FINANCE- Prepare your responses to these assignment problems in a word processing file

Assignment 3
Assignment 3 is due after you complete Lessons 9 to 11. It is
worth 20% of your final grade.

Prepare your responses to these assignment problems in a word
processing file; put financial data in a spreadsheet file. As you complete the
assignment problems for each lesson, add your responses to these files.
Do not submit your answers for grading until you have completed
all parts of Assignment 3.

Note: In assignments, show all calculations to 4 decimal places.
Lesson 9:
Assignment Problems

9.1 The Constant-Growth-Rate Discounted Dividend Model, as described
equation 9.5 on page 247, says that:

P0 = D1 / (k – g)
A. rearrange the terms to solve for:

i. g; and

ii. D1.

As an example, to solve for k, we would do the following:

1. Multiply both sides by (k – g) to get: P0 (k – g) = D1

2. Divide both sides by P0 by to get: (k – g) = D1/
P0

3. Add g to both sides: k = D1/ P0 + g
(8 marks)
9.2 Notation:
Let
Pn
= Price at time n
Dn
= Dividend at time n
Yn
= Earnings in period n

r = retention ratio = (Yn– Dn) / Yn=
1 – Dn/ Yn= 1 – dividend payout ratio

En = Equity at the end of year n

k = discount rate
g =
dividend growth rate = r x ROE
ROE = Yn
/ En-1 for all n>0.

We will further assume that k and ROE are constant, and that r and g are
constant after the first dividend is paid.
A. Using the Discounted Dividend Model, calculate the price P0
if

D1 = 20, k = .15, g = r x ROE = .8 x .15 = .12, and Y1
= 100 per share

B. What, then, will P5 be if:

D6 = 20, k = .15, and g = r x ROE = .8 x .15 = .12?

C.
If P5 = your result from part
B, and assuming no dividends are paid until D6, what would be P0?
P1? P2?

D.
Again, assuming the facts from part B,
what is the relationship between P2 and P1 (i.e., P2/P1)?
Explain why this is the result.

E.
If k = ROE, we can show that the price
P0 doesn’t depend on r. To see this, let
g = r x ROE, and ROE = Yn / En-1, and

since r = (Yn – Dn) / Yn , then D1=
(1 – r) x Y1 and

P0

=

D1
/ (k – g)

P0

=

[(1 –
r) x Y1] / (k – g)

P0

=

[(1 –
r) x Y1] / (k – g), but, since k = ROE = Y1 / E0

P0

=

[(1 – r) x Y1] / (ROE– r x
ROE)

P0

=

[(1 –
r) x Y1] / (Y1 / E0– r x Y1 / E0)

P0

=

[(1 –
r) x Y1] / (1 – r) x Y1 / E0), and
cancelling (1 – r)

P0

=

Y1
/ (Y1/E0) = Y1 x (E0 / Y1)
= E0

So, you see that r is not in the final expression for P0, indicating
that r (i.e., retention ration or, equivalently, dividend policy) doesn’t
matter if k = ROE.
Check that changing r from .8 to .6 does not change your answer in part A of
this question by re-calculating your result using r = .6.
(10
marks)

9.3 You are considering an investment in the
shares of Kirk’s Information Inc. The company is still in its growth phase, so
it won’t pay dividends for the next few years. Kirk’s accountant has determined
that their first year’s earnings per share (EPS) is expected to be $20. The
company expects a return on equity (ROE) of 25% in each of the next 5 years but
in the sixth year they expect to earn 20%. In the seventh year and forever into
the future, they expect to earn 15%. Also, at the end of the sixth year and
every year after that, they expect to pay dividends at a rate of 70% of
earnings, retaining the other 30% in the company. Kirk’s uses a discount rate
of 15%.

A.
Fill in the missing items in the following table:

Year

EPS

ROE

Expected Dividend
(end of year)

Present Value Of Dividend
(at time 0)

0

n/a

n/a

n/a

n/a

1

20

25%

0

0

2

25 =
1.25 x 20

25%

0

0

3

?

25%

0

0

4

?

25%

0

0

5

?

25%

0

0

6

?

20%

?

?

7

?

15%

?

?

8

?

15%

?

?

B. What would the dividend be in year 8?

C.
Calculate the value of all future
dividends at the beginning of year 8. (Hint: P7 depends on D8.)

D.
What is the present value of P7
at the beginning of year 1?

E. What
is the value of the company now, at time 0?
(10 marks)
9.4 You own one share in a company called Invest
Co. Inc. Examining the balance sheet, you have determined that the firm has
$100,000 cash, equipment worth $900,000, and 100,000 shares outstanding.

Calculate the price/value of each share in the firm, and explain how your
wealth is affected if:

A.
The firm pays out dividends of $1 per
share.

B.
The firm buys back 10,000 shares for $10
cash each, and you choose to sell your share back to the company.

C.
The firm buys back 10,000 shares for $10
cash each, and you choose not to sell your share back to the company.

D.
The firm declares a 2-for-1 stock split.

E.
The firm declares a 10% stock dividend.

F. The
firm buys new equipment for $100,000, which will be used to earn a return equal
to the firm’s discount rate.
(12
marks)

Do not submit these questions for grading until you have completed
all parts of Assignment 3, which is due after Lesson 11.

Lesson 10:
Assignment Problems

10.1 A. Calculate the mean and
standard deviation of the following securities’ returns:

Year

Computroids Inc.

Blazers Inc.

