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Unformatted text preview: W Time Value of Money 1. Your Father is about to retire. His ﬁrm has given him the option of $20,000 or an annuity of
$3,000 for ten years. Which is worth more, if an interest rate of 6% is utilized for the annuity?
Do not consider taxes and other factors. Your aunt is 69 years old. She has savings of $28,000. She had made arrangements to enter a
home for the aged on reaching the age of 80. Your aunt wants to decrease her savings by a
constant amount each year for ten years with a zero balance remaining. How much can she
withdraw each year if she cams 6% annuity on her savings? Her ﬁrst withdrawal would be a
year from now? The Beneﬁcent Loan Company has agreed to lend you funds to complete your last year MBA.
The company will give you $15,000 today if you agree to repay the loan four years from now
with a lump sum interest payment of $2,118 together with the principal. What annual rate of
interest is Beneficent charging? Mr. Right would like to buy a house at the end of ten years. How much money does he have to
save now in order to buy the house if hejust puts a lump sum into the bank now at 10% interest?
How much is it if he puts a certain ﬁxed amount at the beginning of every year, at 10% interest.
The house will be worth $260,000 at the end of year 10. Mary is planning to retire in 25 years. Thus far, she has accumulated $15,000 in a bank account,
earning 5% interest. When she retires, she would like to withdraw $24,000 from the account at
the end of the following 15 years. After the last withdrawal, her bank account balance will be zero. How much must Mary deposit (25 deposits) for the next 25 years, ﬁrst deposit start today
to be able to do this? Assume the account will continue to eam 8%. What is the ‘EAR’ for a quoted rate of 9% compounded quarterly? At this rate, how much will
you have accumulated in 5 years with a principal of $500? What if compounding is continuous?
Stephen and Company wants to borrow $100,000 from the Royal Bank at an annual interest rate
of 12%. The loan is to be repaid in 4 equal annual installments with the ﬁrst payment made a
year from now. if Stephen has a taxable rate of 40% and a cost ofcapital of 15%, what is the net
cost of the loan to the company? You want to have $1,000,000 to use for retirement in 35 years. If you can earn 1% per month ,
how much do you need to deposit on a monthly basis if the ﬁrst payment is made in one month?
What if the ﬁrst payment is made today? I You want to receive $5,000 per month for the next 5 years. How much would you need to . deposit today if you can earn 0.75% per month. Suppose you have $200,000 to deposit and can earn 0.75% per month:
a.) for how many months could you receive $5,000 payment? b.) how much could you receive every month for 5 years? Bonds
‘ .1. Given the following: equilibrium rate i*= 3%, 1? =8%, DRP =2%, LP=l% and MRP.=2%,. the rate of inﬂation is expected to stay censtant and a liquid market exists only for very short term government securities. a) What is the nominal risk—free rate? 13) What is the interest rate on long term government bonds? 2. Needsum Cash Company has just issued 15year bonds with a 9% coupon rate. a) What will be the market price of these bonds one year from now if investors at that time
are demanding a return of 10% for bonds of similar risk?
b) Would the market price One year from now for the same interest rates be higher or lower if the bonds have been issued for a 10—year term? 3. A bond issued 5 years ago, has a maturity of 15 years .lt has a coupon rate of 8% and it is
currently trading at $940. What is its Y—TM ? 4. The Southern Telephone Co. issued $20 million of bonds 10 years ago when interest rates
were at their all time high. The coupon rate was 11.5% and there is still 15 years to run on the
term of the bond. The Financial Vice President of Southern is currently considering calling
the bond issue and paying the 8% call premium to reduce the interest costs. Southern could
issue $20 million of debt at 9%. The underwriter would receive $800,000 to ﬂoat the issue.
Extra issue costs which are tax deductible would be $70,000. The timing of the call and the
new issue would also require an overlap of 2 months when Southern would require to service the debt of both the old and new issues. The tax rate is 48%. Should Southern go ahead with the new issue? I 5. What is the yield on a 9 month zerocoupon bond whose purchase price is $965.25 ? 6. What price would you pay for a 3month TBill with a yield of 3% and a face value of
$1,000? What yield would you get for a similar bill selling for $985? 7. A bond with a coupon of 6% and a YTM of 8% is trading at its fair market price; It has 9
years leit to maturity and pays interest semiannually.
