Bài tập môn quản trị tài chính doanh nghiệp MBA (bản dịch tiếng anh)

TRAINING PROGRAM
Global Advanced Master of Business Administration

INDIVIDUAL ASSIGNMENT

CORPORATE FINANCE

Lecturer: Professor Soren Kirchner
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Leaner:

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Class : GaMBA4.C165

Ho Chi Minh City, 2012


Student:

INDIVIDUAL ASSIGNMENT
Question 1. There are a few companies with negative beta. Assuming that
you find a company with a beta = -2.5.
a. What will the stock profitability ratios change if the market profitability ratio

increases 5%? If the market profitability ratios decreases 5%?
b. You have USD 1 million to invest in a share portfolio that is well diversified.
Now you receive an additional USD 20,000 from the will. Which of the
following actions will bring safety for the profitability ratios portfolio?
i.

Invest USD 20,000 in Treasury Bonds (with beta = 0).

ii.

Invest USD 20,000 in the Stocks with beta = 1.

iii.

Invest USD 20,000 in the Stocks with beta = -0,25.

Answer:
In the stock market in the countries with developed market economy, the
information about listed companies such as profits, risks and other important
information are published daily in the market to help investors review, consider
which suitable investment plan will offer them the best results. One of the most
important parameter reflecting the risk is the beta coefficient (β) provided by the
professional financial research organizations.
Risk beta coefficient (β) is defined as a coefficient to measure the level of
volatility, also known as a measure of systematic risk of a security or a portfolio
relative to the overall market. Beta is used in the capital asset pricing model (CAPM)
to calculate the expected profitablity ratios of an asset based on its beta coefficient
and profitablity ratios in the market.
Formual of beta coefficient :
Beta = Covar (RI, Rm)/Var (Rm)
In which:
• Ri: profitablity ratios of the stock.
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Student:

• Rm: profitablity ratios of the market (the VN-Index).
• Var (Rm): Variance of profitability ratios of the market.
• Covar (Ri, Rm): Sum of Variance of profitability ratios of the stock and
profitablity ratios of the market.
Estimate β in reality
In fact, the stock traders use regression models based on historical data to estimate β.
In countries with developed financial markets, there are some companies specializing
in identifing and providing information about β coefficient. For example, in the U.S.,
people can find information about β from the service provider such as Value Line
Investment Survey, Market Guide and Standard & Poor's Stock Reports. In Canada,
information about β is provided by Burns Fry Limited.
The relationship between Risk and Return
Expected profit of stock has a direct variable relationship with the risk of that
stock, it means that investors expect high risk stock will have high profit and vice
versa. In other words, investors hold risky stock only when the expected profit is
large enough to offset the risks. In the previous section, we discussed β coefficient is
used to measure the risk of a stock. Therefore, the expected profit of a stock has a
direct variable relationship with its coefficient β.
Assuming that financial market is efficient and investors diversify the
investment portfolio so that the risk of the system is negligible. Thus, only systemwide risks affect the profits of the stock. The stocks with the greater beta, the greater
the risk is, therefore, it requires high profits to offset the risk. According to the
CAPM model, the relationship between profit and risk is expressed by the formula:
r = β x (rm – rf) + rf

hay (r - rf )= β x (rm – rf)

(1)

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Student:

In which:
• r: expected profitability ratios of the stock
• rf : profitability ratios without risks (profitability ratios of short-term
bonds )
• rm : profitability ratios of market portfolio

• β : the sensitivity of the profitability ratios of the stock with the market
fluctuation
• Thus the profitablity ratios requirements of investors are affected primarily by

the risks. If a stock has a beta coefficient:
• = 1: the fluctuation of the stock price will be equal to the fluctuation of the

market.
• <1: the level of fluctuation of the stock price is lower than the fluctuation of the

market.
• >1 1: the level of stock price fluctuation is greater than the fluctuation of the

market.
Specifically, if a stock has a beta is 1.2, in theory; the fluctuation of this
stock will be 20% higher than the fluctuation of the market.
In the situation that we find a company with beta = -2.5,
a. What will the stock profitability ratios change if the market profitability ratio
increases 5%? If the market profitability ratios decreases 5%?
• If Δrm changes =5%  from formula (1), we have:

