FNCE300v1 – The Constant-Growth-Rate Discounted Dividend Model, as described equation 9.5 on page 247

QUESTION

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.

 

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