1

10%

5%

2

5%

6%

3

–3%

7%

4

12%

8%

5

10%

9%

B. Assuming these observations are drawn from a
normally distributed probability space, we know that about 68% of values drawn
from a normal distribution are within one standard deviation away from the mean
or expected return; about 95% of the values are within two standard deviations;
and about 99.7% lie within three standard deviations.

Using your calculations from part A, calculate the 68%, 95%, and 99% confidence
intervals for the two stocks. To calculate the 68%, you would calculate the top
of the confidence interval range by adding one standard deviation to the
expected return, and calculate the bottom of the confidence interval by
subtracting one standard deviation from the expected return. For 95%, use two
standard deviations, and for 99%, use three.

Your answer should show three ranges from the bottom of the confidence interval
to the top of the confidence interval.

C.
For each security, would a return of 14%
fall into the 68% confidence interval range? If not, what confidence interval
range would it fall into, or would it be outside all three confidence
intervals?

(This is the same as asking whether a return of 14% has less than a 68%
probability of occuring by chance for that security. If it’s not inside the 68%
confidence interval, it’s unlikely to occur, since it will only occur by chance
32% of the time. Of course, the 99% confidence interval is much more likely to
include the observed return, simply by chance. Only 1% of the time will it fall
outside the 99% CI. Pretty rare.)
(14 marks)

10.2 Some Internet research may be required to answer this question,
although it’s not absolutely necessary.

What could you do to protect your bond portfolio against the following kinds of
risk?

A.
Risk of an increasing interest
rate
B.
Risk of inflation increasing
C.
Risk of volatility in the markets
(6 marks)
10.3 You are starting a new business, and you want to open an office in
a local mall. You have been offered two alternative rental arrangements. You
can pay the landlord 10% of your sales revenue, or you can pay a fixed fee of
$1,000 per month. Describe the circumstances in which each of these
arrangements would be your preferred choice.
(10
marks)

Do not submit these questions for grading until you have completed
all parts of Assignment 3, which is due after Lesson 11.

Lesson 11:
Assignment Problems

11.1 In the northeast United States and in eastern Canada, many people
heat their houses with heating oil. Imagine you are one of these people, and
you are expecting a cold winter, so you are planning your heating oil
requirements for the season. The current price is $2.25 per US gallon, but you
think that in six months, when you’ll need the oil, the price could be $3.00,
or it could be $1.50.

A.
If you need 350 gallons to survive the
winter, how much difference does the potential price variance make to your
heating bills?

B. If
your friend Tom is running a heating oil business, and selling 100,000 gallons
over the winter season, how does the price variance affect Tom?

C.
Which one of you benefits from the price
increase? Which of you benefits from price decrease?

D.
What are two strategies you can use to
reduce the risk you face? Could you make an agreement with Tom to mitigate your
risk?

E. Assuming
you are both risk-averse, does such an agreement make you both better off?
(10 marks)

11.2 You have just received good news. You have a rich uncle in France
who has decided to give you a monthly annuity of €2,000 per month. You are
concerned that you will become accustomed to having these funds, but if the
currency exchange rate moves against you, you may have to make do with less.

A.
If you are living in Canada, what does
it mean for the currency exchange rate to move against you?

B.
Would moving to France mitigate some of
the risk? If so, how? If not, why not?

C. If
you want to stay in Canada, and your grandparents, who have retired to
Provence, receive a Canadian pension of C$1100 each, what could you do to
reduce the risk for all of you?
(9 marks)

11.3 You have learned about a
number of ways of reducing risk, specifically hedging, insuring, and
diversifying. In the table below, place an X in the cell for the technique
being used to reduce risk.

Hedging

Insuring

Diversifying

1

Placing
an advance order with Amazon.ca, which agrees to charge you the lower of the
advance price, and the price at the time your order is filled.

2

Purchasing
a call option on a stock you think may go up in price.

3

Selling
200 shares of IBM and buying a mutual fund that holds the same stocks as the
S&P index.

4

Selling
a debt owed to you for $.50 per dollar owed.

5

Agreeing
to a long-term contract with a supplier at a fixed price.

6

Agreeing
to a no-trade clause with the sports team that employs you.

7

Buying
a Mac and a PC.

8

Paying
a clown to perform for your child’s birthday party six months

(16 marks)

11.4 Suppose you own 100 shares of Dell Inc. stock. Today it is trading
at $15 per share, but you’re worried Michael Dell might retire again, causing
the price to go down. How would you protect yourself against his retirement,
assuming you don’t want to sell the shares today?
(5
marks)

When you have completed these questions, check to see that
Assignment 3 is complete and submit it for grading.

Assignment 3
Assignment 3 is due after you complete Lessons 9 to 11. It is
worth 20% of your final grade.

Prepare your responses to these assignment problems in a word
processing file; put financial data in a spreadsheet file. As you complete the
assignment problems for each lesson, add your responses to these files.
Do not submit your answers for grading until you have completed
all parts of Assignment 3.

Note: In assignments, show all calculations to 4 decimal places.
Lesson 9:
Assignment Problems

9.1 The Constant-Growth-Rate Discounted Dividend Model, as described
equation 9.5 on page 247, says that:

P0 = D1 / (k – g)
A. rearrange the terms to solve for:

i. g; and

ii. D1.

