Esc-Clermont Sup de Co

2nd years, 1st semester

Course: Corporate finance

Teacher: André Cabannes

 

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Final exam

December, 2008

 

 

20 questions, each worth 5 points. Write your answers on this document in the blank space below each question.

 

 

Question 1: Your firm has, in its balance sheet, some fixed asset the net value of which is 100 (raw value 600 and cumulated depreciation 500). You sell this asset for 150 in cash. Explain the impact of this transaction on the asset side and the liability side of you balance sheet.

 

 

FA decrease by                                    100

Cash increases by                                 150

Total assets increase by                          50

 

Retained profit increases by                    50

Total liabilities increase by                       50

 

 

 

 

Question 2: At the beginning of the year, the inventories were 230. During the year, the purchases were 550. And at the end of the year, the inventories were 180. What was the cost of goods sold?

 

 

600

 

 

 

Question 3: Explain what is a “non cash yearly expenditure”. Why are they important to get an accurate view of the result of the year?

 

It is a decrease, during the accounting period, of the value of some of the assets of the firm. Typically it is the “wearing out” of Fixed Assets. It can also be provisions for bad client paper. It does not correspond to any cash outlay, but it must be recorded in the IS as an expenditure. It is a non cash expenditure.

 

Remember that double-entry accounting is a “value accounting” system, as opposed to single-entry accounting which is only concerned with cash.

 

 

 

Question 4: The ROCE is defined as

 

[net result + interest charges + income taxes] / [average capital employed]

 

 

while the ROE is defined as

 

[net result] / [average net worth]

 

 

Consider the following year end documents

 

 

 

What is the ROCE? And what is the ROE?

 

 

ROCE = 70 / [ ( 520 + 450 ) / 2 ] = 14,4%

 

ROE   = 47 / [ ( 370 + 350 ) / 2 ]  = 13,1%

 

 

Question 5: Explain what we mean by “the ROCE measures the performance of the firm, disregarding its capital structure”.

 

The ROCE looks at the value generated from operations (before interest and taxes) by the capital employed.

 

Whether the structure of the capital employed is made of much capital and little debt, or on the contrary of much debt and little capital (i.e. a high debt leverage), does not change the total capital employed. And on the numerator side, the result before interest and taxes is not affected by the structure of the capital employed either, because only financial charges and therefore taxes change.

 

So the ROCE is indeed a measure of the value generation capacity of the capital employed disregarding how they are constructed.

 

 

 

Question 6: Establish the cash flow statement of the firm the year documents of which are given above in question 4.

 

 

See course notes lesson 4a

 

 

 

 

Question 7: You have in your pocket today (date t) a security promising to pay you a certain sum X in the future at date T, signed by the issuer. What are the three factors affecting the value of this security today?

 

 

The face value X (the sum written on the security)

The length of time (T – t)

The creditworthiness of the issuer (i.e. the risk that he does not pay you)

 

 

 

 

Question 8: What are the main concepts added by Finance onto Accounting?

 

The role of time, and the role of risk.

 

 

 

Why does the Modern Theory of Finance make use of probability theory?

 

There are circumstances when the future payments we expect are not sure figures but figures which may vary. We then use the modelling framework of probability theory to represent this variable situation: the future sum we shall receive will be the outcome of a random variable in the experiment “wait until payment”.

 

 

 

 

Question 9: We can buy today, in the stock market, a security S for a price PS = 35 euros. We know, from a study of the past behaviour of S, that its value in one year will be a random value X, with the following characteristics:

 

Possible future value (in euros)

25

30

35

40

45

50

55

 

 

 

 

 

 

 

 

Probability

5%

10%

15%

40%

15%

10%

5%

 

What is the expected value of X? (show your calculations)

 

 

Compute the weighted average of the possible values with their probabilities as weights.

 

(25 x 5% )+ (30 x 10%) + … + (55 x 5%)  =  40 euros

 

 

You may also notice that the calculations being “symmetrical around 40” (in the sense that the same weights are put on pairs of figures, each pair averaging 40), this central figure of 40 must be the result, because all the weights add up to 1.

 

 

 

 

Question 10: What is the expected profitability of S?

 

The profitability of S is defined as RS  = (X – P) / P

 

RS is a random variable.

 

E(RS) = (40 – 35) / 35 = 14,3%

 

 

 

 

Question 11: What is the standard deviation of X? And what is the risk of S?

