/(1.05)4 == $16.45)
Call 1/(1+r)T thePresent Value Factor, orDiscount Factor.
Present and Future Value
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Valuing an Office Building
Step 1: Forecast cash flows
Cost of building = C0 = 350
Sale price in Year 1 = C1 = 400
Is it a good investment?
Step 2: We need the opportunity cost of capital
If equally risky investments in the capital market
offer a return of 7%, then
Cost of capital = r = 7%
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Valuing an Office Building
Step 3: Discount future cash flows
Step 4: Go ahead if PV of payoff exceeds investment
37)07.1(
400)1(
1 rC
PV
24374350 NPV
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Net Present Value
Present Value = PV = Discount Factor1 * C1 Discount Factor1 = DF1 = 1/(1+r)
Net Present Value = Required Investment + PV
= C0 + C1/ (1+r)
Decision Rule: Accept investments that have
positive net present value.
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Risk and Present Value
Higher risk projects require a higher rate of return
Higher required rates of return cause lower PV
1PV of C $400 at 12%$400
PV $357
1 .12
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Discount Factor more generally
Discount Factors can be used to compute the presentvalue of any cash flow.
Replacing 1 with t allows the formula to be used forcash flows that exist at any point in time
tt
ttr
CCDFPV)1(
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Present Values
Present values can be added together to evaluatemultiple cash flows.
....22
1
1
)1()1(
r
C
r
CPV
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Present Values
Example
Assume that the cash flows from the
construction and sale of an office buildingare as follows. Given a 7% required rateof return, create a present valueworksheet and show the net presentvalue.
000,300000,100000,150
2Year1Year0Year
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Present Values
Example - continued
Assume that the cash flows from the construction and sale of an office building is asfollows. Given a 7% required rate of return, create a present value worksheet and show
the net present value.
400,18$
900,261000,300873.2
500,93000,100935.1000,150000,1500.10
Value
Present
Flow
Cash
Factor
DiscountPeriod
207.1
1
07.11
TotalNPV
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Why do we use the NPV Rule?
Assume we showed that a project had an NPVof 138. So what?
Share value will rise by NPV:
Market capitalization increases from 1,000 to 1,138
Share price increases from 1 to 1,138/1,000 = 1.14
If:
The stock market is efficient The market agrees with the assessment of project
The project NPV had not already been anticipated
When:
On announcement Not when profits are subsequently realized
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Project Evaluation Techniques
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Applying the methods
The Net Present Value:
Present value of inflows - present value of outflows
Recognizes time value of money: a Pound today is worth more than a Pound tomorrow if you have a Pound today, you can invest it, which will return more
than a Pound tomorrow Takes into account compounding effect: you earn interest oninterest
Recognizes the risk of the project:
the discount rate is higher than the interest rate for a risk-lessinvestment
Net present value = measure of wealth you created
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Example
A project requires an initial investment of 1 million.
The project will generate 500,000 per year for the next 4years assume the cash flows occur at year end(common practice)
Compute: The Net Present Value, assuming a required rate of
return of 20%
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NPV of this project
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Internal Rate of Return
The rate of return that makes the Net Present Value equal to zero
Relation between Discount Rate and Net Present Value
-400,000.00
-200,000.00
0.00
200,000.00
400,000.00
600,000.00
800,000.00
1,000,000.00
1,200,000.00
1% 6% 11% 16% 21% 26% 31% 36% 41% 46% 51%
Discount Rate
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Internal Rate of Return
Methods to calculate the IRR: Method 1: use a calculator (spreadsheet) with the IRR function. Method 2: by trial and error.
In this example?
Decision rule: Invest if IRR > required rate of return
Remark: The IRR rule gives the same answer as the NPV rule if theNPV of a project is a smoothly declining function of the interest rate (asin previous example).
What if the NPV of the project is not a smoothly declining function ofthe interest rate?
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Internal Rate of Return:
No solution
Example 1:
There are no solutions: NPV never becomes zero.
C0 C1 C2Project -100 +120 -90
2
2
120 90100
1 1
120 900 100
1 1
NPV
r r
irr irr
-85
-80
-75
-70
-65
-60
0 1 2 3 4 5 6r
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Internal Rate of Return:
Multiple solutions
Example 2:
Two solutions: 25% and 400%.
C0 C1 C2
Project -4,000 +25,000 -25,000
2
2
25,000 25,0004000
11
25,000 25,0000 4,000
1 1
NPVr
r
irr irr
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Payback
Count the number of years until you get your money back
A project requires an initial investment of 1 million andgenerates 500,000 per year for the next 4 years assume the cash flows occur at year end (common
practice). Payback?
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What are the proper criteria?
NPV > 0
IRR > required rate of return
Be careful when there is no solution or when there aremultiple solutions
Why is the payback method not a proper method?
