Final Assignment

414 – CFIN – Corporate Finance

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Antoine COMPS

ISEG – ISM MBA Program

December 28, 2010


Final Assignment

David Pollon

Word Count : 3600


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Table of Contents

I- Capital Asset Financing Model....................................................................................p. 2

Question a...............................................................................................................................p. 3

Question b..............................................................................................................................p. 5

Question c...............................................................................................................................p. 6

Question d..............................................................................................................................p. 8

II- Weighted Average Cost of Capital.......................................................................p. 10

Question a.............................................................................................................................p. 10

Question b.............................................................................................................................p. 11

Question c.............................................................................................................................p. 12

Question d.............................................................................................................................p. 13

III- Debt and Equity- Financing.......................................................................................p. 15

Question a.............................................................................................................................p. 15

Question b.............................................................................................................................p. 16

Question c.............................................................................................................................p. 17


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Question d.............................................................................................................................p. 18

IV- Cash Management...........................................................................................................p. 21

Question a.............................................................................................................................p. 21

Question b............................................................................................................................p. 22

Question c.............................................................................................................................p. 23

Question d............................................................................................................................p. 24

I- Capital Asset Financing Model

Stock A: Beta= 0.9 Stock B: Return= 8% Beta=1

Stock C: Return = 9.2% Stock D: Return= 14% Beta= 2.5

a- Calculate the Required Return of Stock A

To calculate the required return of stock A, we need to know first the value of Km and Krf.

Km:

We know that when Beta = 1, the required return (Kr) is equal to the required return of the

market (Km).

Stock B has a Beta of 1 and a required return of 8%. As a consequence, we can deduct that

the market required return is equal to stock B required return, that is, 8%.


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Km = 8%

Krf:

To figure out the Risk Free rate (Krf), we are going to use stock D which has a required return

(Kr) of 14% and a Beta of 2.5

Kr = Krf + Beta (Km – Krf)

14% = Krf + 2.5 (8% - Krf)

0.14 = Krf + 2.5 (0.08 – Krf)

0.14 = Krf + 0.2 – 2.5 Krf

Krf – 2.5 Krf = 0.14 – 0.2

- 1.5 Krf = - 0.06

Krf = −0.06−1.5

Krf = 0.04

The Risk Free rate is therefore equal to 4%

We are now able to calculate the Required Return (Kr) for the Stock A.

Required Return of Stock A:



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Kr = 4% + 0.9 (8% - 4%)

Kr = 0.04 + 0.9 (0.08 – 0.04)

Kr = 0.04 + 0.072 – 0.036

Kr= 0.112 – 0.036

Kr = 0.076

The Required return for Stock A is 0.072, that is, 7.6%

b- Calculate the Beta of Stock C

We know that the Required return for Stock C is 9.2%.


9.2% = 4% + Beta (8% - 4%)

0.092 = 0.04 + Beta (0.08 – 0.04)

0.092 = 0.04 + Beta (0.04)


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Beta (0.04) = 0.092 – 0.04

Beta (0.04) = 0.052

Beta = 0.0520.04

Beta = 1.3

The Beta of Stock C is equal to 1.3

c- Using only Stock A and D, calculate the percentage of each stock you would need to

create a portfolio that has a Beta of 1.0. Calculate the required return of this portfolio.

We will call x the percentage of Stock A in the portfolio.

We will call y the percentage of Stock D in the portfolio.