As an example, to solve for k, we would do the following:

1. Multiply both sides by (k – g) to get: P0 (k – g) = D1

2. Divide both sides by P0 by to get: (k – g) = D1/
P0

3. Add g to both sides: k = D1/ P0 + g
(8 marks)
9.2 Notation:
Let
Pn
= Price at time n
Dn
= Dividend at time n
Yn
= Earnings in period n

r = retention ratio = (Yn– Dn) / Yn=
1 – Dn/ Yn= 1 – dividend payout ratio

En = Equity at the end of year n

k = discount rate
g =
dividend growth rate = r x ROE
ROE = Yn
/ En-1 for all n>0.

We will further assume that k and ROE are constant, and that r and g are
constant after the first dividend is paid.
A. Using the Discounted Dividend Model, calculate the price P0
if

D1 = 20, k = .15, g = r x ROE = .8 x .15 = .12, and Y1
= 100 per share

B. What, then, will P5 be if:

D6 = 20, k = .15, and g = r x ROE = .8 x .15 = .12?

C.
If P5 = your result from part
B, and assuming no dividends are paid until D6, what would be P0?
P1? P2?

D.
Again, assuming the facts from part B,
what is the relationship between P2 and P1 (i.e., P2/P1)?
Explain why this is the result.

E.
If k = ROE, we can show that the price
P0 doesn’t depend on r. To see this, let
g = r x ROE, and ROE = Yn / En-1, and

since r = (Yn – Dn) / Yn , then D1=
(1 – r) x Y1 and

P0

=

D1
/ (k – g)

P0

=

[(1 –
r) x Y1] / (k – g)

P0

=

[(1 –
r) x Y1] / (k – g), but, since k = ROE = Y1 / E0

P0

=

[(1 – r) x Y1] / (ROE– r x
ROE)

P0

=

[(1 –
r) x Y1] / (Y1 / E0– r x Y1 / E0)

P0

=

[(1 –
r) x Y1] / (1 – r) x Y1 / E0), and
cancelling (1 – r)

P0

=

Y1
/ (Y1/E0) = Y1 x (E0 / Y1)
= E0

So, you see that r is not in the final expression for P0, indicating
that r (i.e., retention ration or, equivalently, dividend policy) doesn’t
matter if k = ROE.
Check that changing r from .8 to .6 does not change your answer in part A of
this question by re-calculating your result using r = .6.
(10
marks)

9.3 You are considering an investment in the
shares of Kirk’s Information Inc. The company is still in its growth phase, so
it won’t pay dividends for the next few years. Kirk’s accountant has determined
that their first year’s earnings per share (EPS) is expected to be $20. The
company expects a return on equity (ROE) of 25% in each of the next 5 years but
in the sixth year they expect to earn 20%. In the seventh year and forever into
the future, they expect to earn 15%. Also, at the end of the sixth year and
every year after that, they expect to pay dividends at a rate of 70% of
earnings, retaining the other 30% in the company. Kirk’s uses a discount rate
of 15%.

A.
Fill in the missing items in the following table:

Year

EPS

ROE

Expected Dividend
(end of year)

Present Value Of Dividend
(at time 0)

0

n/a

n/a

n/a

n/a

1

20

25%

0

0

2

25 =
1.25 x 20

25%

0

0

3

?

25%

0

0

4

?

25%

0

0

5

?

25%

0

0

6

?

20%

?

?

7

?

15%

?

?

8

?

15%

?

?

B. What would the dividend be in year 8?

C.
Calculate the value of all future
dividends at the beginning of year 8. (Hint: P7 depends on D8.)

D.
What is the present value of P7
at the beginning of year 1?

E. What
is the value of the company now, at time 0?
(10 marks)
9.4 You own one share in a company called Invest
Co. Inc. Examining the balance sheet, you have determined that the firm has
$100,000 cash, equipment worth $900,000, and 100,000 shares outstanding.

Calculate the price/value of each share in the firm, and explain how your
wealth is affected if:

A.
The firm pays out dividends of $1 per
share.

B.
The firm buys back 10,000 shares for $10
cash each, and you choose to sell your share back to the company.

C.
The firm buys back 10,000 shares for $10
cash each, and you choose not to sell your share back to the company.

D.
The firm declares a 2-for-1 stock split.

E.
The firm declares a 10% stock dividend.

F. The
firm buys new equipment for $100,000, which will be used to earn a return equal
to the firm’s discount rate.
(12
marks)

Do not submit these questions for grading until you have completed
all parts of Assignment 3, which is due after Lesson 11.

Lesson 10:
Assignment Problems

10.1 A. Calculate the mean and
standard deviation of the following securities’ returns:

Year

Computroids Inc.

Blazers Inc.

1

10%

5%

2

5%

6%

3

–3%

7%

4

12%

8%

5

10%

9%

B. Assuming these observations are drawn from a
normally distributed probability space, we know that about 68% of values drawn
from a normal distribution are within one standard deviation away from the mean
or expected return; about 95% of the values are within two standard deviations;
and about 99.7% lie within three standard deviations.

Using your calculations from part A, calculate the 68%, 95%, and 99% confidence
intervals for the two stocks. To calculate the 68%, you would calculate the top
of the confidence interval range by adding one standard deviation to the
expected return, and calculate the bottom of the confidence interval by
subtracting one standard deviation from the expected return. For 95%, use two
standard deviations, and for 99%, use three.

Your answer should show three ranges from the bottom of the confidence interval
to the top of the confidence interval.

C.
For each security, would a return of 14%
fall into the 68% confidence interval range? If not, what confidence interval
range would it fall into, or would it be outside all three confidence
intervals?

