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Investment Decisions Present Value. Assessing investment opportunities Present Value & Net Present Value (NPV) Risk and Present Value Different types of investments To make an investment or not ? Choice between different investments Internal Rate of Return (IRR) Pay-back period (PBP)

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investment decisions present value
Investment DecisionsPresent Value
  • Assessing investment opportunities
  • Present Value & Net Present Value (NPV)
  • Risk and Present Value
  • Different types of investments
  • To make an investment or not ?
  • Choice between different investments
  • Internal Rate of Return (IRR)
  • Pay-back period (PBP)
  • Which method is most suited ?
assessing investment opportunities
Assessing Investment opportunities
  • Is it interesting to make an investment ?
  • Example
    • I can buy an house for 40.000 US$ ...
    • .. and sell the house after one year for 42.000 US$
  • Apparently the answer is ... YES it is interesting
    • I make a profit of 2.000 US$
  • BUT : I had an alternate investment possibility
    • to put the money on a saving account
      • with an interest rate of 10%
    • and make a profit of ... 4.000 US$
future value of money
Future Value of Money
  • The basic principle is that the Future Value of money is higherthan its Present Value
    • if C0is the amount today
    • and ifiis the market interest rate
    • we can calculate the future value of this amount after one year
    • FV1(C0) = C0.(1+i)
  • The Future Value of money is equal to
    • The initial amount
    • Plus the interest on this initial amount
future value of money1
Future Value of money
  • We can use the same principle for longer periods
  • We can calculate the Future Value of C0 after 2 years
    • FV2(C0) = C0.(1+i)2
    • be cautious : compounded interest
      • it does mean that we calculate the interests on the interests
  • or after ... n years

FVn(C0) = C0.(1+i)n

future value of money2
Future Value of money
  • Example 1
    • The Future Value of 40.000 US$
    • If the market interest rate is equal to 10%
    • After 4 years
    • FV4(40.000US$) = 40.000.(1+0,10)4 = 58.564 US$
  • Example 2
    • Calculate the Future Value of 1.200 MDong
    • If the market interest rate is equal to 18%
    • After 3 years
net future value
Net Future Value
  • We can now define the Net Future Value of an investment
  • It is equal to the difference between
    • The Future Cash flow generated by the investment
    • And the Future Value of the money invested in year 0
  • For an initial investment C0
    • If C1 is the Cash flow generated after one year
    • We can calculate the Net Future Value after 1 year

NFV1(C0) = C1 - C0.(1+i)

net future value1
Net Future Value
  • The Net Future Value
    • Can be positive
      • it is better to make the investment than to put the money on a saving account
    • Can be negative
      • do not make this investment
      • put your money on a saving account
  • Example
    • calculate the NFV of the house
      • I could buy for 40.000 US$ and
      • Sell after one year for 42.000 US$
      • i=10%
    • NFV1(house) = 42.000 - 40.000.(1+0,1) = - 2.000 US$
present value of money
Present Value of money
  • We can do the reasoning the other way round and calculate the Present Value of future amounts of money
  • The basic principle is that the Present Value of money is lower than its Future Value
    • If C1is the amount in one year
    • And if i is the market interest rate
    • We can calculate the Present Value of C1

PV(C1) = C1 / (1+i)

present value of money1
Present Value of money
  • We can use the same principle for longer periods
  • We can calculate the Present Value of a Cash flow C2 within 2 years
    • PV(C2) = C2 / (1+i)2
  • ... or the PV of a Cash flow Cn after n years
    • PV(Cn) = Cn / (1+i)n
  • The interest rate used to calculate the PV is called the discount rate
net present value
Net Present Value
  • We can now define the Net Present Value of an investment
  • It is equal to the difference between
    • The Present Value of the Cash flow generated by the investment
    • The initial amount of money invested
  • For the initial investment C0
    • If C1 is the Cash flow generated after one year
    • We can calculate the Net Present Value

NPV = C1 / (1+i) - C0

net present value1
Net Present Value
  • The Net Present Value
    • can be positive
      • it is better to make the investment than to put the money on a saving account
    • can be negative
      • do not make this investment
      • put your money on a saving account : you will earn more
net present value2
Net Present Value
  • We can also extend the calculation to many periods and many Cash flows
  • For the initial investment C0
    • IfC1is the Cash flow generated after one year, C2after 2 years, ... Cj after j years
    • we can calculate the Net Present Value

NPV = C1 / (1+i) + C2 / (1+i)2 + C3 / (1+i)3 + . . . + Cj / (1+i)j + ... - C0

net present value3
Net Present Value
  • Example : Calculate the Net Present Value of
    • an investment to buy an house for 40.000 US$ at t = 0
    • generating the following rents
      • 3.200 US$ at t = 1
      • 3.700 US$ at t = 2
      • 3.850 US$ at t = 3
      • 4.100 US$ at t = 4
      • 5.000 US$ at t = 5
    • and sold for 57.500 US $ at t = 6
    • if the discount rate i = 9%
  • Do you buy the house ?
present value special cases
Present Value Special Cases
  • It can be proved that the Present Value of an infinite series of constant Cash flows (C= C1 = C2 = C3 = ...) is equal to this annual Cash flow divided by the discount rate