If the prevailing rate in the market drops to 7%, what is the percentage change in the market price of this bond? How does it compare to the change in market interest rate? Common Shares 1.  A $100 preferred share bearing a dividend rate of 4% is being sold for $50. A new preferred
issue carrying a 10% dividend rate is to be sold by the same company. What price will investors be willing to pay for the new issues? 2. You are interested in purchasing shares of a large company. The current price of the share is
$30. The company is growing at a rate of 10% a year, and this growth rate is expected to
continue indeﬁnitely. The dividend paid for the year just end was 60 cents per share and you require a 13% on your investment. Will this purchase be advisable? 3. The Mann Company is all equity ﬁnanced and belongs to a risk class for which the
capitalization rate is 10%. It currently has outstanding 100,000 shares selling at $100/share.
The ﬁrm is contemplating the declaration of a $5 dividend at the end of the current ﬁscal year,
which just began. I
a) What will be the stock price at the end of the year if a dividend is not declared? What will
it be if one is declared?
b) Assuming that the ﬁrm pays dividend, has net income of $1 million, and makes new
investments of $2 million during the period, how many new shares must be issued if issued costs are negligible. 4. A company pays a current dividend of $4 a share. This is expected to continue until the end of
the ﬁfth year, at which time the dividend will drop to $3/share and continue at that level indefinitely. What price are you willing to pay for this share is you require a 10% return on your investment? 5. How much are you willing to pay for PanCanadian Ltdshares if it is expected to grow at 8%
for the ﬁrst 5 years, then followed by an indeﬁnite growth of 5%? ([tjust paid a dividend of $1.00/share and you require 13% on your investment.) 6. The common share of Company ABC is currently trading at $100 per share. It will generate an EPS of $1 0 a year from now. The company will not pay out any dividends but will invest all the earnings in a project that will generate:
a) 10% return to perpetuity 'b) 20% return to perpetuity and
c) 5% return to perpetuity 1f ABC’s cost of capital is 10%, what would you expect the share pricing to be for cases: a), b) and c). Ignore any tax effect. What can you conclude ﬁ'om this problem? NPV/IRR and Payments 1. XYZ Company is faced with 2 mutually exclusive projects. A will cost $300,000 and provides
cash flows (net) of $100,000 per year for 5 years. B will cost $150,000 and provide net cash
flows of $40,000 per year for 6 years. The cost of capital is 10%. a) Compute NPV, IRR, and payback period of each project. b) Which project should be accepted and why? c) Rework the problem using 18% cost of capital. Does this affect your answer in
part b)? 2. A project to modernize and expand the operations of a company will cost $800,000 now. It will
also increase annual running costs by $160,000. There will be an additional $130,000 per year
for hiring of additional staff to run this modern factory. Projected increased revenues would be
$500,000 per year before taxes. The project will last for 15 years and have no scrap value. The corporate tax rate is 46%. Disregard any depreciation or CCA. ' a) Find the [RR
b) If the IRR= 12%, what will the annual increase in revenue be?
c) What will be the NPV if R=12%? ' 3. Mr. Cyprus Clops, the president of Giant Enterprises, has to make a choice between two possible investments: 
 The opportunity cost of capital is 9%. Mr. Clops is tempted to take B, which has the higher
IRR. 3) Explain to Mr. Clops that this is NOT the correct procedure.
1)) Show him how to adapt the IRR rule to choose the best project
c) Show him which project has the higher NPV, Note: A and B are mutually exclusive Capital Budgeting Decisions 1. The Calgary Cabinet Company Ltd. anticipates an increase in demand for one of its products.
In order to meet this demand, a new cutting and ﬁnishing machine costing $10,000 must be
purchased. The machine will last ﬁve years and it will be sold at the beginning of the sixth year. Based on forecast sales levels, it is expected to generate an increase in net operating income,
before taxes, ofr$3,500 per year for ﬁve years. It is anticipated that when the machine is sold
for scrap, the CCA pool will still have assets in it. The capital cost rate applicable for CCA
calculations 'is 20%. Taxes are at a 40% rate; the salvage value is expected to be equal to the undepreciated capital cost of capital. Should Calgary Cabinet buy this new machine? Leacock Co is considering replacing their manual bookkeeping machines (NCR) with an IBM.