(This is the same as asking whether a return of 14% has less than a 68%
probability of occuring by chance for that security. If it’s not inside the 68%
confidence interval, it’s unlikely to occur, since it will only occur by chance
32% of the time. Of course, the 99% confidence interval is much more likely to
include the observed return, simply by chance. Only 1% of the time will it fall
outside the 99% CI. Pretty rare.)
(14 marks)

10.2 Some Internet research may be required to answer this question,
although it’s not absolutely necessary.

What could you do to protect your bond portfolio against the following kinds of
risk?

A.
Risk of an increasing interest
rate
B.
Risk of inflation increasing
C.
Risk of volatility in the markets
(6 marks)
10.3 You are starting a new business, and you want to open an office in
a local mall. You have been offered two alternative rental arrangements. You
can pay the landlord 10% of your sales revenue, or you can pay a fixed fee of
$1,000 per month. Describe the circumstances in which each of these
arrangements would be your preferred choice.
(10
marks)

Do not submit these questions for grading until you have completed
all parts of Assignment 3, which is due after Lesson 11.

Lesson 11:
Assignment Problems

11.1 In the northeast United States and in eastern Canada, many people
heat their houses with heating oil. Imagine you are one of these people, and
you are expecting a cold winter, so you are planning your heating oil
requirements for the season. The current price is $2.25 per US gallon, but you
think that in six months, when you’ll need the oil, the price could be $3.00,
or it could be $1.50.

A.
If you need 350 gallons to survive the
winter, how much difference does the potential price variance make to your
heating bills?

B. If
your friend Tom is running a heating oil business, and selling 100,000 gallons
over the winter season, how does the price variance affect Tom?

C.
Which one of you benefits from the price
increase? Which of you benefits from price decrease?

D.
What are two strategies you can use to
reduce the risk you face? Could you make an agreement with Tom to mitigate your
risk?

E. Assuming
you are both risk-averse, does such an agreement make you both better off?
(10 marks)

11.2 You have just received good news. You have a rich uncle in France
who has decided to give you a monthly annuity of €2,000 per month. You are
concerned that you will become accustomed to having these funds, but if the
currency exchange rate moves against you, you may have to make do with less.

A.
If you are living in Canada, what does
it mean for the currency exchange rate to move against you?

B.
Would moving to France mitigate some of
the risk? If so, how? If not, why not?

C. If
you want to stay in Canada, and your grandparents, who have retired to
Provence, receive a Canadian pension of C$1100 each, what could you do to
reduce the risk for all of you?
(9 marks)

11.3 You have learned about a
number of ways of reducing risk, specifically hedging, insuring, and
diversifying. In the table below, place an X in the cell for the technique
being used to reduce risk.

Hedging

Insuring

Diversifying

1

Placing
an advance order with Amazon.ca, which agrees to charge you the lower of the
advance price, and the price at the time your order is filled.

2

Purchasing
a call option on a stock you think may go up in price.

3

Selling
200 shares of IBM and buying a mutual fund that holds the same stocks as the
S&P index.

4

Selling
a debt owed to you for $.50 per dollar owed.

5

Agreeing
to a long-term contract with a supplier at a fixed price.

6

Agreeing
to a no-trade clause with the sports team that employs you.

7

Buying
a Mac and a PC.

8

Paying
a clown to perform for your child’s birthday party six months

(16 marks)

11.4 Suppose you own 100 shares of Dell Inc. stock. Today it is trading
at $15 per share, but you’re worried Michael Dell might retire again, causing
the price to go down. How would you protect yourself against his retirement,
assuming you don’t want to sell the shares today?
(5
marks)

When you have completed these questions, check to see that
Assignment 3 is complete and submit it for grading.

Assignment 3
Assignment 3 is due after you complete Lessons 9 to 11. It is
worth 20% of your final grade.

Prepare your responses to these assignment problems in a word
processing file; put financial data in a spreadsheet file. As you complete the
assignment problems for each lesson, add your responses to these files.
Do not submit your answers for grading until you have completed
all parts of Assignment 3.

Note: In assignments, show all calculations to 4 decimal places.
Lesson 9:
Assignment Problems

9.1 The Constant-Growth-Rate Discounted Dividend Model, as described
equation 9.5 on page 247, says that:

P0 = D1 / (k – g)
A. rearrange the terms to solve for:

i. g; and

ii. D1.

As an example, to solve for k, we would do the following:

1. Multiply both sides by (k – g) to get: P0 (k – g) = D1

2. Divide both sides by P0 by to get: (k – g) = D1/
P0

3. Add g to both sides: k = D1/ P0 + g
(8 marks)
9.2 Notation:
Let
Pn
= Price at time n
Dn
= Dividend at time n
Yn
= Earnings in period n

r = retention ratio = (Yn– Dn) / Yn=
1 – Dn/ Yn= 1 – dividend payout ratio

En = Equity at the end of year n

k = discount rate
g =
dividend growth rate = r x ROE
ROE = Yn
/ En-1 for all n>0.

We will further assume that k and ROE are constant, and that r and g are
constant after the first dividend is paid.
A. Using the Discounted Dividend Model, calculate the price P0
if

D1 = 20, k = .15, g = r x ROE = .8 x .15 = .12, and Y1
= 100 per share

B. What, then, will P5 be if:

D6 = 20, k = .15, and g = r x ROE = .8 x .15 = .12?

C.
If P5 = your result from part
B, and assuming no dividends are paid until D6, what would be P0?
P1? P2?

D.
Again, assuming the facts from part B,
what is the relationship between P2 and P1 (i.e., P2/P1)?
Explain why this is the result.

