vietnam master in management – hcmc 2003 investment decisions investment decisions present value...

Vietnam Master in Management – HCMC 2003Investment decisions

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

• 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

• The basic principle is that the Future Value of money is higher than its Present Value if C0 is the amount today and if i is 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 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 yearsFVn(C0) = C0.(1+i)n


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

• 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 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

• 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 C1 is 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 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

• 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 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 Value

• We can also extend the calculation to many periods and many Cash flows

• For the initial investment C0

If C1 is the Cash flow generated after one year, C2 after 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 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

• 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)

• 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

• 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 compensate possible losses)


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

• 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 ?

• 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 ?

• 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



• 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



• 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

• 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 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

• 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

• 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$)

Scenario CapexY1

CapexY6

Yearly impact

increase rate

Yearly impact

increase occupan

cy

Terminal Value

Light 390.000 390.000 180.000(30.000 n)(6 US$/n)

0 0

Medium 3.000.000

0 396.000(33.000 n)(12 US$/n)

180.000(3.000 n)

(60 US$/n)

0

Heavy 6.000.000

0 792.000(33.000 n)(24 US$/n)

180.000(3.000 n)

(60 US$/n)

1.000.000

(Pool)


Saigon Hotel : Cash flow analysis (000 US$)

DCFsaigonhotel.xls - DATA!A1

Y0 Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10

LightCapex -390 -390 Higher rate 180 180 180 180 180 180 180 180 180 180Higher occupancyTerminal Value 0Cash flow -390 180 180 180 180 -210 180 180 180 180 180

MediumCapex -3.000 Higher rate 396 396 396 396 396 396 396 396 396 396Higher occupancy 180 180 180 180 180 180 180 180 180 180Terminal Value 0Cash flow -3.000 576 576 576 576 576 576 576 576 576 576

HeavyCapex -6.000 Higher rate 792 792 792 792 792 792 792 792 792 792Higher occupancy 180 180 180 180 180 180 180 180 180 180Terminal Value 1.000Cash flow -6.000 972 972 972 972 972 972 972 972 972 1.972


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 decisionInvestment Table (000 US$)

Scenario r = 8 % r = 10 % r = 15 %

Light 552 474 319

Medium 865 539 -109

Heavy 985 358 -875

DCFsaigonhotel.xls - NPV2!A1


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 zero0 = C1/(1+IRR) + C2/(1+IRR)2 + ... + Cj/(1+IRR)j + ... - C0


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

DCFsaigonhotel.xls - IRR!A1

Scenario IRR NPVr=8%

NPVr=10%

NPVr=15%

Light 36,4% 552 474 319

Medium 14,0% 865 539 -109

Heavy 11,3% 985 358 -875


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

• 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

• 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 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 facts not 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 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 !

vietnam master in management – hcmc 2003 investment decisions investment decisions present value...

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