Does not take into account the time value of money
Cut-off period (benchmark) is arbitrary Ignores cash flows beyond cut-off period
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Example
C0 C1 C2 C3 Payback Time NPV
ProjectA -2,000 +2,000 0 0 1 year -182
ProjectB -2,000 +1,000 +1,000 +5,000 2 years +3,492
2 3
2 3
2, 000 0 0
2, 000 182.821 0.10 1 0.10 1 0.10
1, 000 1, 000 5, 0002, 000 3, 492.11
1 0.10 1 0.10 1 0.10
A
B
NPV
NPV
Based on Payback Rule, Project A is preferable since it has a smaller paybacktime (it takes a shorter amount of time start generating positive profits). However theNPV of Project A is negative!
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Exercise
A project requires an initial investment of 400,000. Theproject will generate 200,000 per year for the next 2
years, and 100,000 in 3 years assume the cash flowsoccur at year end (common practice). Compute:
The Net Present Value, assuming a required rate ofreturn of 10%
The Internal Rate of Return
The Payback Period
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Exercise solution
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Keep in mind
Investment decisions should not be made without a proper
valuation and NPV analysis
Investment decision should not be made without having
a champion to support this project and who is heldaccountable
a reasonable story: the champion has to be able to
explain why the NPV is positive
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Summing Up
Net present value is the best technique to evaluate
investment projects Internal rate of return and benefit/cost ratio are acceptable
in most cases
Payback has important limitations
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Perpetuities and Annuities
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In Capital Budgeting sometimes computations become easier. This can be the casewhen cash flows are perpetuities, growing perpetuities or annuities.
Example: Consider the case of the purchase of a machine that costs today $5,000, withrunning costs equal to $2,000 which generates revenues equal to $5,000. Supposethat as long as we keep maintaining the machine, we will be able to sustain theprevious revenues. If the interest rate is 10%, what is the Net Present Value of theinvestment?
The constant stream of cash flows equal to +$3,000 that start in period 1 and last for
ever is a perpetuity.
time 0 1 2 3 forever
Capital Expenditure -$5,000
Running Costs -$2,000 -$2,000 -$2,000 -$2,000
Revenues $5,000 $5,000 $5,000 $5,000
Cash Flows -$5,000
Perpetuities
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0
0
$3,000
0.10
$3,000$5,000
0.10
$25,000
PV
NPV
0
0
$3,000
0.10
$3,000$5,000
0.10
$25,000
PV
NPV
Instead of calculating the PV with long calculations, we can use theshort cut:
time 0 1 2 3 forever
Capital Expenditure -$5,000
Running Costs -$2,000 -$2,000 -$2,000 -$2,000
Revenues $5,000 $5,000 $5,000 $5,000
Cash Flows -$5,000
Perpetuities
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Definition: A Perpetuity is a financial Asset that promises to pay a fixed nominal amountC forever
The Present Value at time t= 0 of a perpetuity that starts paying C next period is:
Example 1: What is the Present Value of a Perpetuity that pays $50 forever starting nextperiod? Assume that the opportunity cost of capital is 1%
Example of perpetuities: UK government securities.
time 0 1 2 3 4 .. forever
Cash-flow C C C C .. C
0CPVr
0 CPVr
0
$50$5000
0.01PV 0
$50$5000
0.01PV
Perpetuities
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0 44 4
1 $ 5 0 0 0$ 4 8 0 4 . 9
( 1 ) ( 1 . 0 1 )P V P V
r
0 44 4
1 $ 5 0 0 0$ 4 8 0 4 . 9
( 1 ) ( 1 . 0 1 )P V P V
r
4
$ 5 0$ 5 0 0 0
0 . 0 1
CP V
r 4
$ 5 0$ 5 0 0 0
0 . 0 1
CP V
r
time 0 1 2 5 forever
Cash-flow C C
Example 2: What is the Present Value of a Perpetuity that pays $50 foreverstarting in period 5? Assume r = 1%.
Perpetuities
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Example: Consider the case of the purchase of a machine that costs today $5,000,with running costs equal to $2,000 growing at a rate of 2% every year and thatgenerates revenues equal to $5,000 growing at rate of 2% forever. Suppose that as
long as we keep maintaining the machine, we will be able to sustain the previousrevenues. If the interest rate is 10%, what is the Net Present Value of theinvestment?
The stream of cash flows equal to +$3,000 starting in period 1 and growing at aconstant rate forever is a growing perpetuity.
time 0 1 2 3 . forever
Cap. Exp. -$5k .Costs -$2k -$2k (1.02) -$2k (1.02)2 -$2k (1.02)t
Revenues $5k $5k (1.02) $5k (1.02)2 $5k (1.02)t
Cash Flows -$5k
Growing Perpetuities
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0
0
$3,000
0.10 0.02
$3,000$5,0000.10 0.02
$32,500
PV
NPV
0
0
$3,000
0.10 0.02
$3,000$5,0000.10 0.02
$32,500
PV
NPV
Instead of calculating the PV with long calculations, we can use the far simpler short cut:
time 0 1 2 3 . forever
Cap. Exp. -$5k .
Costs -$2k -$2k (1.02) -$2k (1.02)2 -$2k (1.02)t
Revenues $5k $5k (1.02) $5k (1.02)2 $5k (1.02)t
Cash Flows -$5k
Growing Perpetuities
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A Growing Perpetuity is a financial Asset that gives the right to receive acash flow growing at a rate equal to gforever.
