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Chapter One
Introduction to Net Present Value andInvestment Criteria
Based on:
Ross, Westerfield & Jordan, Financial Foundations
Blank & Tarquin, Engineering Economy
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Financial Management - Review
There are three basic forms of business organization: SoleProprietorship (Empresa Individual), General or Limited Partnership(Soc. Colectiva, SAC), and Corporation (S.A.A.)
Corporations: The most important form of business organization. Canoccur debts, can sue and be sued, enter into legal contracts. Exists asa separate legal entity from the owners.
Advantages:
- Separation of ownership and management
- Limited liability of owners (share holders)
- Transfer of ownership is easy (shares of common stock easily transferred)
- Unlimited lifespan
- Easier to raise capital
Disadvantages:
- Separation of ownership and management (Agency Problem)
- Double taxation (corporate income tax + dividends are taxed)
- Slightly complicated to setup (Articles of incorporation (charter), Bylaws)
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Financial Management - Review What should be the firms objective? (A for-profit business)
Maximize market value?
Maintain steady earnings growth?
Maximize sales revenue or market share?
Maximize profits?
Minimize costs?
To avoid bankruptcy and financial distress?
To defeat the competitors
To survive
Maximize CEO wealth?
What about these other goals?
Maximize customer satisfaction
Environmental responsibility Ethical behavior
The goal of the financial management of the firm is to increase themarket value of the shares, it means, the value of the firm.
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Financial Management - Review There are three questions on Finance:
1. How do they manage their Working Capital? (Which and howmuch s h o r t t e r m r e s o u r ce s do they prefer? How do theymanage their cash, receivables, stocks and payables?) - Day-to-day operations or L i q u i d i t y D e c i si o n s .
2. From where and which mix are t h e l o n g t e r m r e s ou r c e s to paytheir investments? (Do they ask for more equity or do they borrowmore debt?) Cap i t a l S t r u c t u r e or Financing Decisions.
3. What and how much f i x e d a s s e t s are necessary to buy? (Whichlong term investments: buildings, machinery or equipment; Whichproduct lines to have) - Budget Capital or I n v e s t m e n t D e c is io n s .
4. How should the firm Identify, measure and hedge the riskexposure? Financial Risk Management
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Capital Structure (2) Addresses the question of how a firm should obtain and manage the long term
financing needed to support its long term investments:
it is the specific mixture of long term debt and equity capital
the decision on how much debt vs. Equity impacts the risk level for the firmand the firms cost of capital
Capital Structure is the specific mix of short-term debt, long-term debt andequity.
Raising long-term financing can be expensive, so the different possibilities mustconsidered carefully.
A firms capital structure is the specific mix of debt and equity used to finance thefirms operations.
Decisions need to be made on both the financing mix and how and where to raisethe money.
Key Questions
How should the firm pay for its assets? Debt or equity?
How much should the firm borrow?
What is the least expensive source of funds?
How, when and where to raise the money?
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The Capital Structure Decision
How should the firm
raise funds for the
selected investments?
Shareholders
Equity
Current Liabilities
Long-Term Debt
Current Assets
Fixed Assets
1 Tangible
2 Intangible
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Capital StructureThe value of the firm can be thought of as a pie.
The goal of the manager is toincrease the size of the pie.
The Capital Structure decision can be viewed ashow best to slice up a the pie.
If how your slice of the pie
affects the size of the pie,then the capital structuredecision matters.
50%Debt
25%Debt
75%Equity
70%Debt
30%
Equity
50%Debt
50%Equity
50%Equity
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Financial Risk Management (4)
The process of identifying, quantifying and decisions to managecertain types of risk:
currency risks
interest rate risks
commodity price risk
Other risks such as strategic, operating and commercial risks need tobe considered by the firm as a whole - ideally looking at risk onan enterprise wide basis (holistic risk management)
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Strategic-technology & information
- knowledge management-industry value chain transformation
Crisis Management-environmental disasters-brand crisis/computer system failure
Operating Risks-distribution networks-manufacturing
Commercial Risks- new competitor(s)- customer service expectations- new pricing models
- supply chain management
Financial Risk-price - interest & fx. rate-commodity price
Organization wide
Risk
Identification Impact Response
Integrated Risk Management
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Investing Decisions
Interesting issues are the way in which the firm decide its CapitalStructure on the long term, or the way it manage its day-by-dayoperational activities with its Working Capital, but the fixed assets arewhich define the firms business.
