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(10 marks)
1. We have the following information for Athabasca Inc.
Athabasca, Inc.
2010 Income Statement
($ in millions)
Net Sales
Less: Cost of Goods Sold
Less: Depreciation
Earnings before interest and taxes
Less: Interest paid
Taxable Income
Less: Taxes
Net Income
Addition to retained earnings
Cash dividends paid
Cash
A/R
Inventory
Total CA
Net fixed assets
Total assets
2009
$ 100
350
440
$ 890
1,556
$2,446
519
$ 254
$1,384
605
180
599
80
156
$ 363
109
Athabasca, Inc.
12/31/09 and 12/31/10 Balance Sheet
($ in millions)
2010
2009
$ 121 Accounts payable
$ 400
425 Notes payable
390
410
Total CL
$ 790
$ 956 Long-term debt
500
1,704 Owners equity
Common stock
600
Retained Earnings
556
$2,660
Total liabilities
$2,446
2010
$ 350
370
$ 720
550
580
810
$2,660
The firm has 180 million common shares outstanding. Calculate the following:
a. Earnings retention ratio for 2010.
b. The dividend to be paid (in dollars) in 2011. Assume Athabasca is projecting a 20% increase in sales
c.
d.
e.
f.
for the coming year, and that cost of goods sold and general/administrative expenses remain a
constant percentage of sales. Also assume that depreciation, interest paid, and the firms tax rate
remain unchanged and that the firms dividend payout is 40%.
Capital intensity ratio based on the 2010 results.
Full capacity sales if Athabasca is currently operating at 70% capacity.
External financing needed (EFN) for 2011 if Athabasca is projecting a 20% increase in sales for the
coming year. Assume that assets, all costs, and current liabilities are proportional to sales but that
longterm debt is not proportional to sales. Also assume that the firms tax rate remains unchanged
and the dividend payout is 40%.
External financing needed (EFN) for 2011 if Athabasca is projecting a 20% increase in sales for the
coming year, with current assets, all costs, and current liabilities proportional to sales. Longterm debt
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g.
h.
2.
is not proportional to sales. Assume the firms tax rate remains unchanged, the dividend payout is
40%, and Athabasca is operating at 70% capacity.
Internal growth rate for 2010 (assume the dividend payout ratio is fixed at 40%).
Sustainable growth rate for 2010 (assume the dividend payout ratio is fixed at 40%).
State the assumptions that underlie the sustainable growth rate and interpret what the sustainable
growth rate means.
(5 marks)
The usual assumptions are: Costs and assets increase proportionately with sales, the dividend
payout ratio is fixed (or is given), the current debtequity ratio is optimal, no new equity sales are
possible. The sustainable growth rate is the maximum rate at which sales can increase with the
restriction that no new equity sales are possible and longterm debt increases only in an amount that
keeps the debtequity ratio fixed.
3.
Suppose a firm calculates its EFN and finds that it is negative. What are the firms options in this
case?
(3 marks)
With negative EFN, the firm has a surplus of funds that it can use to reduce current liabilities, reduce
longterm debt, buy back common stock, or increase dividends. As a leastbest alternative, the firm
could choose to add assets, but this requires some additional assumptions about NPVs, etc.
4.
a.
Fill in the blanks in the tables below.
For each of the following, compute the present value
c.
Solve for the unknown time period in each of the
d.
Solve for the unknown interest rate in each of the
5. Suppose your firm is planning to invest in a project that will generate the following income stream: a
negative flow $300,000 per year for 5 years, a positive flow of $450,000 in the sixth year, and a
positive flow of $650,000 per year in
years 7 through 9.
What is the present value of this income stream if the appropriate discount rate is 10% for the first 3
years and 13% thereafter?
(6 marks)
6.
Annuity A makes annual yearend payments of $976.50 for each of the next 10 years, while
investment B makes annual yearend payments of $600 per year forever.
Show your work for the following two questions:
(6 marks)
a. At what interest rate would you be indifferent between the two investments?
b. At interest rates above/below this breakeven rate, which investment would you choose and why?
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7.