Δrx = β*Δrm = -2.5*(5%) = -12.5%
Expected stock profitability ratios will reduce 12.5%
• Similarly, if Δrm changes = -5%  Expected stock profitability ratios
Δrx = β*Δrm = -2.5*(-5) = 12.5%
Expected profitability rate of the shares will increase 12.5%
b. One million dollars for investing in well diversified stock portfolio is

available. Now we receive additional USD 20,000 from the will, to choose
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Student:

which action will bring safety for profitability ratios portfolio, we will
analyze the following:
From formula (1) we have:
With β=0, profitability ratio of the stock r1= profitability ratio of short-term
Treasury bonds
With β=1, profitability ratio of stock r2 = profitability ratio in the market rm
With β=-0.25, we have r3 =rf -0.25*(rm-rf)
Perform r1, r2,r3 on the same graph we have the following diagram:

Comments: The investment decision depends on market growth factors:
1. If rm < rf we will invest in stock with r3 (β=-0.25)
2. If rm = rf we will invest in any stock
3. If rm > rf we will invest in stock with β =1
Question 2: If you can either keep cash or invest in stock with an interest rate of
8%. You can not sell stock when you need money, so, you have to make up for
the cash deficit by using a bank credit quota with 10% of interest rate. Should
you invest more or less in stock in each situation below?

a. Sometimes you are not sure about future cash flows.
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Student:

b. Bank interest rate rises to 11%.
c. Interest rates of stock and bank loan interest rates increase at the same rate.
d. You adjust the forecast of future cash needs lower.
Answer :
a. In the case we are uncertain about the cash flow in the future; we should invest less
in stocks. When we are unsure about the future cash flow, which means that we are
not sure about the demand for the capital in the future. Then we should reduce
investment in stocks for the occurrence of lack of money, the cost of interest on bank
loans will be higher than rates of investment stocks leading to the financial cost
incurred in this case.
b. If the interest rate rises to 11%, we should also invest less in stocks. Because when
interest rates increase, this means borrowing costs will increase while the interest rate
of stock investment is unchanged. This causes the increase in financial costs, so, we
should less invest in stock.
c. If the bank interest rate and stock interest rate increase at the same ratio, as the
first. Because once the bank interest rate and stock investment rate increase
respectively, this means that the difference between bank interest and interest rate
stock investment is unchanged. This leads the financial costs do not change, so we
remain the same rate as the original investment.
d. If we adjust the demand of forecasts for future cash lower, we should be invest
more in stocks. When the future cash needs decreasing, this means the amount of idle
money increasing. In this case, we should invest more in stock in order to increase the
effectiveness of financial investment.
Question 3. VDEC company is concerning about the cost of using capital

for the company. According to the current investigations, we have the following
data. Suppose the corporate income tax rate is 40%.

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Student:

Debit: The Company can increase unlimited debt by selling the coupon bonds
with interest rate of 10% annually; the bonds have denominations of USD 1,000. The
cost of commissions paid to the underwriter is USD 30 / stock, issuance cost is USD
20 / stock, the term is 10 years
Preferred stock: The Company may sell preferred stock unlimitedly in
number with price of USD 100 / stock, the interest rate is 11% / year. Issuance cost is
USD 20 / stock.
Common stock: The Company's common stock is currently being sold at
USD 80 / stock. The company expects to pay dividends in cash USD 6 / stock next
year. Company's dividend growth of 6% / year and does not change in the future.
Stock will be sold at the price less than USD 4 / stock, the issuance cost is USD 4 /
stock. Company can sell with unlimited quantities.
Retained profit: The Company expects to keep USD 225,000 of profit in the next
year. If there is not retained profit, the company will issue new common stock.
a. Calculate the cost for each funding source.
b. Calculate the average capital cost, assuming the target capital structure is:
Source

Ratio

Long term debt

40%

Preferred stock

15%

Common stock

45%

Total
100%
(1) Determine breaking point of retained profit.
(2) Calculate the cost of using marginal capital and the cost of using
average capital related to the entire new funding sources.
c. Use information about the investment opportunities in the following table to
draw the line of using of Weighted Marginal Cost of Capital – (WMCC) and
Investment opportunity schedules (IOS) on the same graph.

