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Finance and Derivatives: Theory and Practice Sébastien Bossu and Philippe Henrotte

Chapter 2 Investment decision criteria 


Chapter 2 Investment decision criteria

1 Rate of return 

The gross rate of return of an investment of cost or  price P and earnings or income E for the period  between t = 0 and t = T is:

E ROR = P 

For a financial security with price P0, final value PT and  income I:

PT − P0 + I ROR = P0

Sébastien Bossu & Philippe Henrotte, Finance and Derivatives: Theory and Practice. Copyright © Dunod, Paris, 2002. English translation published by John Wiley & Sons Ltd, 2006.

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Chapter 2 Investment decision criteria

2 Net present value 

 

Finance is essentially about analyzing future cash  flows Positive cash flows correspond to income Negative cash flows correspond to expenses

Sébastien Bossu & Philippe Henrotte, Finance and Derivatives: Theory and Practice. Copyright © Dunod, Paris, 2002. English translation published by John Wiley & Sons Ltd, 2006.

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Chapter 2 Investment decision criteria

2 Net present value (2) 

When considering an investment the financier always  starts with the table of future cash flows:

Time

t1

t2

Cash flow

F1

F2

Sébastien Bossu & Philippe Henrotte, Finance and Derivatives: Theory and Practice. Copyright © Dunod, Paris, 2002. English translation published by John Wiley & Sons Ltd, 2006.

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Chapter 2 Investment decision criteria

2 Net present value (3) 

The next step is to discount the cash flows and  calculate the present value of the investment as a  whole, which is simply the sum of each cash flow’s  present value: +∞

Fi PV = ∑ ti (1 + r ) i =1 F1 F2 PV = + + ... t1 t2 (1 + r ) (1 + r ) Sébastien Bossu & Philippe Henrotte, Finance and Derivatives: Theory and Practice. Copyright © Dunod, Paris, 2002. English translation published by John Wiley & Sons Ltd, 2006.

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Chapter 2 Investment decision criteria

2 Net present value (4) 

If  the  investment  cost  is  already  known,  the  net  present value (NPV) is defined as the present value  net of the initial cost: +∞

Fi NPV = −C0 + ∑ ti i =1 (1 + r ) F1 F2 = −C0 + + + ... t1 t2 (1 + r ) (1 + r ) Sébastien Bossu & Philippe Henrotte, Finance and Derivatives: Theory and Practice. Copyright © Dunod, Paris, 2002. English translation published by John Wiley & Sons Ltd, 2006.

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Chapter 2 Investment decision criteria

2 Net present value (5)  

There are then three cases: NPV > 0: The investment is profitable and may be  carried out. NPV < 0: The investment would be at a loss and  should be rejected. NPV = 0: The investment is neutral (theoretical case.)

Sébastien Bossu & Philippe Henrotte, Finance and Derivatives: Theory and Practice. Copyright © Dunod, Paris, 2002. English translation published by John Wiley & Sons Ltd, 2006.

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Chapter 2 Investment decision criteria

3 Internal rate of return 

The problem of selecting the appropriate discount  rate to compute the NPV is difficult and raises the  issue of the investor’s expected return. We  can  reverse  the  problem  and  calculate  instead  the  internal  rate  of  return  r  which  makes  the  NPV  equal  zero,  in  other  words  find  the  indifference  point  for the investor. In mathematical terms find r* such that:  +∞

−C0 + ∑ i =1

Fi

(1+ r)

ti

=0

Sébastien Bossu & Philippe Henrotte, Finance and Derivatives: Theory and Practice. Copyright © Dunod, Paris, 2002. English translation published by John Wiley & Sons Ltd, 2006.

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Chapter 2 Investment decision criteria

4 Price­Earnings Ratio 

Many accounting criteria are used in finance to  assess the suitability of an investment For instance the Price­Earnings Ratio measures the  wait time for a stockholder to get her money back  through earnings:

Price (per share) PER = Earnings (per share and per annum)

Sébastien Bossu & Philippe Henrotte, Finance and Derivatives: Theory and Practice. Copyright © Dunod, Paris, 2002. English translation published by John Wiley & Sons Ltd, 2006.

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