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.
2
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.
3
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.
4
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.
5
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.
6
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.
7
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.
8
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.
9