Investment decisions present value
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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


Scenarios analysis us

Scenarios analysis (US$)


Saigon hotel cash flow analysis 000 us

Saigon Hotel : Cash flow analysis (000 US$)

DCFsaigonhotel.xls - DATA!A1


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


Saigon hotel the decision investment table 000 us

Saigon Hotel : the decisionInvestment Table (000 US$)

DCFsaigonhotel.xls - NPV2!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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