Beta Portfolio = x (Beta A) + y (Beta 2)


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1.0 = x0.9 + y2.5

1.0 = 0.9x + 2.5y

We know that: x + y = 100% or Beta 1

x + y = 1.0

x = 1 – y

We are now able to figure out y:

1.0 = 0.9x + 2.5y

1.0 = 0.9 (1 – y) + 2.5y

1.0 = 0.9 – 0.9y + 2.5y

1.0 = 0.9 + 1.6y

1.6y = 1- 0.9

1.6y = 0.1

y = 0.11.6

y = 0.0625

The percentage of Stock D into the portfolio has to be equal to 0.0625, that is, 6.25%


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Determination of x:

x = 1 – y

x = 1 – 0.0625

x = 0.9375

The percentage of Stock A into the portfolio has to be equal to 0.9375, that is, 93.75%

Solution: In order to obtain a portfolio that has a Beta of 1, we should purchase 6.25% of

Stock D with a Beta of 2.5 and 93.75% of Stock A with a Beta of 0.9.

Required return of the portfolio:

K Portfolio = % of Stock A x required return of stock A + % of Stock D x required return of Stock D

K Portfolio = 93.75% x 7.6% + 6.25% x 14%

K Portfolio = 0.9375 x 0.076 + 0.0625 x 0.14

K Portfolio = 0.07125 + 0.00875

K Portfolio = 0.08%

The required Return of this portfolio is logically of 8%.


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d- Explain each element of the CAPM Formula and answer the Following questions.


Kr : It Represent the required return for Shareholders

Krf: It is the risk Free Rate of the Investment

Beta: It is the Representation of the relative risk related to market

Km: It is the average return of the market

What does Beta mean and how is it determined?

The Beta is a kind of index that measures the volatility of a stock or portfolio in order to

know if its risk is either higher or lower than the market risk average. In other words, the

Beta tells how risky is a stock or portfolio in comparison to the market. The beta is

determined based on the degree of volatility of the portfolio or stock compared to its

market, that is, that is the degree with which its performance follows market trends. The

CAPM formula can help to determine the Beta of a specific Stock or portfolio.

Which types of Stocks have Higher or lower Beta

A stock has a high beta when its volatility is high and a lower beta when it has a lower

volatility. The rule is that a stock having a Beta superior to 1 is more volatile than the market

average and thus, is potentially riskier. On the other hand, it would probably make more

benefits than the market average in the case of an increase in value. Concerning stock with a

Beta equal to one, it means that they stick to the market average. Finally a stock having a

Beta lower than one is a stock with volatility lower than the market average. This means that


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the stock will be less risky but it will also have a lower return. The stock’s Beta of companies

operating in industries such as Luxury goods, construction, technology, jewellery, etc..? are

usually high. On the Other hand, Stock’s Beta of companies such as Coca Cola and

Supermarkets are rather lower.

What does the Risk Free Rate mean and how is it determined? How could you find

today’s risk free rate?

The Risk Free Rate is the rate of return that one would get if he would invest in a source

completely free of risk. The risk free rate is generally determined by the rate offered for the

investment in government securities such as US bonds. Indeed, Governments and countries

are usually considered as being references for the certainty of the return on investment. As

the certainty is high, of course, the rate offered is not extremely important. To find today’s

risk free rate, we can usually look at the benchmark rates set by central banks such as the

ECB in Europe or the Fed in the United States.

What does required return mean? How do we calculate this number?

The required return is the minimum rate that has to be paid to investors in order to ensure a

fair compensation for the risk they have taken by investing in a specific stock or bond. It is

important to determine the required rate of return in order to determine the kind of

investment we want to get in. Generally the highest the risk is, the higher the required

return will be. It is possible to calculate this number thanks to the CAPM formula presented

above.


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II- Weighted Average Cost of Capital

Cost of Equity: 20% Bank Interest Rate: 8% Tax Rate: 25% Percentage Equity: 75%

Project A-IRR: 12% Project B-IRR: 16% Project C-IRR: 18%

a- Calculate the after-tax cost of debt

After Tax Cost of Debt = Cost of Debt (1-Taxe Rate)

Here we consider that the cost of debt is the bank interest rate

After Tax Cost of Debt = 8% (1-25%)

After Tax Cost of Debt = 0.08 (1-0.25)

After Tax Cost of Debt = 0.08 x 0.75

After Tax Cost of Debt = 0.06

The After Tax Cost of Debt is 6%


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b- Calculate the Weighted Average Cost of Capital (WACC)

WACC = % Debt x Cost of Debt After Tax + % Equity x Cost of Equity

We know that the percentage of Equity is 75%. Therefore we can deduct that the percentage

of Debt is equal to the remaining part of the capital, that is, 25%.

