Assignment 3Assignment 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 datain a spreadsheet file. As you complete the assignment problems for each lesson, add yourresponses 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 Problems9.1The Constant-Growth-Rate Discounted Dividend Model, as described equation 9.5 onpage 247, says that:P0 = D1 / (k g)A.rearrange the terms to solve for:i. g; andii. 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) = D12. Divide both sides by P0 by to get: (k g) = D1 / P03. Add g to both sides: k = D1 / P0 + g(8 marks)9.2 Notation: LetPn = Price at time nDn = Dividend at time nYn = Earnings in period nr = retention ratio = (Yn Dn) / Yn = 1 Dn/ Yn = 1 – dividend payout ratioEn = Equity at the end of year nk = discount rateg = dividend growth rate = r x ROEROE = Yn / En-1 for all n>0.We will further assume that k and ROE are constant, and that r and g are constantafter the first dividend is paid.FNCE 300v1Assignment 3August 5, 2014A.Using the Discounted Dividend Model, calculate the price P 0 ifD1 = 20, k = .15, g = r x ROE = .8 x .15 = .12, and Y1 = 100 per shareB.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 D 6, whatwould be P0? P1? P2?D.Again, assuming the facts from part B, what is the relationship between P 2 and P1(i.e., P2/P1)? Explain why this is the result.E.If k = ROE, we can show that the price P0 doesnt depend on r. To see this, letg = r x ROE, and ROE = Yn / En-1, andsince r = (Yn Dn) / Yn , then D1 = (1 r) x Y1 andP0=D1 / (k g)P0=[(1 r) x Y1] / (k g)P0=[(1 r) x Y1] / (k g), but, since k = ROE = Y1 / E0P0=[(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) = E0So, you see that r is not in the final expression for P0, indicating that r (i.e., retentionration or, equivalently, dividend policy) doesnt matter if k = ROE.Check that changing r from .8 to .6 does not change your answer in part A of thisquestion by re-calculating your result using r = .6.(10 marks)9.3You are considering an investment in the shares of Kirk’s Information Inc. The companyis still in its growth phase, so it wont pay dividends for the next few years. Kirksaccountant has determined that their first year’s earnings per share (EPS) is expectedto be $20. The company expects a return on equity (ROE) of 25% in each of the next 5years but in the sixth year they expect to earn 20%. In the seventh year and foreverinto the future, they expect to earn 15%. Also, at the end of the sixth year and everyyear after that, they expect to pay dividends at a rate of 70% of earnings, retaining theother 30% in the company. Kirk’s uses a discount rate of 15%.A. Fill in the missing items in the following table:FNCE 300v1Assignment 3August 5, 2014YearEPSROEExpectedDividend(end of year)Present ValueOf Dividend(at time 0)0n/an/an/an/a12025%00225 = 1.25 x 2025%003?25%004?25%005?25%006?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: P7depends 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)9.4You 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 isaffected 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 yourshare back to the company.C.The firm buys back 10,000 shares for $10 cash each, and you choose not to sellyour share back to the company.D.The firm declares a 2-for-1 stock split.E.The firm declares a 10% stock dividend.FNCE 300v1Assignment 3August 5, 2014F.The firm buys new equipment for $100,000, which will be used to earn a returnequal 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 Problems10.1A. Calculate the mean and standard deviation of the following securities returns:YearComputroids Inc.Blazers Inc.110%5%25%6%33%7%412%8%510%9%B. Assuming these observations are drawn from a normally distributed probabilityspace, we know that about 68% of values drawn from a normal distribution are withinone standard deviation away from the mean or expected return; about 95% of thevalues are within two standard deviations; and about 99.7% lie within three standarddeviations.Using your calculations from part A, calculate the 68%, 95%, and 99% confidenceintervals for the two stocks. To calculate the 68%, you would calculate the top of theconfidence interval range by adding one standard deviation to the expected return,and calculate the bottom of the confidence interval by subtracting one standarddeviation from the expected return. For 95%, use two standard deviations, and for99%, use three.Your answer should show three ranges from the bottom of the confidence interval tothe 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 threeconfidence intervals?(This is the same as asking whether a return of 14% has less than a 68% probabilityof occurring by chance for that security. If its not inside the 68% confidence interval,its 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)FNCE 300v1Assignment 3August 5, 201410.2Some Internet research may be required to answer this question, although its notabsolutely necessary.What could you do to protect your bond portfolio against the following kinds of risk?A. Risk of an increasing interest rateB. Risk of inflation increasingC. Risk of volatility in the markets(6 marks)10.3You are starting a new business, and you want to open an office in a local mall. Youhave 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 thecircumstances 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 Problems11.1In the northeast United States and in eastern Canada, many people heat their houseswith heating oil. Imagine you are one of these people, and you are expecting a coldwinter, so you are planning your heating oil requirements for the season. The currentprice is $2.25 per US gallon, but you think that in six months, when you’ll need theoil, the price could be $3.00, or it could be $1.50.A.B.If your friend Tom is running a heating oil business, and selling 100,000 gallonsover the winter season, how does the price variance affect Tom?C.Which one of you benefits from the price increase? Which of you benefits fromprice decrease?D.What are two strategies you can use to reduce the risk you face? Could youmake an agreement with Tom to mitigate your risk?E.11.2If you need 350 gallons to survive the winter, how much difference does thepotential price variance make to your heating bills?Assuming you are both risk-averse, does such an agreement make you bothbetter off?(10 marks)You have just received good news. You have a rich uncle in France who has decided togive you a monthly annuity of 2,000 per month. You are concerned that you willbecome accustomed to having these funds, but if the currency exchange rate movesagainst 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 tomove against you?B.Would moving to France mitigate some of the risk? If so, how? If not, why not?FNCE 300v1Assignment 3August 5, 2014C.11.3If you want to stay in Canada, and your grandparents, who have retired toProvence, receive a Canadian pension of C$1100 each, what could you do toreduce the risk for all of you?(9 marks)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 techniquebeing used to reduce risk.Hedging1Purchasing a call option on a stockyou think may go up in price.3Selling 200 shares of IBM and buying amutual fund that holds the samestocks as the S&P index.4Selling a debt owed to you for $.50per dollar owed.5Agreeing to a long-term contract witha supplier at a fixed price.6Agreeing to a no-trade clause with thesports team that employs you.7Buying a Mac and a PC.8DiversifyingPlacing an advance order withAmazon.ca, which agrees to chargeyou the lower of the advance price,and the price at the time your order isfilled.2InsuringPaying a clown to perform for yourchild’s birthday party six monthsbefore the birthday.(16 marks)FNCE 300v1Assignment 3August 5, 201411.4Suppose 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. Howwould you protect yourself against his retirement, assuming you don’t want to sellthe shares today?(5 marks)When you have completed these questions, check to see that Assignment 3 is complete andsubmit it for grading.FNCE 300v1Assignment 3August 5, 2014
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