Problem 1
The
Teenie Tiny
Company is currently an un-levered firm with a beta of 1.3925. Since this is a start-up
company with significant impact on the social well-being of the country, the firm was given a tax-
exempt status for the first five years of operation. In the market, you observe that the latest
Government of Canada T-bill issue is yielding 3% and the market risk premium is 8%. This is the last
year for the company’s tax-exempt status. Assuming that the tax rate will be 40% and that there is no
cost for the risk of default. Use the following table to answer these questions:
Value of
Debt
R
D
Beta
EBIT
800,000
0
5.0%
1.392500
Tax Rate
40%
250,000
5.0%
1.483015
T-bill Rate
3.0%
500,000
5.0%
1.542274
TSX
11.0%
750,000
5.0%
1.607016
1,000,000
5.0%
1.678038
1,250,000
5.0%
1.756303
1,500,000
5.0%
1.842075
1,750,000
5.0%
1.939488
2,000,000
5.0%
2.047619
a)
Calculate the required rate of return for the un-levered firm.
(2 marks)
b)
Calculate the market value of the un-levered firm in proposition I.
(2 marks)
c)
Calculate the WACC for an un-levered firm in proposition II. No calculation required
(1
mark)
d)
Using the information from the table, calculate the value of the firm (proposition I), cost
of equity, and the WACC (proposition II) of the firm for each level of debt.
(16 marks)
Debt
Un-levered
TD
Levered
Equity
–
250,000.00
500,000.00
750,000.00
1,000,000.00
1,250,000.00
1,500,000.00
1,750,000.00
2,000,000.00
2
WACC
Wd
r*(1-T)
We
re
e)
Using the information from your calculations draw the graphs for proposition I and
proposition II.
(4 marks)
Problem 2 (31 marks)
Your best friend is in a senior position of the finance department of
Teenie Tiny
and you are having
lunch together after a round at the golf course. The discussion gets around to the fact that
Teenie Tiny
will lose their tax-exempt status and your friend mentions that all the debt that the company needs
will be financed using bonds with a 5 percent coupon. However, you remember that during a lecture
at SMU, it was mentioned that as a company issues more and more debt, the risk for the bondholders
will increase and bondholders will require coupon interest rates to increase as the amount of debt
increases. You have prepared the following table to assist in answering these questions:
Value of
Debt
R
D
Beta
EBIT
800,000
0
5.0%
1.392500
Tax Rate
40%
250,000
5.5%
1.483015
T-bill Rate
3.0%
500,000
6.0%
1.542274
TSX
11.0%
750,000
6.5%
1.607016
1,000,000
7.0%
1.678038
1,250,000
9.0%
1.756303
1,500,000
11.0%
1.842075
1,750,000
13.0%
1.939488
2,000,000
15.0%
2.047619
a)
Calculate the required rate of return for the un-levered firm.
(2 marks)
b)
Calculate the market value of the un-levered firm in proposition I.
(2 marks)
c)
Calculate the WACC for an un-levered firm in proposition II.
(1 mark)
d.
Using the information from the table, calculate the value of the firm (proposition I), cost of
equity, and the WACC (proposition II) each level of debt.
(16 marks)
Value of
Debt
r
D
Beta
Value of
the Firm
Cost of
Equity (r
e
)
WACC
0
250,000
500,000
3
750,000
1,000,000
1,250,000
1,500,000
1,750,000
2,000,000
e)
Calculate the present value of distress.
(4 marks)
Value of
Debt
PV of
Distress
0
250,000
500,000
750,000
1,000,000
1,250,000
1,500,000
1,750,000
2,000,000
f)
Graph (on 2 separate graphs) the information for proposition I and proposition II.
(4 marks)
g)
Briefly explain the amount of debt the company should use as a levered company.
(2 marks)
Problem 3 (4 marks)
The Halifax Corporation expects next year’s net income to be $15 million. The firms’ debt to equity
ratio is currently 2. The Halifax Corporation has $12 million of capital expenditures planned for
projects with positive NPV’s for next year. Management plans to maintain its existing debt to equity
ratio. According to the residual distribution model (assuming all payments are in the form of
dividends), how large should The Halifax Corporation’s dividend be next year?
Clearly label and show
your work!
Problem 4 (7 marks)
The Tooth Fairy Company’s stock currently sells on the Toronto Stock Exchange at $90 per share.
Below is their partial balance sheet:
Common Stock (1,500,000 shares outstanding)
30,000,000
Retained Earnings
15,000,000
Total
45,000,000
a)
The company is considering a 3 for 2 stock split. What will be the company’s stock price following
the stock split? How many shares will be outstanding? Show any changes to the Balance sheet.
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b)
If instead, the company does a 7.5% stock dividend. What will be the company’s stock price
following the stock dividend? How many shares will be outstanding? Show any changes to the
Problem 5 (4 marks)
Blue Jays Corp. declared a dividend of $1.10 per share on Wednesday July 4, payable on Thursday
August 16 to shareholders of record as of Thursday August 9. You will buy 1,000 shares of the Blue
Jays Corp. on Tuesday August 7 while your best friend plans to sell 500 shares on Wednesday August 8.
Include a time line with the key dates.
a)
Will you receive a dividend? If so, how much will you receive? Briefly explain.
b)
Will your best friend receive a dividend? If so, how much will they receive? Briefly explain.
Problem 6 (6 marks)
Dartmouth Discount Marketing Corporation (DDM) currently has 4,000,000 shares outstanding. The
market price is $80. What will the new number of shares and share price be after:
a)
DDM has a 4 for 1 stock split?
b)
DDM has a 15% stock dividend?
c)
DDM has a 2 for 7 reverse split?