EXAMPLE:
Next Years Cash Flow = $100Constant Expected Growth Rate = 10%
Cost of Capital = 15%
CPV
r g
CPV
r g
$1002000
0.15 0.10
$1002000
0.15 0.10
Growing Perpetuities
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An Annuity is a financial asset that gives the right to receive a constant cash-flow C for tperiods starting next one.
EXAMPLE: Consider a 20-year mortgage. The Annual Payment is equalto $100,000. If you were the Chief Financial Officer of Barclays and theinterest rate were 20%, what is the maximum amount you would lend at the
previous annual payment schedule?You would lend at most the Present Value of thefuture Cash Flows from the mortgage payments. Using the shortcut the result can beeasily obtained:
Yr 0 Yr 1 Yr 2 Yr 3 Yr 4 Yr 5 Yr 6 Yr 7
C C C C C C 0
0
1 1
1
tPV C
r r r
0
1 1
1
tPV C
r r r
20
1 1100, 000 $487, 000
0.2 0.2 1 0.2PV
20
1 1100, 000 $487, 000
0.2 0.2 1 0.2PV
Annuities
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Example: You are offered a building for $5Ml today (Year 0). After some extensiveresearch on the housing market and on interest rates, your expectations are thatyou will be able to sell the building for $7Ml in 10 years from now (Year 10). If the
Cost of Capital is 15%, what is the smallest fixed rent that does not make the dealunprofitable?
Let xbe the rent such that:
time 0 1 2 3 4 5 6 7 8 9 10
sale $7Ml
rent x x x x x x x x x x
9
11
1 0 . 1 5o
xP V
r
10.15 910
$7 1$5
1.15 0.15 1 0.15
MlMl x x
10.15 910
$7 1$5
1.15 0.15 1 0.15
MlMl x x
Annuities: Example
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1 0
75 / 5 . 7 7 1 6 $ 5 6 6 , 5 2 0
1 . 1 5
M lx M l
1 0
75 / 5 . 7 7 1 6 $ 5 6 6 , 5 2 0
1 . 1 5
M lx M l
Solving forx:
Annuities: Example
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Summary
Growing Perpetuities, first payment year 1: Growing Perpetuities, first payment year 1:C
PVr g
CPV
r g
Growing Perpetuities, first payment year (t+1): Growing Perpetuities, first payment year (t+1): 1
(1 )t
CPV
r g r
1
(1 )t
CPV
r g r
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Compound Interest and Inflation
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Compound Interest
Most interest rates are stated in annual terms. This does not,however, mean that interest is paid only once a year. Many securities
pay interest semi-annually (e.g. corporate Bonds), monthly (somesavings accounts), daily, or even continually.
If the compounding frequency is not annual, then the stated interestrate is not equal to the actual return you are earning (effective annualyield). If the compounding frequency increases, so does the effectiveannual yield.
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Compound Interest
i ii iii iv v
Periods Interest Value Annually
per per after compounded
year period (i x ii) one year interest rate
1 6% 6% 1.06 6.000%
2 3 6 1.032 = 1.0609 6.090
4 1.5 6 1.0154 = 1.06136 6.136
12 .5 6 1.00512 = 1.06168 6.168
52 .1154 6 1.00115452
= 1.06180 6.180365 .0164 6 1.000164365 = 1.06183 6.183
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Compound Interest
0
2
4
6
8
10
12
14
16
18
0 3 6 9 12 15 18 21 24 27 30
Number of Years
F
V
of$1
10% Simple
10% Compound
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Compound Interest
We can convert r (as stated by the bank) into the effective annualyield.
We can then use the effective annual yield in order to compareinterest rates that are paid with differing compounding frequencies.
Example:Suppose you are offered an automobile loan at an APR of6% per year. What does that mean, and what is the true rate ofinterest, given monthly payments?
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Compound InterestExample - continued
Suppose you are offered an automobile loan at 6% per year. What does thatmean, and what is the true rate of interest, given monthly payments?Assume$10,000 loan amount.
12Loan Pmt 10, 000 (1.005)
10,616.78
6.1678%Effective Rate
Inflation
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Inflation
Inflation - Rate at which prices as a whole are increasing.
We should distinguish between real and nominal cash flows
Always discount nominal cash flows with the nominal rate
and real cash flows with the real rate.
Nominal Interest Rate - Rate at which money invested grows.
Real Interest Rate - Rate at which the purchasing power of aninvestment increases.
Inflation
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Inflation
rateinflation+1
rateinterestnominal+1
=rateinterestreal1
Approximation formula:
Real int. rate nominal int. rate - inflation rate
Inflation
7/29/2019 Corporate Finance Lecture Notes 1
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Lecture Notes 1: Net Present Value and Investment Decisions Page 64
Inflation
Example: If the interest rate on one year govt. bonds is 5.9% and theinflation rate is 3.3%, what is the real interest rate?
1
1
+
+
real interest rate =
real interest rate = 1.025
real interest rate = .025 or 2.5%
Approximation =.059-.033 =.026 or 2.6%
1+.0591+.033