PV = C / i

present value special cases gordon shapiro formula
Present Value Special Cases(Gordon-Shapiro formula)
  • The Present Value of an infinite series of Cash flows growing at an annual constant rate can also be calculated
    • the Cash flow of year 1, C1, is equal to C
    • the growth rate is g
      • C2 = C.(1+g)
      • C3 = C.(1+g)2
      • C4 = C.(1+g)3
      • . . .

PV = C / (i – g)

risk and present value
Risk and Present Value
  • Until now we used as discount rate the market interest rate (i)
    • This rate is basically the “risk free” interest rate
      • interest rate for Government debt
  • But the investments we will analyze are not “risk free”
    • Most future Cash flows are uncertain
    • We have to consider the risks related to the future Cash flows
  • It is logical to use an higher discount rate for an investment in a risky project
    • There is a risk to achieve lower Cash flows than expected or even to lose all the Cash flows
    • This higher risk must be balanced by an higher discount rate (higher return is needed to compensatepossible losses)
risk and present value1
Risk and Present Value
  • So to calculate the NPV of a risky project it is logical to use an higher discount rate than the “risk free” interest rate
    • r > i
  • If the future Cash flows are absolutely safe then the discount rate can be the “risk free” interest rate
  • The higher the risk the higher the discount rate
    • A more risky dollar within one year is worth less than a safer dollar within one year
risk and cost of capital
Risk and Cost of capital
  • For each company or even for each project there is a specific discount rate (Cost of Capital)
    • It depends from the risk associated to the company or to the project
  • The difference between the discount rate of a project and the “risk free” interest rate is called the risk premium
how high is the risk premium
How high is the risk premium ?
  • It can be observed on the financial markets
    • “All shares” risk premium
      • 2% to 4% depending on the period of time
    • Specific company risk premium
      • varies from industry to industry
      • inside the industry varies from company to company
      • between 1% and . . . 20% ... and more
  • Each specific project has its own risk premium
    • Basically the risk premium of the company
    • To be be increased if the risk is higher than average
      • high risk of failure (research, oil exploration)
    • To be lowered if the risk is lower than average or for strategic reasons
      • consolidation of position (market share, eliminate new entrant)
      • long-term vision
to make an investment or not
To make an investment or not ?
  • The decision to make or not to make an investment is mainly a financial one . . .
    • The investment must bring a return
      • NPV > 0
    • The company must be able to finance the project
      • existing cash
      • new debt
      • paid-in capital increase
    • There will always be money to finance a sound project
to make an investment or not1
To make an investment or not ?
  • other aspects must considered with a valuable financial impact

. . . or not

  • Strategy
    • Opportunities and . . . missed opportunities
    • Barriers for new entrants
  • Quality
  • Image
    • Location
    • Visibility or presence on the market
  • Safety
  • Regulations
    • Environment, etc.
  • Social aspects
    • Working conditions
    • Loyalty of employees and management
to make an investment or not2
To make an investment or not ?
  • The big risk is that other criteria . . .
  • . . . may lead to decide to make unprofitable or poorly profitable investments
  • It can become dangerous if it happens often or for big amounts
    • “the Ego syndrome”
    • Sanction by the market or by the shareholders
choice between different investments
Choice between different investments
  • In most cases there is a choice to do between different projects
    • different new products to launch
    • different new locations for a new factory
    • different new machines for the same process
  • The choice must be based on facts and not on impressions
    • avoid decision criteria like :
      • “I feel that . . .”
      • “Believe my experience . . .”
  • The best fact is a serious financial assessment
choice between different investments1
Choice between different investments
  • Different types of choice :
    • Mutually exclusive investments
      • different solutions for the same problem
      • machine 1 … or machine 2 … or machine 3
    • Ranking of different opportunities
      • they can be done simultaneously
      • the risks are similar
      • there is enough money to do more than one project
      • but which one is the most profitable ?
    • To make or not to make small capex proposed by the production manager
mutually exclusive investments
Mutually exclusive investments
  • The company has the choice between different solutions to solve one problem
  • There is no budget constraint
  • But you want to choose the best solution
    • Depending on the Cost of Capital of the company