The most important part of the Financial Management is the CapitalBudgeting.
Any firm have many possible investment opportunities, some arevaluable, some are not.
The type of investment opportunities are supposed to depend on thenature of the firms business, and they must have more value thantheir of acquisition. It means that they generate more cash inflowvalue than their cost.
This chapters goal is to learn how to identify them.
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The Capital Budgeting Decision
What long-terminvestmentsshould the firm
choose?
Current Assets
Fixed Assets
1 Tangible
2 Intangible
Shareholders
Equity
Current
Liabilities
Long-Term Debt
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Investing Decisions
St r at e g ic P la nn in g a nd Ca p i t a l B ud g et in g : The most importantdecision of the firm have to do with its product lines. What services willthey supply? In which markets will they compete? What new productswil l launch? Each question implies the use of its scarce and valuablecapital in certain assets.
T im e a n d Co st s : Its useful to think on the future having two parts,the short term and the long term; but they arent mean periods of time, they depend on the type of cost we are talking of. If the costsere fixed, we are talking of the short term. In the long term every costis variable.
We are interested on the volume o s i z e o f t h e am o un t s , the specificmoment or t i m i n g , and in the r i s k or uncertainty of the future cash
flows.
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Valuation of Durable Assets
Simple and Compound Interest One period (time value of the money)
1
1
Many periods 1
1
Due vs. in advance
105100
100 1 100
10095
1001001
: 1 1
1
1
1 1
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Valuation of Durable Assets
Simple and Compound Interest
In advance
105
100
1
1 1
100
95
1
1 1
1
1 1 1
1
1
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Valuation of Durable AssetsPresent Value of a Perpetuity
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Valuation of Durable AssetsPresent Value of a Growing Perpetuity
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1 1 2 1 3 1 .Then, 11 1 11 1 11 2 11 1 11 1
11 1 11 11 1
11 1 11
11 1 11 1
1 11 1 1
1 11 1 1 11 1 11 1 11
1 1 .Note: | 1 1
Present Value of an Annuity
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Valuation of Durable Assets
Future Value of an Annuity 1 1 1 2 1 2 1 1 1 1 1 2 1 2 1 1 1
1 1 1 1 1 1 1 1 .
Note1: 1 1 1 1 1 1
1 1 .Note2: | 1 1
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Valuation of Durable AssetsPresent Value of a Growing Annuity
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Valuation of Durable Assets
Future Value of a Growing Annuity1. FutureValue
1 1 1 1 2 1 21 1 1 1
1 11 11 11 1 2 1 21 1 1 1
1 11 1 1 1 21 2
1 11 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1 1
1
1 1 1
1
1
1
1 1
1
1
1 1 1 1
.
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Valuation of Durable Assets
Due vs. In advance Annuities
1r
Immediately and Deferred
In advance (PV & FV)
Perpetuity
Constant (PV)
G. Growing (PV)
Annuities
Constant (PV & FV)
G. Growing (PV & FV)
Due (PV & FV)
Perpetuity
Constant (PV)
G. Growing (PV)
Annuities
Constant (PV & FV)
G. Growing (PV & FV)
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Valuation of Durable AssetsConsol - Perpetuity
Characteristics
debt instrument
Term - infinite
Fixed interest payment
Price adjusts to accommodate risk
PInt
rm0 00967
12 $15
. $155.
Anual TEA Sem. TEA
IntC= 15 7.5 Cuntos15hayen 1,000.00
rm= 9.67% 4.84% 66.67
r= 1.50% 1.500% 0.75% 1.506%
PV= Po = 155.12 155.12 Cuntos7.5hayen 1,000.00
1,000.00 1,000.00 133.33
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Valuation of Durable Assets
Pure Discount Bonds
Information needed for valuing pure discount bonds:
Time to maturity (T) = Maturity date - todays date
Face value (F)
Discount rate (r)
Tr
FPV
)1(
Present value of a pure discount bond at time 0:
0
0$
1
0$
2
0$
1T
F$
T
A bond that will make only one payment of principal and interest. Alsocalled a zero-coupon bond or a single-payment bond.