We can thus calculate the WACC:

WACC = (25% x 6%) + (75% x 20%)

WACC= (0.25 x 0.06) + (0.75 x 0.2)

WACC= 0.015 + 0.15

WACC = 0.165

The Weighted Average Cost of Capital here is equal to 16.5%


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c- For any amounts borrowed over $10 million, the bank will increase the interest rate by

2%. The company has three projects and each project cost $10million. Calculate which of

the following three projects the company should pursue.

Project A: IRR 12%, Project B: IRR 16%, Project C: IRR 18%

In this case we don’t need to calculate anything as the WACC is 16.5%. This means that only-

project C will be profitable. Indeed, to be profitable, the IRR of a project has to higher than

the WACC. Here, Project A (12%) and project B (16%) have an IRR lower than the WACC.

Therefore, only the Project C which has an IRR of 18% should be pursued as it is higher than

the WACC of 16.5%.


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d- Explain why it is riskier for a company to issue debt instead of equity, and answer the

following questions:

Basically it is riskier for a company to issue debt rather than equity because debts have to be

imperatively reimbursed and a failure to do so could lead to the seizure of the company’s

capital, whereas for Equity, there is no promise of reimbursement despite often a higher

cost for the company in case of profit.

Which has a lower cost of capital and why: Debt or Equity?

Equity has the higher cost of capital compared to Debt. The reason why the cost of Equity is

higher than the cost of Debt is that investors are taking a higher risk while investing in equity


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as they are not sure to get their money back. Conversely, for the Debts, the lender has a

much higher certainty of being paid back; the cost for raising debt is thus much lower. The

perfect example that represents well the higher risk taken by equity investors is the

bankruptcy. Indeed, in case of bankruptcy, debt holders are the first to be paid back while

equity investors are among the last which increase the risk to simply not being paid back.

Why would some companies only issue equity?

Some company would only issue Equity in the case they need to raise fund during periods

where bank are not really willing to lend large amounts of money. Another reason that could

push a company to seek only for equity would be the will to spread the risks of an

investment among a large number of shareholders. Finally, a company would choose to

issue only equity if it tries to raise funds for expensive long term projects that might not

payoff over the short term. As equity investors are willing to take more risk and to wait for

profit over a long term period, it is generally not the case for bank professionals for example,

as they don’t seek for risky investment but rather for a regular secured pay back.

Why would some companies only issue debt?

Some company may decide to only issue debt when benchmark interest rates are low which

gives them access to a cheaper source of capital. Moreover, while issuing debt, the company

keeps the full control on her decision making process and does not need to share decisions

with other counterparts. Finally we could add that it is easier to use a leverage effect with


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debt financing as the cost of debts is lower. It allows the company to invest debt funded cash

into projects with a much higher expected pay back which would lead to high profits.

III- Debt and Equity Financing


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a- This company needs to raise additional equity funds for 2012 by selling stock. Calculate

how many new shares it would need to issue to have the additional needed equity funds.

(After paying the investment bankers and paying for its own expenses).

Additional Equity Funds Needed (2012): $30,000,000 Price per Share to Public: $7.50

Flotation Costs: 8% Corporation Expenses: $600,000

We will call x the number of shares that need to be sold in order to obtain the $30,000,000

additional equity funds needed.

30,000,000=7.5x−(600,000+7.5 x ×8%)

30,000,000=7.5x−(600,000+7.5 x ×0,08)

30,000,000+600,000=7.5 x−0.6 x

30,600,000=6.9x

x=30,600,0006,9

x=4,434,782.6

The company would need to issue 4,434,782 new shares in order to raise the $30,000,000

of the equity- fund needed after having paid back the investment bankers and its own

expenses.