 

The standard deviation of a random variable is the expected value of the squared deviation of the random variable around its mean.

 

Standard deviation of X = sX = 7,07 euros

 

The risk of S is defined as the standard deviation of RS

 

It is 7,07 / 35 = 20,2%

 

 

 

 

Question 12: There is available in the stock market a security T for a price PT. The value of T in one year will be a random value Y, with the following characteristics:

 

 

 

Possible future value

75

90

105

120

135

150

165

 

 

 

 

 

 

 

 

Probability

2%

6%

18%

48%

18%

6%

2%

 

 

Is T more or less risky than S?

 

We compute E(Y) and sY.

 

E(Y) = 120 euros

sY = 16,43 euros

 

Then we observe that Y is relatively less variable around it mean than is X

 

sY / E(Y) = 0,137  while  sX / E(X) = 0,177 

 

so T is less risky than S.

 

 

 

What can we already say about the price of T?

 

Since T is less risky than S, T will have less profitability than S.

 

The profitability of S is (40 – 35)/35, which is also (120 – 105)/105.

 

So T has to be worth more than 105 euros on a rational market with no arbitrage possibilities.

 

 

 

 

Question 13: We are considering making the following physical investment in our firm

 

 

year

0

1

2

3

 

 

 

 

 

CF (millions of euros)

-80

40

40

40

 

 

What are the two fundamental rates attached to this investment?

 

 

The opportunity cost of capital

 

The IRR

 

 

 

 

Question 14: Suppose that this investment belongs to the same class of risk as the security S of question 9 above. Is this investment worth making? (show your calculations)

 

If this investment belongs to the same class of risk as the security S, then its opportunity cost of capital is the expected profitability of S, that is 14,286% (if we want to be – overly – precise).

 

Then the PV of the first cash flow in one year is 35 million euros.

The PV of the second cash flow in two years is 30,63 million euros.

And the PV of the third cash flow in three years is 26,80 millon euros.

 

In other words, the three cash flows we expect to receive are worth today 92,42 million euros.

 

If we can create this project for 80 million euros, it is a good deal.

 

 

 

 

Question 15: What is the IRR of the investment of question 13?

 

We know that the IRR must be more than 14,3%

 

We try calculations with 20%, and we still a positive NPV of 4,3 million euros.

 

The we try a discounting rate of 25%, and we get NPV = -1,92 million euros.

 

Then we may do a linear interpolation between 20% and 25%,

 

 

 

x satisfies the equation

 

x / 4,3  = ( 5 – x ) / 1,92

 

this yields x = 3,46

 

and therefore an approximate IRR of 23,46%

 

The exact result is 23,37%

 

 

 

Question 16: We have a big firm making some widgets. We are considering buying 100% of another firm, which will help us produce more widgets more efficiently. Why the standalone cash flows of the projected acquisition are not what is important to us in evaluating the price we should be willing to pay?

 

 

If we buy the entire firm and it will help us produce widget more efficiently, the new firm will change (for the better) our cash flows, independently of the standalone cash flows of the new firm.

 

It is like the key to a treasure trunk (like Skype was for eBay). Then the standalone cash flows of the new firm are irrelevant. What matters is what extra cash flows it will release for us.

 

 

 

 

Question 17: We buy today for $1000 a 5year 6% bond (of the most basic type, paying yearly coupons). What is the series of cash flows we are expecting in the future?

 

 

year

1

2

3

4

5

 

 

 

 

 

 

cash flow

60

60

60

60

1060

 

 

 

 

Question 18: Two years have passed (and we have pocketed two coupon payments), and now we want to sell this bond. The current rate for 3year bonds with the same ratings is 4%. What is the value of our bond in the secondary market?

 

 

new discount rate

 

 

 

 

4%

0

1

2

3

 

 

 

 

 

cash flows

 

60

60

1060

 

 

 

 

 

yearly PV

 

57,6923

55,4734

942,336

 

 

 

 

 

total PV

1055,501821

 

 

 

 

 

Our second hand bond is worth 1055,5 dollars.

 

 

 

Question 19: What is a junk bond?

 

 

It is a bond with a very high risk of failure of the issuer, but also a very high expected profitability (even taking into account the risk of the issuer).

 

 

 

 

 

Question 20: Suggest another way than probability theory to assign present values to promises of future payments. (Any suggestion will be worth a few points. Thoughtful suggestions will be worth 5 points.)