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Valuation of Durable AssetsLevel-Coupon Bonds
Information needed to value level-coupon bonds:
Coupon payment dates and time to maturity (T)
Coupon payment (C) per period and Face value (F)
Discount rate
TTr
F
rr
CPV
)1()1(
11
Value of a Level-coupon bond= PV of coupon payment annuity + PV of face value
0
C$
1
C$
2
C$
1T
FC $$
T
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Valuation of Durable Assets
Zero Growth Dividends Shares Assume that dividends will remain at the same level forever
rP
rrrP
Div
)1(
Div
)1(
Div
)1(
Div
0
3
3
2
2
1
10
321 DivDivDiv
Since future cash flows are constant, the value of a zero growth stockis the present value of a perpetuity:
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Valuation of Durable AssetsConstant Growth Dividends Shares
)1(DivDiv 01 g
Since future cash flows grow at a constant rate forever, the value of aconstant growth stock is the present value of a growing perpetuity:
grP
10
Div
Assume that dividends will grow at a constant rate, g, forever. i.e.
2
012 )1(Div)1(DivDiv gg
3
023 )1(Div)1(DivDiv gg .
.
.
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Delayed Differential Growth Dividends
Share
Year 0 1 2 3
Cash flow $1.50 $1.65 $1.82 dividend + P3
PV of cash flow 22.38$05.10.
05.182.13
P
81.32$)10.1(
22.38$82.1$
)10.1(
65.1$
)10.1(
50.1$320
P
= $1.82 + $38.22
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Valuation of Durable AssetsLoans
n P ri nci p I nt ere st A mo rt iz . P ay me nt
0 1000.00
1 750.00 100.00 250.00 350.00
2 500.00 75.00 250.00 325.00
3 250.00 50.00 250.00 300.00
4 0.00 25.00 250.00 275.00
Total 250.00 1000.00 1250.00
n P ri nci p I nte re st A mo rti z. P ay me nt
0 1000.00
1 1000.00 100.00 0.00 100.00
2 1000.00 100.00 0.00 100.00
3 1000.00 100.00 0.00 100.00
4 0.00 100.00 1000.00 1100.00
Total 400.00 1000.00 1400.00
n P ri nci p I nt ere st A mo rt iz. P ay me nt
0 1000.00
1 784.53 100.00 215.47 315.47
2 547.51 78.45 237.02 315.47
3 286.79 54.75 260.72 315.47
4 0.00 28.68 286.79 315.47
Total 261.88 1000.00 1261.88
There are three types: Discount Loans Pure Interest Loans Amortization Loans
1,000.00
10%
4
. .
1 1
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Valuation of Durable Assets
Arithmetic Growing Annuity (1) 1 1 2 21 3 31 4 11 1 1 11 1 11 2 11 3 11 1
1 2 21 3 31 4 31 2 21 1 11 .1st.Step:
1 1 11 1 11
1 1 1 1 1
1
1 1 .2nd.Step:
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Arithmetic Growing Annuity (2)Multiplyingbothsidesby1 , 1 1 21 2 31 3 31 3 21 2 11 1So1
1 21 2 1 2 31 3 21 3 21 2 31 2 11 1 21 1 11
1 1 2 1 3 1 2 1 1 11
1
1 2
1 3
1 1
1 1
11 11 2 11 3 11 1 11 1 1 1 11 11 2 11 3 11 1 1
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Then,
1 1 11 1 11
1 1 1 11 1 11
1 1 1 1
1 1 1 1 1 1
1
11 1
Then, 1 1 1 1 1
Arithmetic Growing Annuity (3)
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Arithmetic Growing Annuity (Ex.)
Calculate the cash flow of an arithmetic progression starting inS/.1,000 with an increase of S/.300 until the period 10. Then calculateits PV and FV at a 10% of minimum rate of return .
1,000; 1,300; 1,600; 1,900; 2,200; 2,500; 2,800; 3,100; 3,400; 3,700
1,0001 1.10
.10
300
.10
1 1.10
.10
10
1.10 13,011.97
1.10 33,749.70
FAS(10%,10)= 6. 144567
10/1.10^10
= 3.85543
r= 10.0%
T= 10.00 PV= 13,011.97
C= 1, 000. 00 FV= 33,749.70
G= 300.00
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Arithmetic Growing Annuity (Ex.) Calculate the cash flow of an geometric progression starting in S/.1,000
with an increase of 3.00% until the period 10. Then calculate its PV andFV at a 10% of minimum rate of return .