 Use tne NPV of each project and choose the highest NPV

saigon hotel an example of investment choice
Saigon hotel : an example of investment choice
  • To renovate the 130 rooms there are 3 alternatives
    • « Light Solution »
      • Capex of 3.000 US$/room (total 0,39 Mio US$)
      • Same amount to be reinvested every 5 years
      • Unit rate increase of 6 US$ (from 80 US$)
      • No change in occupancy : 30.000 nights/year
    • « Medium Solution »
      • Capex of 20.000 US$/room + 0,4 Mio US$ for lobby (total 3 Mio US$)
      • Valid for 10 years
      • Unit rate increase of 12 US$ (from US$)
      • Higher occupancy : 33.000 nights/year
        • Additional margin per night 72 US$ (60 initial + 12 unit rate increase)
    • « Heavy Solution »
      • Capex of 30.000 US$/room + 2,1 Mio US$ (lobby & pool) (6 Mio US$)
      • Valid for 10 years + Terminal value of 1 Mio US$ (pool)
      • Luxury hotel : unit rate increase of 24 US$
      • Higher occupancy : 33.000 nights/year
saigon hotel the decision
Saigon Hotel : the decision
  • By using the NPV method which alternative will you choose ?
    • if the Cost of capital is 10 % ?
    • if the business is more risky and the Cost of capital is 15 % ?
    • if the business is less risky and the Cost of capital is 8 % ?
  • Calculation of NPV (Excel formula NPV)
    • NPV(discount rate;data)
    • Be careful
      • In the formula the 1st data is after 12 months
      • The data of Y1 should not be discounted
    • The data of Y0 must be out of the formula
    • NPV = -C0 + NPV(discount rate;C1:C10)

DCFsaigonhotel.xls - NPV1!A1

internal rate of return irr
Internal rate of return (IRR)
  • NPV is useful but
    • Uncomplete if you want to rank different projects in competition when your budget is limited
    • The NPV says : GO or DO NOT GO (NPV>0)
    • The NPV says : This project gives the highest result for each Cost of Capital independently of the size
  • But you do not know which project gives the best ROCE
  • Introducing the Internal Rate of Return (IRR)
  • It is the value of the Cost of Capital bringing the NPV of the project to exactly zero
  • 0 = C1/(1+IRR) + C2/(1+IRR)2 + ... + Cj/(1+IRR)j + ... - C0
internal rate of return irr1
Internal rate of return (IRR)
  • How to calculate the IRR ?
  • Iterative process
    • is it higher than 0 % and lower than 20% ?
    • is it higher than 1% . . . 2% . . . 3% . . . ?
    • is it lower than 19% . . . 18% . . . 17% . . . ?
  • On most calculators a standard formula
  • Excel
    • Goal seek : NPV = 0
    • function IRR
saigon hotel irr calculation
Saigon Hotel : IRR calculation

DCFsaigonhotel.xls - IRR!A1

use of irr to decide on investments
Use of IRR to decide on investments
  • All projects with IRR higher than Cost of Capital are financially interesting
  • If different projects are in competition and if the budget is limited, the most interesting projects are the projects with the highest IRR’s
    • They can be ranked
  • All projects with IRR lower than the Cost of Capital are financially uninteresting

if IRR < r : DO NOT INVEST IN THE PROJECT

pay back period
Pay-back period
  • The Pay Back Period is the number of years necessary to have a positive NPV for an investment
    • The PBP is the lowest value of N so that

C1/(1+r) + C2/(1+r)2 + ... + CN/(1+r)N - C0 > 0

  • The Pay Back Period is a very useful tool to decide rapidly if it is worth to do a small investment proposed by a local manager
    • If Pay Back Period is short (max 4 years) : OK
conclusions of the lesson
Conclusions of the Lesson
  • The Future Value of money is equal to
    • The initial amount
    • Plus the compounded interest on this initial amount
  • The Present Value of a future Cash Flow is calculated using a discount rate r
    • PV(Cn) = Cn / (1+r)n
  • The Net Present Value is equal to
    • The PV of the Cash Flows generated by the investment
    • Less the initial amount of money invested
conclusions of the lesson1
Conclusions of the Lesson
  • Investments must be decided on the base of
    • Financial criteria
    • If justified other criteria
      • Long term Strategy
      • Quality (not always with direct financial return)
      • Safety
      • Regulations (environment, social protection, etc.)
    • Choice must be based in any case on factsnot on impressions
  • It is logical to use an higher discount rate for an investment in a more risky project
    • The difference between the discount rate of a project and the “risk free” interest rate is called the risk premium
    • The risk related to one project can vary from person to person
  • The lower the discount rate the more interesting are the capital intensive projects
conclusions of the lesson which method is most suited
Conclusions of the LessonWhich method is most suited ?
  • To decide not to invest in a project
    • NPV < 0
    • IRR < r
  • To make a choice between mutually exclusive projects
    • highest NPV
  • To make a ranking of competing projects if the budget is limited
    • Ranking by IRR (1st = higher IRR)
  • To decide on small marginal capex
    • Short Pay-Back Period (4 years)
  • Never forget the residual value of the investments !
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