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.
B.
Blazers Inc.
1
10%
5%
2
5%
6%
3
–3%
7%
4
12%
8%
5
10%
9%
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.
11.2
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)
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
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 before the birthday.
Insuring
Diversifying
(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.