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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 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 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 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 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 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
- 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 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 compensatepossible 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

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 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

- 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

Saigon Hotel : Cash flow analysis (000 US$)

DCFsaigonhotel.xls - DATA!A1

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$)

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 zero

- 0 = 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

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 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 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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