A friend who owns a perpetuity that promises to pay $1,000 at the end of each year, forever, comes to
you and offers to sell you all of the payments to be received after the 25 th year for a price of $1,000.
Assume an interest rate of 10%. Be sure to show your work.
(5 marks)
a. Should you pay the $1,000 today to receive payments from the end of year 26 and onwards?
b. What value would you be willing to pay?
c. What does this suggest to you about the value of perpetual payments?
8.
Rob and Laura wish to buy a new home. The price is $300,000 and they plan to put 25% down. New
Rochelle Savings and Loan will lend them the remainder at 8% per annum, compounded semi
annually for a 25year term. The monthly payments are to begin in one month.
(10 marks)
a. How much will their monthly payments be?
b. Assuming they pay off the loan over the 25year period as planned, what will be the total cost
(principal + interest + down payment) of the house?
c. What will the outstanding balance of the loan be after 10 years, assuming they make the first 120
payments on time?
d. Suppose they want to pay off the loan in 15 years. How much extra must they pay each month to
do so?
e. Show the first six months in the amortization table for the 25year mortgage.
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9.
You are making plans for your retirement. You have just turned 30 and want to retire on your 65 th
birthday. At that time, you plan to move to the Caribbean, where you believe you can live comfortably
on $200,000 per year. You also understand that inflation can impact your enjoyment of retirement so
you would like the annual payments you receive to increase at a rate of 5% per annum. Your first
payment of $200,000 will occur at age 66. You intend to live in the Caribbean until your 85 th birthday,
when you will receive your last installment from your retirement fund, move back to Canada, and
freeload off your kids. You would also like to save enough money so that you can buy a new car when
you are 35, and pay for a big retirement party when you are 65. You figure you will need to have
$35,000 for the car and $10,000 for the party.
You estimate that you can earn an average return of 10% per annum on any money you invest over
the next 60 years. You have just begun working and plan on saving $11,000 per year until you are 35
years old. You will make your first deposit one year from now. To ensure that you are able to achieve
your objectives, you must first answer the following questions:
(15 marks)
a. How much will you have to accumulate before you retire?
b. How much will you have to save yearly, from your 36th to your 65th birthday, in order to accumulate
the amount from part (a) and also pay for your retirement party?
10. A bond is currently selling at 0.85 on its par value of $1,000. This bond has a maturity of 10 years and
a coupon rate of 8%, payable semiannually. If the inflation rate is 5%, what is the real yield on this
bond?
(5 marks)
11. The bonds of Microhard, Inc. carry a 12% annual coupon, have a $1,000 face value, and mature in 4
years. Bonds of equivalent risk yield 10%. Microhard is having cash flow problems and has asked its
bondholders to accept the following deal:
The firm would like to make the next three coupon payments at half the scheduled amount, and make
the final coupon payment be $300. If this plan is implemented and investors still demand a 10%
return, what will happen to the market price of the bond?
(5 marks)
12. J&J Enterprises wants to issue eighty 15year, $1,000 zerocoupon bonds. If each bond is priced to
yield 9%, how much will J&J receive (ignoring issuance costs) when the bonds are first sold?
(5 marks)
13. McGonigals Meats, Inc. currently pays no dividends. The firm plans to begin paying dividends in 3
years (at the end of t3). The first dividend at that time will be $1 and dividends are expected to grow at
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5% per annum thereafter.
Given shareholders demand a 12% return on their investments, what is the price of the stock today
(t0)?
(5 marks)
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14. Suppose that sales and profits of Oly Enterprises are growing at a rate of 30% per year. At the end of
4 years (t4) the growth rate will drop to a steady 5%. Oly recently paid a dividend of $1 per share. If
the required return is 20%, what is the value of one Oly share today (t 0)?
(Assume dividends grow at the same rate as earnings after year 4.) (5 marks)
15. Bradley Broadcasting expects to pay dividends of $1.12, $1.25, and $1.40 in one, two, and three
years, respectively. After that, dividends are expected to grow at a constant rate of 5% forever (so, t 4
to ). Stocks of similar risk yield 12%.
