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Investment Decisions Present Value

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

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  1. 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 ?

  2. 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$

  3. 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

  4. 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

  5. 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

  6. 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)

  7. 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$

  8. 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)

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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 ?

  14. 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

  15. 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)

  16. 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)

  17. 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

  18. 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

  19. 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

  20. 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

  21. 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

  22. 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

  23. 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

  24. 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

  25. 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

  26. 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

  27. Scenarios analysis (US$)

  28. Saigon Hotel : Cash flow analysis (000 US$) DCFsaigonhotel.xls - DATA!A1

  29. 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

  30. Saigon Hotel : the decisionInvestment Table (000 US$) DCFsaigonhotel.xls - NPV2!A1

  31. 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

  32. 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

  33. Saigon Hotel : IRR calculation DCFsaigonhotel.xls - IRR!A1

  34. 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

  35. 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

  36. 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

  37. 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

  38. 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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