Leacock’s three NCRs were purchased 5 years ago for $10,000 each. Their life expectancy was
10 years with a salvage value of nothing. Current resale value is $3,000 each. The cost of the
IBM is $50,000 and it will have a zero disposal value in 5 years. Total costs of operating the
IBM is $46,500 per year and operating cost for each of the NCRs is $20,000. Tax rate is 40%;
Leacock’s cost of capital is 12% and depreciation is assumed to be a straight line. Should Leacock replace the machine? (Find the NPV, etc.) Myke Tyson Inc. is considering the purchase of a new ‘earcutting’ machine. This machine will
reduce manufacturing costs by $6,000 annually. The new machine will be in CCA class 8
(d=20%). The ﬁrm expects to sell the machine at the end of its 5year life for $10,000. The
ﬁrm also expects to be able to reduce net working capital by $18,000 when the machine is
installed. The ﬁrm’s marginal tax rate is 40% and it uses a 12% cost of capital to evaluate projects of this nature. If the machine costs $60,000, what is the NPV of the project? Clean Inc. has several detergent brands on the market. A recent market study costing $200,000,
indicated that the company should launch a new type of detergent called “Bright Whites”
(BW). The company has an empty building to house the new plant if the project proceeds.
Otherwise, the building can be rented out at $150,000 per year, payable at the beginning of
each year. Introducing BW will result in sales erosion of existing product lines estimated at
$90,000 per year. New machinery worth $4 million would be required for this facility and the
applicable CCA rate is 20%. The following table summarizes estimates of sales and production costs for “Bright Whites” for the next 10 cars. (In $million) _ Variable Cost 1st to inclusive 10 inclusive 7"" to inclusive Additional working capital of $0.5 million will also be required at the start of this project.
Salvage value on the machinery is expected to be $0.9 million. Clean Inc’s tax rate is 40%
and its minimum required return is 10%. Should Clean Inc. introduce “Bright Writes”?. Show all workings. 5. The Borstal Company has to choose between two machines which do the same job but have different life spans. The two machines have the following costs: —
—
— If the discount rate is 12%= which machine should Borstal buy? Risk and Return and CAPM 1. A ﬁrm is considering two mutually exclusive projects, their cash inﬂow probability distributions are summarized: Cash inﬂow Probabilit
n— 3) Determine the expected cash inﬂow from each project. b) Determine the standard deviation for each project’s probability distribution of cash
inﬂows. 0) Determine the coefﬁcient of variation of cash inﬂow. 2. The treasury bill rate is 4% and the expected return of the market is 12%. Based on the CAPM: a) Draw a graph showing how expected return varies with [3. b) What is the risk premium on the market, assuming that treasury bills arerisk free? e) What is the required return on an investment with a B of 1.5? d) If an investment with a B of 08 offers an expected return of 9.8%, does it have a
positive NPV? e) If the market expects a retum of 11.2% from a stock X, what is its 13 ? 3. The stock of United Merchants has a beta of 1.0 and a very high unique (diversiﬁed) risk. if the expected return on the market is 20%, what is the expected retum of the United Merchants’
stock? 4. If you are holding a stock which is currently in equilibrium and the required return on the stock
is 15% when the retum on the average asset is 10%, what will be the percentage change in the return of the stock if the return on the average asset increases by 30% and the stock has a beta
of2? 5. You believe that there is a 40 percent chance that stock A will decline by 10% and a 60 percent
chance that it will rise by 20%. Similarly, there is a 30% chance that Stock B will decline by
10% and a 70% chance that it will rise by 20%. The correlation coefficient between the two
stocks is 0.7. Calculate the expected return, the variance, and the standard deviation for each stock. Now calculate the covariance between their returns. 6. The standard deviation of the rate of return for Casper Products is 26%, while that for Doom
industries is 12%. If the correlation between their returns is 0.83, what is the standard
deviation of a portfolio composed of 20% of Casper and the remainder of Doom common stock? 7. The expected returns of four shares are presented below together with their corresponding E 13.0% 0.7
15.5%
12.0% — if the current riskfree rate is 9%, the expected rate of return on the market is 14%, which of the above share(s) is overvalued in the market? 8. There are 2 assets in the economy: the market index and the risk free T—Bill. The return of the
market index is 12% and that on the tBill is 5%. Can you create a portfolio with a [3 of 0.8.
What is the expected return of this portfolio? Cost of Capital 1. Ace Company currently has a capital structure composed only of mortgage bonds with a 10%
coupon and common share equity. It has never issued preferred shares. Current liabilities are
insigniﬁcant. Total assets at the most recent ﬁscal yearend were $l8 million and the ﬁrm’s total debt to asset ratio is 33%, which is considered optimal. The ﬁrm is considering investment projects requiring ﬁnancing of $1,200,000. The possible sources are as follows: D_eb_t; Could be issued today at a 12% coupon rate with a tenntomaturity of
10 years. Preferred: Could be issued today at a dividend rate of 7% and with underwriting fees
equivalent to I year’s dividend payment per $50 per value share. Common: New shares could be issued to net the ﬁrm 95% of the market price of common
shares, currently trading at $37.50. The ﬁnn’s annual dividend of $3.00 has not
changed since it was set 4 years ago. However, management feels that new
investments to be undertaken in ﬁxture years will allow an increase in annual
dividends at a rate of 5% per year. This increase is not expected to occur until
after the current dividend payment. The ﬁrm’s tax rate is 40% and it expects to have $424,000 available for asset expansion from
internally generated sources.