(7 marks)
a. What should the price of Bradley Broadcasting stock be today?
b. What is growth rate of the Bradley Broadcasting dividend during year 2?
c. How much is Bradleys stock price expected to increase during the first year?
d. What is the expected capital gains yield on Bradley Broadcasting stock during year 8?
1.
Define mutually exclusive investment decisions, and give an example of this type of decision.
(3 marks)
2.
Consider the following cash flow [100, + 230, 132]. We want to decide under what range of discount
rate this is an advantageous investment. But noting the change in sign, we conclude IRR is not a
suitable instrument.
(10 marks)
a.
Write the expression for NPV using the unknown r as discount rate.
b.
Write this expression as a function of [1/(1+r)].
c.
Show that the expression in (b) as a quadratic equation. Look this up if necessary.
d.
Solve the quadratic equation for its two roots.
e.
Prepare a table of NPV vs. r for r= 0,10,20,40,100%.
f.
Draw the graph of NVP vs. r.
g.
Under what range of r values is this an acceptable investment?
Noting that NPV increases then declines as r grows from 0 to 40%, determine at what
level of r NPV is a maximum (recall that d(NPV)/ds = 0, where NPV is a maximum). If you have
sufficient background, solve this using calculus. If not, graphically find the top of the NPV hill
h.
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(where slope = 0).
What is the maximum value of NPV? (There is one bonus point for the correct answer using
calculus).
3.
Consider the following information for projects A and B, which are mutually exclusive.
Year
0
1
2
3
4
5
Project A
100,000
31,250
31,250
31,250
31,250
31,250
Project B
120,000
0
0
0
0
200,000
(7 marks)
Note
A B = 100,000 (120,000) = +20,000
a.
At what discount rate will the two projects have the same net present value?
b.
At the discount rate of 10%, which is the better project?
(Hint 1: If the two projects have the same NPV, then NPV A NPVB = 0. You can subtract line by line.)
(Hint 2: If the difference in initial investment comes out positive and your financial calculator is
programmed to accept negative PV, adjust the FV accordingly.)
4.
Canadian Classics manufactures parts for classic automobiles. The CFO is considering the purchase
of a twoton press, which will allow the firm to stamp auto fenders. The equipment costs $250,000.
The project is expected to produce aftertax cash flows of $80,000 per year. Liquidating the equipment
will net the firm $10,000 in cash at the end of five years. The firm requires a 15% rate of return on all
investments. The firms tax rate is 38%. Ignore the effects of CCA.
(10 marks)
a. What is the payback period for the proposed investment?
b. What would happen to the payback period if the sale of the equipment at the end of five years
nets the firm $200,000, rather than $10,000?
c. What is the projects discounted payback period?
d. What is the projects net present value?
e. What is the projects profitability index?
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f. What is the projects internal rate of return?
(4 marks)
5.
a. Why is it important to consider additions to net working capital in developing cash flows?
b. What is the effect of an increase in net working capital on a projects operating cash flow?
c. What normally happens to the additions to net working capital as the project winds down?
6.
Given the following cash flows for two mutually exclusive projects (A and B), which project should be
chosen?
Assume that the required rate of return of both projects is 11%.
(Hint: Use EAC.)
Year\Project
0
1
2
3
4
5
6
7
8
A
$1,000,000
300,000
300,000
300,000
300,000
300,000
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B
$850,000
187,500
187,500
187,500
187,500
187,500
187,500
187,500
187,500
(10 marks)
7.
A firm is considering bidding on a project to produce eight widgets per year for the next four years. In
order to complete the project, the firm must lease facilities for $30,000 per year, purchase equipment
that costs $100,000, as well as pay labour and material costs of $19,000 per unit produced. The
equipment can be depreciated at the Class 8 CCA rate of 20%. At the end of the fourth year, it can be
sold for $10,000, and the asset class will remain open after the disposal of the equipment. In addition,
net working capital will increase by $50,000 if the project is undertaken, but these can be recovered at
the end of the project. The companys tax rate is 40%.
What is the minimum bid per widget if the firm requires 18% return on its investment?
(10 marks)
8.