E.
If k = ROE, we can show that the price
P0 doesn’t depend on r. To see this, let
g = r x ROE, and ROE = Yn / En-1, and

since r = (Yn – Dn) / Yn , then D1=
(1 – r) x Y1 and

P0

=

D1
/ (k – g)

P0

=

[(1 –
r) x Y1] / (k – g)

P0

=

[(1 –
r) x Y1] / (k – g), but, since k = ROE = Y1 / E0

P0

=

[(1 – r) x Y1] / (ROE– r x
ROE)

P0

=

[(1 –
r) x Y1] / (Y1 / E0– r x Y1 / E0)

P0

=

[(1 –
r) x Y1] / (1 – r) x Y1 / E0), and
cancelling (1 – r)

P0

=

Y1
/ (Y1/E0) = Y1 x (E0 / Y1)
= E0

So, you see that r is not in the final expression for P0, indicating
that r (i.e., retention ration or, equivalently, dividend policy) doesn’t
matter if k = ROE.
Check that changing r from .8 to .6 does not change your answer in part A of
this question by re-calculating your result using r = .6.
(10
marks)

9.3 You are considering an investment in the
shares of Kirk’s Information Inc. The company is still in its growth phase, so
it won’t pay dividends for the next few years. Kirk’s accountant has determined
that their first year’s earnings per share (EPS) is expected to be $20. The
company expects a return on equity (ROE) of 25% in each of the next 5 years but
in the sixth year they expect to earn 20%. In the seventh year and forever into
the future, they expect to earn 15%. Also, at the end of the sixth year and
every year after that, they expect to pay dividends at a rate of 70% of
earnings, retaining the other 30% in the company. Kirk’s uses a discount rate
of 15%.

A.
Fill in the missing items in the following table:

Year

EPS

ROE

Expected Dividend
(end of year)

Present Value Of Dividend
(at time 0)

0

n/a

n/a

n/a

n/a

1

20

25%

0

0

2

25 =
1.25 x 20

25%

0

0

3

?

25%

0

0

4

?

25%

0

0

5

?

25%

0

0

6

?

20%

?

?

7

?

15%

?

?

8

?

15%

?

?

B. What would the dividend be in year 8?

C.
Calculate the value of all future
dividends at the beginning of year 8. (Hint: P7 depends on D8.)

D.
What is the present value of P7
at the beginning of year 1?

E. What
is the value of the company now, at time 0?
(10 marks)
9.4 You own one share in a company called Invest
Co. Inc. Examining the balance sheet, you have determined that the firm has
$100,000 cash, equipment worth $900,000, and 100,000 shares outstanding.

Calculate the price/value of each share in the firm, and explain how your
wealth is affected if:

A.
The firm pays out dividends of $1 per
share.

B.
The firm buys back 10,000 shares for $10
cash each, and you choose to sell your share back to the company.

C.
The firm buys back 10,000 shares for $10
cash each, and you choose not to sell your share back to the company.

D.
The firm declares a 2-for-1 stock split.

E.
The firm declares a 10% stock dividend.

F. The
firm buys new equipment for $100,000, which will be used to earn a return equal
to the firm’s discount rate.
(12
marks)

Do not submit these questions for grading until you have completed
all parts of Assignment 3, which is due after Lesson 11.

Lesson 10:
Assignment Problems

10.1 A. Calculate the mean and
standard deviation of the following securities’ returns:

Year

Computroids Inc.

Blazers Inc.

1

10%

5%

2

5%

6%

3

–3%

7%

4

12%

8%

5

10%

9%

B. Assuming these observations are drawn from a
normally distributed probability space, we know that about 68% of values drawn
from a normal distribution are within one standard deviation away from the mean
or expected return; about 95% of the values are within two standard deviations;
and about 99.7% lie within three standard deviations.

Using your calculations from part A, calculate the 68%, 95%, and 99% confidence
intervals for the two stocks. To calculate the 68%, you would calculate the top
of the confidence interval range by adding one standard deviation to the
expected return, and calculate the bottom of the confidence interval by
subtracting one standard deviation from the expected return. For 95%, use two
standard deviations, and for 99%, use three.

Your answer should show three ranges from the bottom of the confidence interval
to the top of the confidence interval.

C.
For each security, would a return of 14%
fall into the 68% confidence interval range? If not, what confidence interval
range would it fall into, or would it be outside all three confidence
intervals?

(This is the same as asking whether a return of 14% has less than a 68%
probability of occuring by chance for that security. If it’s not inside the 68%
confidence interval, it’s unlikely to occur, since it will only occur by chance
32% of the time. Of course, the 99% confidence interval is much more likely to
include the observed return, simply by chance. Only 1% of the time will it fall
outside the 99% CI. Pretty rare.)
(14 marks)

10.2 Some Internet research may be required to answer this question,
although it’s not absolutely necessary.

What could you do to protect your bond portfolio against the following kinds of
risk?

A.
Risk of an increasing interest
rate
B.
Risk of inflation increasing
C.
Risk of volatility in the markets
(6 marks)
10.3 You are starting a new business, and you want to open an office in
a local mall. You have been offered two alternative rental arrangements. You
can pay the landlord 10% of your sales revenue, or you can pay a fixed fee of
$1,000 per month. Describe the circumstances in which each of these
arrangements would be your preferred choice.
(10
marks)

Do not submit these questions for grading until you have completed
all parts of Assignment 3, which is due after Lesson 11.