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b- Calculate the price at which the corporation should issue each new zero coupon bond, if

it wants to compete with the market rates.

Market Interest Rate: 7% Face Value Zero Coupon Bonds: $ 1,000

Length of zero coupon bonds: 10 years

We have to look for the present value of the zero coupon bond that will have a $1000 face

ten years later at an interest rate of 7% per year.

FV=PV (1+i)n

1000=PV (1+7%)10

1000=PV (1+0.07)10

1000=PV ×1.0710

1000=PV ×1.967151357

PV= 10001.967151357

PV=508.35

The company should issue the zero coupon bonds at a price of $508.35 if it wants to

compete with the market rates.


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c- Calculate the amount of debt the company needs to issue in 2012 to maintain its same

debt ratio from 2011. Include the new Stock issued in part A in your calculations.

Total Debt (12/31/11): $30,000,000 Com Stk/Inv Cap (12/31/11): $20,000,000

Retained Earnings (12/31/11): $25,000,000 Net Income (2012): $12,000,000

Dividends (2012): $12,000,000

I could not find the answer


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d- Discuss the reason that investment bankers will charge much higher flotation costs to

issue Equity than to issue Debt. Discuss the various types of bonds that the company could

issue and their advantages and disadvantages.

Investment banker will probably charge a higher flotation to issue Equity than to issue debt

because the risk is higher, especially if the investment bank invests its own funds. Moreover,

if the bank tries to find investors, it will probably be more time consuming to find equity

investors than lending money to the company, a premium is thus charged for this reason.

Concerning the bonds, they are much diversified and each one has a special way of working.

Debenture bond: It is the classic bond issued. It is often issued by governments or

corporations and the risk of not getting paid is rather low. Debenture bonds don’t have many

disadvantages. We could however say that there is a risk the company goes out of business

without paying back the bond. Another downturn that could face a bond holder is an

unfavorable market evolution. For example if the interest rate goes up compared to the

interest rate paid by coupons of the previously purchased debenture bond.

Mortgage/Secured Bonds: A mortgage or secured bond is a bond that is guaranteed by a

company’s asset. It’s the safest investment as it mortgage bond holders will be paid back


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first in case of bankruptcy. The price of a mortgage bond might however be higher than the

price of other bonds due to its certainty. Finally there is always a risk that the asset backing

the bond will lost value over time and won’t cover completely the bond’s value in the case

where a repayment would be needed.

Convertible Bond: A convertible bond is a bond that can be converted into common stocks

during a given, pre-determined time period. The main advantage of convertible bonds lies in

the fact that they can be converted into common stocks so that they offer alternatively the

advantages of bonds and stocks. The disadvantage that could be highlighted is that

convertible bonds often paid lower interest rates than classic bonds. If the bond holder can’t

make a premium by reselling the bond or by converting it into common stocks it will likely-

not be a very profitable investment compared to other bonds.

Callable and Puttable bonds: A callable bond is a bond that the issuer is free to buy back at

any time before its maturity. A Puttable bond is somehow the opposite of a callable bond as

it is a bond that allows the bondholder to sell it back to the issuer at any time before it

reaches its maturity. With callable bonds the advantage is rather for the issuer than can call

the bonds back when interest rates paid are no longer competitive. For the holder of a

callable bond the disadvantage is the uncertainty of benefit due to the fact that the band can

be called at any time. One advantage for the band holder, however, would rely- on its ability-

to speculate and sell the bond at the right time in order to get some added value.


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Concerning puttable bonds, the big advantage for investors is that their investment is kind of

secured by- the fact that they can sell their bond back to the issuer at any time. On the other

hand the drawback might be that the investor will receive lower interest payments.