You are evaluating a project for Ultimate Inc. The project produces chewresistant doghouses. You
estimate the sales price of these doghouses to be $500 and sales volume to be 2,500 units per year
over the projects threeyear life. Variable costs amount to $300 per unit and fixed costs (not including
depreciation) are $150,000 per year. The project requires an initial investment of $250,000 and this
will be depreciated on a straightline basis to zero over the threeyear project life. There will be an
initial net working capital investment of $90,000 (t0) and two further investments of $90,000 at the
beginning of each year thereafter. The full amount of working capital will be recovered at the end of
the projects life (i.e., $270,000 at t3). The tax rate is 35% and the required return on the project is
15%.
(10 marks)
a. What is the EBIT for the project in the first year?
b. What is the operating cash flow for the project in year 2?
c. Suppose the actual market value of the initial investment at the end of year 3 is $50,000. What is
the effect of the $50,000 salvage value on year 2 cash flows?
d. What is the NPV of this project?
9.
Describe how the inclusion of a strategic option can affect setting a bid price.
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(4 marks)
10. A project requires an initial investment of $10,000, straightline depreciable to zero over four years.
The discount rate is 10%. The firms tax bracket is 34%, and they receive a tax credit for negative
earnings in the year in which the loss occurs. Additional information for variables with forecast error is
shown below:
(10 marks)
Item
Unit Sales
Price/Unit
Variable cost/unit
Fixed costs
Base Case
3,000
$14
$9
$9,000
Lower Bound
2,750
$13
$10
$10,000
Upper Bound
3,250
$16
$8
$8,500
a.
What is the base case NPV for the project?
b.
What is the worst case NPV for the project?
c.
What is the best case NPV for the project?
d.
Suppose you want to conduct a sensitivity analysis for the possible changes from the base case
in unit sales. What is the IRR when the sales level equals 3,250 units?
e.
Suppose you are interested in the projects sensitivity to unit price. What is the NPV for the base
case at a price of $13 per unit?
f.
What is the base case accounting breakeven point?
g.
What is the base case cash breakeven point?
h.
What is the base case financial breakeven point? Ignore taxes.
11. A firm is considering the purchase of equipment which will cost $3 million. This equipment will last for
10 years, at the end of which it can be sold for $800,000. The CCA rate for this asset class is 30%,
and the firm expects to have other assets in this asset class at the end of year 10. This equipment is
expected to increase beforetax operating cash flows by $750,000 per year. However, in order to put
the equipment to use, an additional $150,000 will need to be invested in net working capital initially
(i.e., at t=0). The required rate of return is 16% and the firms marginal tax rate is 35%.
(12 marks)
a. Should the firm purchase this equipment?
b. Suppose that to arrive at the beforetax operating cash flows in part (a), we have used the
following estimates:
Fixed costs = $120,000
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Variable costs = 60% of sales
What is the Net Present Value of the new equipment if, in the bestcase scenario, we estimate
that fixed costs could be lower by 20% and sales revenues could be higher by 25%?
c. Given the information in (a), and assuming that fixed costs are $120,000 and variables costs are
60% of sales, what is the sales level at which Net Present Value equals zero? (In other words,
what is the financial breakeven sales level?)
12. A project has the following estimated data: price = $65 per unit; variable costs = $33 per unit; fixed
costs = $4,000; required return= 16%; initial investment = $9,000;
life = three years.
Ignore the effect of taxes and assume straightline depreciation to zero. (10 marks)
a. What is the accounting breakeven quantity?
b. What is the cash breakeven quantity?
c. What is the financial breakeven quantity?
d. What is the degree of operating leverage at the financial breakeven level of output?
1.
Explain the interactions among market efficiency, capital budgeting, and the cost of capital.
(5 marks)
2.
a. Give two examples of anomalies in the financial markets.
(5 marks)
b. What does the existence of these anomalies say about financial market efficiency?
3.
You bought one of BB Co.s 9% coupon bonds one year ago for $1020. These bonds make annual
payments and mature six years from now. Suppose you decide to sell your bonds today, when the
required return on the bonds is 10%. If the inflation rate was 4.2% over the past year, what would be
your total real return on investment?