FINANCIAL ANALYSIS
Academic
year: 20102011
Professor:
Andrι Cabannes
Duration: 1
hour 30
Books and
class notes forbidden
Computers
forbidden
Hand held
calculators (including scientific ones) allowed
Write your name in the
box :
Financial Analysis
FINAL EXAMINATION with answers
2nd semester
Write your answers in
the blank space below each question.
Question 1: Explain the difference between
Accounting and Finance.
The main difference concerns the role
of time. Accounting is a technique of recording transactions on an ongoing basis. When a sale is paid with an IOU, the IOU
is recorded at its face value, even though it corresponds to cash which will
arrive at a future date.
In finance a promise, signed at time
t, to pay a sum of money M at a future date T, has a value today (at time t)
which is less than M. To calculate the present value of the promise, one must
take into account external market conditions, the risk of the promise not to be
paid, etc.
See course for more explanations.
Question 2: Suppose agent A is considering
making an investment. The investment would be the purchase of an activity. If A
does not buy the activity, the future cash flows of A will be
today 
in 1 year 
in 2 years 
in 3 years 
in 4 years 
etc. 







50 
60 
70 
80 
etc. 
And if the activity is not bought by A, it will have, as a standalone, the following cash
flows:

5 
5 
0 
0 
etc. 
(that is, the activity
will have only two non zero future cash flows)
Suppose if A buys the activity, the future cash
flows of A will become

60 
70 
70 
80 
etc. 
(that is, in year 3
and after, the cash flows will be the same as without the purchase).
Would it be a physical investment or a
financial investment? Explain.
We observe that the cash flows for
A, in the case A buys the activity, will be higher than the sum of [the cash
flows of A without the activity] + [the cash flows of the activity as a
standalone].
We explained in class that this is
the characteristic of physical investments. That is, there is a synergy
between A and the purchased activity which creates
extra cash flows for A, higher than those of the activity if it staid a
standalone.
Question 3: Explain why in financial
investments NPV is zero.
On the other hand, when the cash
flows for [A + the activity] are simply the sum of [the cash flows of A without
the activity] + [the cash flows of the activity as a standalone] we are talking
of a financial investment.
In that case the seller to A of the
activity will sell it at a price equal to [the present value of the future cash
flows of the activity as a standalone,] therefore for A it will be a purchase
with NPV = 0.
Question 4: A security S will have a unique
expected cash flow in one year of 250. Its price today is 185.
If you buy it, what is your expected
profitability?
(250 185) / 185 = 35,1%
Question 5: Consider this wheel of chance n°1
What is the expected payoff?
Each of the five sectors, paying a
sum of money between 90 and 130, has the same probability 72°/360°, that is
1/5. So the calculation of the expected payoff is
What is the standard deviation of the payoff?
If we call X the random payoff, the
standard deviation of X is the square root of the variance of X. And the
variance of X is given by the formula
This yields var(X)
= 200, and standard deviation of X = 14,1
Question 6: Suppose you play the following
game:
What is your expected profitability?
Our expected payoff is 110.
So our expected profitability is
(110 95) / 95 = 15,8%
Question 7: Consider the wheel of chance n°2
What is the expected payoff?
The payoffs have changed, but the
probabilities are the same. The new calculation is
So as we see the mean hasnt
changed.
What is the standard deviation of the payoff?
The new variance is 800, and the new
standard deviation 28,3.
Question 8: Suppose the game with wheel n°2
also has an entry ticket of 95. Between the two games, n°1 and n°2, what would
an investor prefer? Explain.
The two games offer the same
expected payoff, but with different risk.
As we explained in class, investors
are risk averse (for reasons linked to the SaintPetersburg
paradox, explained in 1738 by Daniel Bernoulli), so they will prefer game
n°1.
Question 9: Explain why a gambler would not
necessarily have the same attitude as the investor.
The
For this reason, youd normally
prefer to have 1000 for sure, than the result of a game where youll win 950
with probability 50% and 1050 with probability 50%.
But there are situations where the
extra 50, which you may win on top of the 1000, have more utility than the
other 50 which you may lose from 1000.
It is the situation of gamblers,
which you see in gambling spots every morning scratching lotos,
rapidos, and other astros.
They prefer the situation where they will lose most certainly their 10 of bets
but may have the remote possibility of winning 1 000 000
(yet their net expected gain is close to 10€), to just keeping their 10.
Question 10: Consider the following investment
(figures in millions of euros)

year 0 
year 1 
year 2 
year 3 





cash flows 
100 
50 
50 
50 
What is the NPV if the opportunity cost of
capital is 10%?
We have to compute the present value
of each future cash flow C_{n}, using the
formula
where r is the discounting
rate (here 10%).

year 0 
year 1 
year 2 
year 3 





cash flows 
100 
50 
50 
50 





present values 
100 
45,45 
41,32 
37,57 





sum 
24,34 



(including 100) 




So the NPV is 24,34
million of euros.
Question 11: What is the IRR of the investment
of question 10? (display your calculations)
One way to solve for the IRR is to
try various discounting rates
For r = 10%, the NPV is 24,24
For r = 20%, the NPV is 5,32
For r = 30%, the NPV is 9,19
So the IRR is between 20% and 30%.
Some further trials and errors (or a
linear interpolation) gives
IRR equals (approximately) 23,4%.
Question 12: Consider the following two
investments (figures in millions of euros)
Investment 1 
year 0 
year 1 
year 2 
year 3 





cash flows 
100 
50 
50 
50 
and
Investment 2 
year 0 
year 1 
year 2 
year 3 





cash flows 
100 
0 
150 
0 
Compare them using two different methods of
evaluation of investments.
With the payback period, investment
2 is the preferred one, because you get your money back faster.
But with the standard discounting
method, computing the NPV, investment 1 is always the best (no matter which
discounting rate you use) because the 50 gotten year 1
more than counterbalance the 50 gotten only year 3.