1 / 38

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)

Pat_Xavi
Télécharger la présentation

Investment Decisions Present Value

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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 !

More Related