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Student:

Project
A

Primary investment
USD 100,000

IRR
17.4%

B

USD 200,000

16.0

C

USD 100,000

14.2

D

USD 200,000

13.7

E
USD 100,000
10.0
e. Do you have any advice about financial sources that the company should
choose? Total optimal funding for the company? And explain your point of
view.
Answer:
a. Cost of using capital for each funding source:
Cost of selling a bond = Nominal value – Commission cost –Issuance cost =

1.000-30-20= USD 950
+ Cost of using capital for Coupon bonds project:
950= 100[(1- (1+ rd )-10] / rd
 rd = 6,51%
+ Capital cost of preferred stock:
rp = Dp / ( Pp – f ) = ( USD 100x 11% ) / ( USD 100 - USD 20 )
 rp = 13.75%
+ Capital cost of common stock:
re = ( DIV1 / Po ) + g = 6/80 + 6%
 re = 13.5%
+ Capital cost of new common stock:
rne = ( DIV / Pne ) + g = [ 6/ ( 800- 4 – 4 ) ] + 6%
 rne = 14.33%
b. Part b.1 : Identify the breaking point of Retained profit
BPe = Amount of Retained profit/ Ratio of common stock
= Aj / Wj = USD 225,000/45% = USD 500,000

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Student:

Thus, there is a breaking point occurs when USD 225,000 of retained profit
is used up.
Part b.2: Cost of using marginal capital and drawing the graph for choosing
the options:
Make a table of segment of BPe profit
Range of capital
source

Ri – capital

Wi capital

WACC cost for

cost

ratio

using average
capital

0 < I < USD 500,000

I > USD 500,000

re = 13.5%

45%

rp = 13,.75%

15%

rd = 6.51%
re = 14.33%

40%
45%

rp = 13.75%

15%

rd = 6.51%

40%

10.74%

11.11%

To select investment projects, we should draw the line of cost for using Weighted
Marginal Cost of Capital – (WMCC) and Investment Opportunity Schedules (IOS) on
the same graph as follows:

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Student:
WACC (%)
17,4

A

16.0

B

C

14,2

D

11,7

WMCC

11,0
10,74
10,0

E

IOS
I (1.000$)

100

200

300

500

600

700

Based on the graph: we see
• A project with investment capital: USD 100,000 with profitability rate IRR = 17.4%
higher than the cost of using Weighted Marginal Cost of Capital – (WMCC) (10,
74%).
• Project B with investment capital: USD 200,000 profitability rate IRR = 16.0%
higher than the cost of using Weighted Marginal Cost of Capital (10, 74%)
• C project with investment capital: USD 300,000 has the highest profitability rate
IRR = 14.2% higher than the cost of using Weighted Marginal Cost of Capital (10,
74%).
• D project with investment capital: USD 600,000 profitability rate IRR = 11.7%
higher than the cost of using Weighted Marginal Cost of Capital (10, 74%).
• E project with investment capital: USD 700,000 profitability rate IRR = 10.0%,
lower than the cost of using Weighted Marginal Cost of Capital (10, 74%).

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Student:

Thus, the lines of investment opportunities of the four projects A, B, C, D are
located higher than WMCC line (the cost of using Weighted Marginal Cost of
Capital) so, the profit from each project is expected to be higher than the cost of
using Weighted Marginal Cost of Capital and in accordance with the objective of
maximizing the value of assets of the company. Therefore, VDEC Company should
invest in four projects A, B, C, D with optimum total funding for the company is
USD 1,200,000. The company should not invest in the project E as it is inefficient
project financially because the project's profitability rate is lower than the cost of
using Weighted Marginal Cost of Capital.

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