1,000; 1,300; 1,690;2,197; 2,856; 3,713; 4,827; 6,275; 8,157; 10,604
1,000
.10 0.03 1
1.03
1.10
6,883.74
1.10 17,854.66
1 2 3 4 5 6 7 8 9 10
1,000
1,300
1,690
2,197
2,856
3,713
4,827
6,275
8,157
10,604
r= 10. 0%
T= 10. 00 PV= 6,883.74
C= 1, 000 FV= 17, 854. 66
g= 3.0%
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Valuation of Durable Assets
Different Economic Life
Machinery
G
Machinery
H
Initial Cost, P US$.62,500 US$.77,000
Operating Anual Cost 15,000 21,000
Rescue Value, VS 8,000 10,000
Economic life, aos 4 6
Consider two machines for a continuous production process, that havethe following costs. Use an interest rate of 15%, and decide whichmachine might be kept on the firm.
0 4 8 12
0 6 12
77,000 21,0001 1.15
0.15
10,000
1.15
77,000
1.15
10,000
1.15 217,929.82
62,500 15,0001 1.15
0.15
8,000
1.15
62,500
1.15
8,000
1.15
62,500
1.15
8,0001.15
191,290.73
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It is the owning and operating cost per year of an asset over its entirelifespan.
It is useful when the NPV or IRR is not possible. It is often used whencomparing investment projects of unequal lifespans. We must chose thelower cost EAC or CAUE.
EAC is calculated by dividing the NPV of a project by the present value ofan annuity factor. Equivalently, the NPV of the project may be multipliedby the loan repayment factor.
We do not need mcm for appraise two project with different economiclife.
Formulae
1 1
1 1
1 1
1 1
/,, /,,
Valuation of Durable Assets
Annual Equivalent Cost
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If the life cycle project runs one or more times, the EquivalentAnnual Cost (CAUE) doesnt change.
Example: An asset has a cost of US$20,000, an annual operatingcost of US$8,000 and a useful life of 3 years. Find the CAUE ofone lifecycle. Use a discount rate of 22%.
20,0000.22
1 1.22 8,000 9,793.16 8,000 17,793.16
Find the CAUE for two lifecycles.
20,0000.22
1 1.22 20,000
0.22
1 1.221
1.22
8,000
17,793.16
Valuation of Durable Assets
Annual Equivalent Cost
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Example: An asset has a cost of US$20,000, an annual operating cost ofUS$8,000 and a useful life of 3 years. Find the CAUE of one lifecycle. Usea discount rate of 22%.
Valuation of Durable Assets
Annual Equivalent Cost - Excel
0 1 2 3
Cost 20,000
AnualOp. 8,000 8,000 8,000
Total 20,000 8,000 8,000 8,000
VNA@22% 36,338 CAUE@22% 17,793.16
CAUE= 17,793.16 FAS(22%,3) 2.042241421
FAS(22%,3)^1 0.489658074
22%,4:4 4 22%, 3,5
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Calculate the AEC from one machine with an initial cost of US$8,000and a salvage value of US$500 after 8 years. The annual operatingcosts (AOC) for the machine are estimated at a US$900 and theinterest rate is 20%.
8,000 /, 20%, 8 500 /,20%,8 900
8,000.2
1 1.2 500
.2
1.2 1 900
2,084.88 30.30 900 2,954.57
Valuation of Durable Assets
Annual Equivalent Cost
0 1 2 3 4 5 6 7 8
Cost 8,000
SalvageVa lue 500
Anual Op. 900 900 900 900 900 900 900 900
Total 8,000 900 900 900 900 900 900 900 400
VNA@20% 11,337.2 CAUE@20% 2,954.57
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When the project has an indefinite operating life (perpetuity) , we usecapitalized cost.
Steps:
1. Draw the Cash Flow Diagram
2. PV of all the non periodic expenses
3. Find the EAC from periodic expenses and annual costs series ofone life cycle
4. Divide the EAC by the interest rate.
Valuation of Durable Assets
The Capitalized Cost
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Calculate the capitalized cost of a project that has an initial investment of US$150,000 and an additional investment of US$50,000 after 10 years. Annualoperating costs are US$5,000 for the first 4 years and US$8,000 thereafter. Inaddition is expected to be a recurrent cost of over hold for US$15,000 every 13years. Assume that 15%
1 150,000 50,000
1.15 162,359.23 . 1
3 5,0001 1.15
.15 1.15
8,000
.15
1
1.15
1.15 14,274.89 30,493.51
44,768.40
2 3,000
.15
1
1.15
11,435.06 2
Mantainance Cost3 15,000.15
1.15 1 436.66
436.66 5,000
.15 2,911.11 33,333.33 36,244.44 3
1 2 3 210,038.74 1 44,768.40 2,911.11 210,038.74
The Capitalized Cost
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