Problem 7 (8 marks)
Queensland Lobster has 20 million shares of common stock outstanding and maintains a D/E ratio of 2.
The company expects earnings to be $60 million this year.
a)
Calculate the maximum investment funds available without issuing new equity and the increase
in debt financing required
(2 marks)
b)
If the firm uses a residual dividend policy and capital expenditures of $70 million are planned
for the coming year, what will the dividend per share be?
(3 marks)
c)
In part (b) how much borrowing will take place?
(1 mark)
d)
If no capital expenditures are planned for the coming year, what will the dividend per share be
under a residual dividend policy? How much will the company need to borrow?
(2 marks)
Problem 8 (10 marks)
Pasta Spaghetti Farms has decided to purchase a new spaghetti harvesting machine. The cost of the
machine is $450,000 and it has an economic life of 10 years. At the end of 7 years, the estimated
residual or salvage value is expected to be $110,000. Financing for the asset can be arranged through a
7 year commercial loan at 10 percent per year. An alternative is to lease the asset from Farmer Bill’s
Leasing Store making annual lease payments of $77,500 per year for the next 7 years with the first
payment due upon signing of the operating lease. The equipment has a CCA rate of 20 percent and the
farm has a tax rate of 25 percent. Pasta Spaghetti Farms cost of capital is 16 percent. Assuming the
project adds value for the owners, should the farm lease or buy the assets?
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The following problems do not need to be handed in as part of the
assignment. They are problems for you to practice in preparation for the
final exam.
Problem 10 (18 marks)
Your friend is the financial manager at Fish Oils Inc. in Eastern Passage that is a major supplier of fish oil
– a source of omega 3. Your friend is desperate and has asked you to examine the capital structure of
the firm and to make any necessary recommendations for the maximization of the value of the firm
and for the maximization of shareholder’s wealth. Your friend has provided the following information
on the firm:
Corporate tax rate 40%
Debt Outstanding $700,000 with a 12.0 percent coupon
Expected EBIT – expected forever.
State of
Probability
Expected
Nature
of State
EBIT
Boom
0.25
1,000,000
Normal
0.50
600,000
Recession
0.25
200,000
Company’s Beta 1.75958
Your research has provided the following information:
T-bill rate 4%
Return on the TSX 10%
a.
Given the above information, what is the value of the firm?
(4 marks)
b.
Given the above information, what is the WACC of the firm?
(2 marks)
c.
Additional research you have done has indicated the following information:
Level of
Interest
Debt
Rate
Beta
300,000
7.00%
1.59870
400,000
7.50%
1.63542
500,000
9.00%
1.67433
600,000
10.50%
1.71564
700,000
12.00%
1.75958
800,000
13.50%
1.80640
Prepare a short consulting report for your friend that provides a schedule of the value of the firm
and the WACC for the firm at the various levels of debt. In this report, include a graph of the value
of the firm (proposition I) and the cost of capital for the firm (proposition II)
(7 marks)
d
.
What significant finding does your report indicate for your friend and what is your
recommendation for the capital structure of the firm?
(2 marks)
e.
The company currently has 34,300 shares issued and outstanding. What is the market value of
each share?
(2 marks)
f.
You have decided to recommend a change in the capital for the firm. Assuming the markets are
efficient and that you have recommended a change in the capital structure that will maximize the
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value of the firm and maximize the value of the shareholders’ wealth. What is the issue price or
offer price for the shares?
(2 marks)
g.
Provide proof that the issue price or offer price is a fair price for all shareholders.
(2 marks)
Problem 11 (28 marks)
The following options price quotations are from the TSX Montreal Exchange.
a)
Compute the time value and intrinsic value for the following options.
Show your work!
(4 marks)
b)
Using the above information, you take the long position in a call option with an
exercise price of $40.00
and that expires in August
. Prepare a profit/loss (net payoff) schedule for your investments for market
prices of $25, $30, $35, $40, $45, $50 and $55 (
2 marks
)
c)
Graph your payoff from the call option.
(2 marks)
d)
Using the above information, you take the short position in a call option with an
exercise price of $40.00
and that expires in August
. Prepare a profit/loss (net payoff) schedule for your investments for market
prices of $25, $30, $35, $40, $45, $50 and $55 (
2 marks
)
e)
Graph your payoff from the call option.
(2 marks)
f)
Using the above information, you take the long position in a put option with an
exercise price of $40.00
and that expires in September
. Prepare a profit/loss (net payoff) schedule for your investments for
market prices of $25, $30, $35, $40, $45, $50 and $55 (
2 marks
)
g)
Graph your payoff from the put option.
(2 marks)
h)
Using the above information, you take the short position in a put option with an
exercise price of $40.00
and that expires in September
. Prepare a profit/loss (net payoff) schedule for your investments for
market prices of $25, $30, $35, $40, $45, $50 and $55 (
2 marks
)
i)
Graph your payoff from the put option
. (2 marks)
j)
Using the above information, you take the long position in the share and the long position in a put
option with an
exercise price of $40.00 and that expires in September
. Prepare a profit/loss (net payoff)
schedule for your investments for market prices of $25, $30, $35, $40, $45, $50 and $55 (
2 marks
)
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k)
Graph your payoff from the holding the share and buying the put option on the share. (2 marks)
l)
Using the above information,
you take the short position in a call option with an exercise price of
$40.00 and that expires in September and
the short position in a put option with an exercise price of
$40.00 and that expires in September.
Prepare a profit/loss (net payoff) schedule for your investments
for market prices of $25, $30, $35, $40, $45, $50 and $55 (
2 marks
)
m)
Graph your payoff from the call option.
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