Lesson 11:
Assignment Problems

11.1 In the northeast United States and in eastern Canada, many people
heat their houses with heating oil. Imagine you are one of these people, and
you are expecting a cold winter, so you are planning your heating oil
requirements for the season. The current price is $2.25 per US gallon, but you
think that in six months, when you’ll need the oil, the price could be $3.00,
or it could be $1.50.

A.
If you need 350 gallons to survive the
winter, how much difference does the potential price variance make to your
heating bills?

B. If
your friend Tom is running a heating oil business, and selling 100,000 gallons
over the winter season, how does the price variance affect Tom?

C.
Which one of you benefits from the price
increase? Which of you benefits from price decrease?

D.
What are two strategies you can use to
reduce the risk you face? Could you make an agreement with Tom to mitigate your
risk?

E. Assuming
you are both risk-averse, does such an agreement make you both better off?
(10 marks)

11.2 You have just received good news. You have a rich uncle in France
who has decided to give you a monthly annuity of €2,000 per month. You are
concerned that you will become accustomed to having these funds, but if the
currency exchange rate moves against you, you may have to make do with less.

A.
If you are living in Canada, what does
it mean for the currency exchange rate to move against you?

B.
Would moving to France mitigate some of
the risk? If so, how? If not, why not?

C. If
you want to stay in Canada, and your grandparents, who have retired to
Provence, receive a Canadian pension of C$1100 each, what could you do to
reduce the risk for all of you?
(9 marks)

11.3 You have learned about a
number of ways of reducing risk, specifically hedging, insuring, and
diversifying. In the table below, place an X in the cell for the technique
being used to reduce risk.

Hedging

Insuring

Diversifying

1

Placing
an advance order with Amazon.ca, which agrees to charge you the lower of the
advance price, and the price at the time your order is filled.

2

Purchasing
a call option on a stock you think may go up in price.

3

Selling
200 shares of IBM and buying a mutual fund that holds the same stocks as the
S&P index.

4

Selling
a debt owed to you for $.50 per dollar owed.

5

Agreeing
to a long-term contract with a supplier at a fixed price.

6

Agreeing
to a no-trade clause with the sports team that employs you.

7

Buying
a Mac and a PC.

8

Paying
a clown to perform for your child’s birthday party six months

(16 marks)

11.4 Suppose you own 100 shares of Dell Inc. stock. Today it is trading
at $15 per share, but you’re worried Michael Dell might retire again, causing
the price to go down. How would you protect yourself against his retirement,
assuming you don’t want to sell the shares today?
(5
marks)

When you have completed these questions, check to see that
Assignment 3 is complete and submit it for grading.

Assignment 3
Assignment 3 is due after you complete Lessons 9 to 11. It is
worth 20% of your final grade.



Prepare your responses to these assignment problems in a word
processing file; put financial data in a spreadsheet file. As you complete the
assignment problems for each lesson, add your responses to these files.
Do not submit your answers for grading until you have completed
all parts of Assignment 3.





Note: In assignments, show all calculations to 4 decimal places.
Lesson 9:
Assignment Problems



9.1 The Constant-Growth-Rate Discounted Dividend Model, as described
equation 9.5 on page 247, says that:


P0 = D1 / (k – g)
A. rearrange the terms to solve for:


i. g; and

ii. D1.

As an example, to solve for k, we would do the following:

1. Multiply both sides by (k – g) to get: P0 (k – g) = D1

2. Divide both sides by P0 by to get: (k – g) = D1/
P0


3. Add g to both sides: k = D1/ P0 + g
(8 marks)
9.2 Notation:
Let
Pn
= Price at time n
Dn
= Dividend at time n
Yn
= Earnings in period n










r = retention ratio = (Yn– Dn) / Yn=
1 – Dn/ Yn= 1 – dividend payout ratio


En = Equity at the end of year n

k = discount rate
g =
dividend growth rate = r x ROE
ROE = Yn
/ En-1 for all n>0.





We will further assume that k and ROE are constant, and that r and g are
constant after the first dividend is paid.
A. Using the Discounted Dividend Model, calculate the price P0
if




D1 = 20, k = .15, g = r x ROE = .8 x .15 = .12, and Y1
= 100 per share


B. What, then, will P5 be if:

D6 = 20, k = .15, and g = r x ROE = .8 x .15 = .12?

C.
If P5 = your result from part
B, and assuming no dividends are paid until D6, what would be P0?
P1? P2?




D.
Again, assuming the facts from part B,
what is the relationship between P2 and P1 (i.e., P2/P1)?
Explain why this is the result.




E.
If k = ROE, we can show that the price
P0 doesn’t depend on r. To see this, let
g = r x ROE, and ROE = Yn / En-1, and




since r = (Yn – Dn) / Yn , then D1=
(1 – r) x Y1 and


P0

=

D1
/ (k – g)


P0

=

[(1 –
r) x Y1] / (k – g)


P0

=

[(1 –
r) x Y1] / (k – g), but, since k = ROE = Y1 / E0


P0

=

[(1 – r) x Y1] / (ROE– r x
ROE)


P0

=

[(1 –
r) x Y1] / (Y1 / E0– r x Y1 / E0)


P0

=

[(1 –
r) x Y1] / (1 – r) x Y1 / E0), and
cancelling (1 – r)



P0

=

Y1
/ (Y1/E0) = Y1 x (E0 / Y1)
= E0



So, you see that r is not in the final expression for P0, indicating
that r (i.e., retention ration or, equivalently, dividend policy) doesn’t
matter if k = ROE.
Check that changing r from .8 to .6 does not change your answer in part A of
this question by re-calculating your result using r = .6.
(10
marks)







9.3 You are considering an investment in the
shares of Kirk’s Information Inc. The company is still in its growth phase, so
it won’t pay dividends for the next few years. Kirk’s accountant has determined
that their first year’s earnings per share (EPS) is expected to be $20. The
company expects a return on equity (ROE) of 25% in each of the next 5 years but
in the sixth year they expect to earn 20%. In the seventh year and forever into
the future, they expect to earn 15%. Also, at the end of the sixth year and
every year after that, they expect to pay dividends at a rate of 70% of
earnings, retaining the other 30% in the company. Kirk’s uses a discount rate
of 15%.










