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)

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)

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)

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 is due after you complete Lessons 9 to 11. It is

worth 20% of your final grade.

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

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

(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.

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?

If P5 = your result from part

B, and assuming no dividends are paid until D6, what would be
P0?

P1? P2?

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.

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

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)

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?

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.

The firm buys back 10,000 shares for $10

cash each, and you choose to sell your share back to the
company.

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.

firm buys new equipment for $100,000, which will be used to
earn a return equal

to the firm’s discount rate.

(12

marks)

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%

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.

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.

to the top of the confidence interval.

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?

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)

although it’s not absolutely necessary.

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

risk?

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)

all parts of Assignment 3, which is due after Lesson 11.

Lesson 11:

Assignment Problems

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.

If you need 350 gallons to survive the

winter, how much difference does the potential price variance
make to your

heating bills?

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?

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)

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.

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?

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)

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

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)

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)

Assignment 3 is complete and submit it for grading.