a) Will the ﬁrm be forced to issue new common equity? If so, what is the dollar amount of
external equity? b) What is the marginal cost of capitalf‘k” for the company? 2. Moquin Mouldings Inc. is a manufacturer of aluminum window frames. The firm is planning
to expand its production facilities and this will require an investment of $2.6 million. Having
been asked by the president to determine the ﬁrm’s weighted average cost of capital, you have assembled the following information for your calculations: Present Ca  ital Structure Mortae Bonds (8% cou on $5,000,000 Preferred Stock (7% dividend) $2,000,000 Common Stock ($10 ar value) $5,000,000 Retained Eamins $2,000,000 A a) New 10 year bonds, with a face value of $1000 and a coupon rate of 10%, can be sold to net the company $1000. b) New preferred stock, with a par value of $60 and paying a dividend of 10%, can be sold at a par value of $60 per share but the ﬁrm will incur ﬂoatation costs of $4 per share. 0) New common stock can be sold to net the ﬁrm $30 per share. Moquin common stock is
presently trading on the market at $33 with a price/earnings ratio of 11. Earnings and
dividends have been growing steadily over the past ﬁve years at a rate of 6% per year and
this trend is expected to continue. The ﬁrm has adopted a payout ratio of 50% as its dividend policy. Moquin considers its present capital structure to be optimal. There will be a $750,000 in retained earnings available for this expansion and the ﬁrm’s taxation rate is 40%.
a) What is the marginal or incremental cost of new debt, new preferred stock, new common stock and retained earnings? b) What is the ﬁrm’s weighted average ecst of marginal or incremental capital for 2004, if
it decides to raise the new capital in proportions equivalent to its present capital
structure, but within the limits of the due retained earnings which will be available for this expansion. Financial Leverage 1. Collins Electronics Ltd is considering additional ﬁnancing of $20,000. They currently have
$100,000 of 6% bonds and 10,000 common shares outstanding. The ﬁrm can obtain the ﬁnancing
through a 6% bond issue or sale of 1,000 common shares. The expected EBIT is $30,000 and a
40% tax rate: At what level of EBIT does the bond plan become superior to the common share plan? I I ,, "Formatted: Bullets and
"' Numbering i 2, ,Jason Inc. is considering the ﬁnancing of a $500,000 project with the following 2 plans: $500,000 debt at 3% interest Issue common shares at $20/share As it stands, the company does not have any debt and there are 200,000 common shares
outstanding trading at $20/share. Tax rate is 40%. a) What is the BE EBIT so that Jason would be indifferent in terms of EPS impact? [3) What is EPS for part a)? c) If EBIT is expected to be $420,000, what would be the corresponding EPS for each plan? d) Repeat c) for EBIT of $260,000. 3. You are given that Company ABC has a DIE ratio of 0.7, 3 ROI of 15% and a cost of borrowing Of 6%. If its DIE ratio is increased to 0.8, what is its percentage change in ROE? ABC’s tax
rate is 40%. Options 1.) Supposed you purchase7 call options with an exercise price of $50, where each call is priced at $4. You also purchase put contracts with an exercise price. of $50, where the puts are valued at $15. The current price per share is $55. Both options expire in 3 months. One contract calls for the sale of purchase of 100 shares. a.) What is the value of the call option investment if the share price at expiration drops
to $53 per share? b.) What is the value of the put option investment if the share price at expiration drOps
to $53per share? 2.) Assume the price of Stock X is $100 which is the same as the exercise price and in a
year’s time, it will be selling either at $125 or $80. The riskfree rate for both lending
and borrowing are at 8% for the time period under consideration.  Determine the fair value of the call today? 3.) A call option on ABC Corp stock with exercise price of $45 and 150 days to maturity
costs $2. The stock is currently selling at $44 and the riskfree rate is 2.75%.
According to the put—call parity, what must be the value of a put with the same exercise
price and time to maturity? ...
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This note was uploaded on 02/27/2012 for the course BUSINESS 101 taught by Professor All during the Spring '09 term at McGill.
 Spring '09
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