A.
Fill in the missing items in the following table:


Year

EPS

ROE

Expected Dividend
(end of year)


Present Value Of Dividend
(at time 0)


0

n/a

n/a

n/a

n/a

1

20

25%

0

0

2

25 =
1.25 x 20


25%

0

0

3

?

25%

0

0

4

?

25%

0

0

5

?

25%

0

0

6

?

20%

?

?

7

?

15%

?

?

8

?

15%

?

?

B. What would the dividend be in year 8?

C.
Calculate the value of all future
dividends at the beginning of year 8. (Hint: P7 depends on D8.)



D.
What is the present value of P7
at the beginning of year 1?



E. What
is the value of the company now, at time 0?
(10 marks)
9.4 You own one share in a company called Invest
Co. Inc. Examining the balance sheet, you have determined that the firm has
$100,000 cash, equipment worth $900,000, and 100,000 shares outstanding.






Calculate the price/value of each share in the firm, and explain how your
wealth is affected if:


A.
The firm pays out dividends of $1 per
share.



B.
The firm buys back 10,000 shares for $10
cash each, and you choose to sell your share back to the company.



C.
The firm buys back 10,000 shares for $10
cash each, and you choose not to sell your share back to the company.



D.
The firm declares a 2-for-1 stock split.


E.
The firm declares a 10% stock dividend.


F. The
firm buys new equipment for $100,000, which will be used to earn a return equal
to the firm’s discount rate.
(12
marks)





Do not submit these questions for grading until you have completed
all parts of Assignment 3, which is due after Lesson 11.


Lesson 10:
Assignment Problems


10.1 A. Calculate the mean and
standard deviation of the following securities’ returns:


Year

Computroids Inc.

Blazers Inc.

1

10%

5%

2

5%

6%

3

–3%

7%

4

12%

8%

5

10%

9%

B. Assuming these observations are drawn from a
normally distributed probability space, we know that about 68% of values drawn
from a normal distribution are within one standard deviation away from the mean
or expected return; about 95% of the values are within two standard deviations;
and about 99.7% lie within three standard deviations.





Using your calculations from part A, calculate the 68%, 95%, and 99% confidence
intervals for the two stocks. To calculate the 68%, you would calculate the top
of the confidence interval range by adding one standard deviation to the
expected return, and calculate the bottom of the confidence interval by
subtracting one standard deviation from the expected return. For 95%, use two
standard deviations, and for 99%, use three.






Your answer should show three ranges from the bottom of the confidence interval
to the top of the confidence interval.


C.
For each security, would a return of 14%
fall into the 68% confidence interval range? If not, what confidence interval
range would it fall into, or would it be outside all three confidence
intervals?





(This is the same as asking whether a return of 14% has less than a 68%
probability of occuring by chance for that security. If it’s not inside the 68%
confidence interval, it’s unlikely to occur, since it will only occur by chance
32% of the time. Of course, the 99% confidence interval is much more likely to
include the observed return, simply by chance. Only 1% of the time will it fall
outside the 99% CI. Pretty rare.)
(14 marks)







10.2 Some Internet research may be required to answer this question,
although it’s not absolutely necessary.


What could you do to protect your bond portfolio against the following kinds of
risk?


A.
Risk of an increasing interest
rate
B.
Risk of inflation increasing
C.
Risk of volatility in the markets
(6 marks)
10.3 You are starting a new business, and you want to open an office in
a local mall. You have been offered two alternative rental arrangements. You
can pay the landlord 10% of your sales revenue, or you can pay a fixed fee of
$1,000 per month. Describe the circumstances in which each of these
arrangements would be your preferred choice.
(10
marks)















Do not submit these questions for grading until you have completed
all parts of Assignment 3, which is due after Lesson 11.


Lesson 11:
Assignment Problems


11.1 In the northeast United States and in eastern Canada, many people
heat their houses with heating oil. Imagine you are one of these people, and
you are expecting a cold winter, so you are planning your heating oil
requirements for the season. The current price is $2.25 per US gallon, but you
think that in six months, when you’ll need the oil, the price could be $3.00,
or it could be $1.50.






A.
If you need 350 gallons to survive the
winter, how much difference does the potential price variance make to your
heating bills?




B. If
your friend Tom is running a heating oil business, and selling 100,000 gallons
over the winter season, how does the price variance affect Tom?



C.
Which one of you benefits from the price
increase? Which of you benefits from price decrease?



D.
What are two strategies you can use to
reduce the risk you face? Could you make an agreement with Tom to mitigate your
risk?




E. Assuming
you are both risk-averse, does such an agreement make you both better off?
(10 marks)



11.2 You have just received good news. You have a rich uncle in France
who has decided to give you a monthly annuity of €2,000 per month. You are
concerned that you will become accustomed to having these funds, but if the
currency exchange rate moves against you, you may have to make do with less.