Income Bonds: An income bond is a bond that pays interests only if the company has

enough income. The obvious disadvantage is the risk of not getting interest if the company

doesn’t make any benefit. The advantage, on the other hand, is that if the company makes

profits, interest rates paid are higher than with normal bonds.

Junk bond: It is a kind of bond with a very high risk. It is also called high yield bonds. The

disadvantage of this kind of bond is that it is very risky and that the probability to not get

paid is high, but the advantage is that the interest rate paid is usually very high.

Zero Coupon Bonds: A zero coupon bond is a coupon bond that doesn’t pay any interest

until maturity. The disadvantage for the bondholder is that he cannot make any benefit until

the bond’s maturity or unless he sells it for an higher than what he paid to acquire it.

However the advantage of a zero coupon bond is that it is sold for a price lower than its face

value.


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IV- Cash Management

Supplier Terms: 3/10 Net 90 Bank Loan Interest Rate: 8%

Annual Sales: €15,000,000 Annual COGS: €9,000,000 Days per Year: 360

Average Accounts Receivable Balance: €1,250,000 Average Inventory Balance: €2,000,000

a- Calculate the effective interest rate if you do not take the discount from your supplier.

Here we decide to not take the discount from our supplier. We will thus calculate the

effective interest rate for a classic bank loan.

Effective Interest Rate= InterestUsable Funds


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To calculate the Effective Interest Rate we will take a benchmark of $100 as being our usable

funds.

Effective Interest Rate=0.08×100100

Effective Interest Rate= 8100

Effective Interest Rate=8%

The Effective Interest Rate is equal to 8%, that is, the bank loan Interest rate.

b- Calculate the effective interest rate that this bank is charging you on the loan if it is a

discount loan. Should you take the supplier discount offered in part a then?

Effective Interest Rate charged by the bank in the case of a discount loan:

Discount Loan Effective Interest Rate= InterestUsable Funds−Interests

We will still use $100 as a benchmark for the usable funds.

Discount Loan Effective Interest Rate= 0.08×100100−(0.08×100)


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Discount Loan Effective Interest Rate= 8100−8

Discount Loan Effective Interest Rate= 892

Discount Loan Effective Interest Rate=0.087=8.7%

The effective Interest rate charged by this bank for a bank loan will be 8.7%.

c- Calculate the number of days of the cash collection cycle. Assume all sales are for credit,

and you do not take the discount from your supplier.

CashCollectionCycle= Average InventoryCost of Goods Sold /360

+ Average Account ReceivableCredit sale /360

− Average Account PayableCost of Goods Sold /360

We have to calculate the Average Account Payable:


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We know that if we don’t take our supplier discount we have 90 days to pay.

For a year of 360 days, there will thus be 4 periods of payment: 36090

=4

The annual Cost of Goods Sold is €9,000,000 so assuming that all the cost of goods sold are

money due to suppliers, the average account payable correspond to the following:

Average Account Payable=9,000,0004

=2,250,000

We can now calculate the cash collection cycle:

CashCollectionCycle= 2,000,0009,000,000 /360

+ 1,250,00015,000,000/360

− 2,250,0009,000,000/360

CashCollectionCycle=2,000,00025,000

+ 1,250,00041,666.67

−2,250,00025,000

CashCollectionCycle=80+30−90

CashCollectionCycle=110−90

CashCollectionCycle=20

The Cash collection cycle is equal to 20 days.

d- Describe the role of the credit department in an organization and list some of the duties

it performs.


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The credit department is the department that manages account receivables. They usually

take care of credit policy, terms of credit or else the collection policy, that is, they determine

the actions to be taken in the case where customers wouldn’t pay in time. For example they

can define steps to follow such as issuing the bill, then a warning letter followed by the

appointment of a collection agency in last resort, if the customer is still not willing to pay. It

is also the credit department which is in charge of checking the customer solvability and they

credit history. Credit departments can also exchange between each other information

concerning the credit history of a specific borrower.

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