A.
If you are living in Canada, what does
it mean for the currency exchange rate to move against you?



B.
Would moving to France mitigate some of
the risk? If so, how? If not, why not?



C. If
you want to stay in Canada, and your grandparents, who have retired to
Provence, receive a Canadian pension of C$1100 each, what could you do to
reduce the risk for all of you?
(9 marks)





11.3 You have learned about a
number of ways of reducing risk, specifically hedging, insuring, and
diversifying. In the table below, place an X in the cell for the technique
being used to reduce risk.




Hedging

Insuring

Diversifying

1

Placing
an advance order with Amazon.ca, which agrees to charge you the lower of the
advance price, and the price at the time your order is filled.



2

Purchasing
a call option on a stock you think may go up in price.


3

Selling
200 shares of IBM and buying a mutual fund that holds the same stocks as the
S&P index.



4

Selling
a debt owed to you for $.50 per dollar owed.


5

Agreeing
to a long-term contract with a supplier at a fixed price.


6

Agreeing
to a no-trade clause with the sports team that employs you.


7

Buying
a Mac and a PC.


8

Paying
a clown to perform for your child’s birthday party six months


(16 marks)

11.4 Suppose you own 100 shares of Dell Inc. stock. Today it is trading
at $15 per share, but you’re worried Michael Dell might retire again, causing
the price to go down. How would you protect yourself against his retirement,
assuming you don’t want to sell the shares today?
(5
marks)






When you have completed these questions, check to see that
Assignment 3 is complete and submit it for grading.


Answers

Related Questions

Science : Conduct a literature review that relate...

Conduct a literature review that relates directly to the length of stay or cost of adverse events associated with epidural use or drawbacks of epidura...

Writing : Discussion 1: The NYS Next Generation E...

Discussion 1: The NYS Next Generation ELA Standards Discussion #1:This is information you will need to reference throughout the course. Please bookmar...

Business Finance : Discussion question...

My class discussion question needs to be answer with at least 170 words with example. I would like for it to be in your own words. If not please cite...

Writing : Written Assignment:Initial Steps: Guidi...

***Content Area - English Grade 10 NYS***Written Assignment:Initial Steps: Guiding Questions- Begin with the end in mind:Here are 7 initial steps for...

Programming : User Interface Testing...

For this assignment, you will be conducting the usability test utilizing the usability questionnaire that you developed in Week 3. First, you will nee...

Writing : Program Budget Assignment...

Consider we all work for the same organization and your team has been assembled to create the budget for our brand new grant funded program, to improv...

Business Finance : Business project report...

See the attached file for details. It is a project report for setting up a new business. It is a team assignment and I need to complete the Executive...

Humanities : Written Assignment 1: Where I'm...

Written Assignment 1: Where I'm FromLiteracy is a major component of our individual lives, as well as society as a whole. It is something we are e...

Business Finance : The crowd and ecosystem projec...

Please see the attached files for assignment details. This is a team assignment and my part is to write Introduction for whole report, product descrip...

Humanities : Discuss the different views of the w...

Using at least three of the pre- Socratic philosophers in our textbook (you may use any of the figures we covered in class as well as those we didn’...

Business Finance : Answer questions...

Why did the “Great Stagflation” present a huge problem to the Keynesian Theory? Why could this theory not explain the phenomenon of stagflation?Su...

Science : I want you to write a project report...

Hi brother I want you to write a project report about HEC-RAS program, so please if you are not good in this program don't do this workMy course i...

Humanities : answer all the questions...

The first midterm exam is due **** at 11:59 p.m.Once the exam is accessed you will have three hours to complete it.Please review the instructions on t...

Business Finance : Economic Review Questions...

Review Questions (Final Exam)1. Why did the “Great Stagflation” present a huge problem to the Keynesian Theory? Why could this theory not explain...

Business Finance : Research the Internet for rece...

Examples of litigation cases against national public accounting firms include fines by regulatory authorities and censures by professional societies.W...

Writing : Christianity...

The Christian worldview provides an explanation for human nature and the story of the creation and fall (Gen. 1-3). A great deal of the suffering that...

Humanities : Please answer the following question...

Please answer two of the following questions in essays of approximately 4-5 double-spaced pages EACH. Your answers should be thoughtful, well organize...

Programming : i want some one to help me with the...

i need you to help me to check the grammer and you will see that i highlited the introdution part by red color that part you need to rewrite it and fi...

Humanities : Models of Grieving...

The death of a loved one is a significant event that everyone experiences. An individual's social environment, including societal and familial cul...

Business Finance : Six Sigma Yellow Belt Training...

Purpose of Assignment The purpose of this assignment is for students to receive Six Sigma Yellow Belt Training - Executing DMAIC (Define, Measure Anal...

Science : Rough Draft Quantitative Research Criti...

Use the practice problem and a quantitative, peer-reviewed research article you identified in the Topic 1 assignment to complete this assignment.Topic...

Business Finance : Oct 13 2018...

1,250-word count minimum with three scholarly sources in APA format. The questions ask for your opinion – be sure and back up your opinion through c...

Humanities : 3 short summaries and connotative...

carefully read the three "This I Believe" examples below. For each one, figure out how you can summarize the main belief and specific examples in your...

Programming : Write out an algorithm...

Review the information about designing an algorithm at the link below. Be sure to read pages two and three about pseudocode and flow charting as well....

If you didn't find the right answer

Ask Your Questions, We'll notify you once someone answers it