AP/ADMS 4540 Financial Management Winter 2011 Mid-term Exam Answer Key Instructor: Question 1 Question 2

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1 1 AP/ADMS 4540 Financial Management Winter 2011 Mid-term Exam Answer Key Instructor: Dr. William Lim Question 1 (8 marks) Calculate the duration and volatility of a 5-year, $1,000 face value, 14 percent coupon bond yielding 15 percent with coupons paid annually. Using its duration and volatility, calculate what happens to the price of the bond when the yield to maturity falls to 14 percent. What are the consequences for a financial institution that does not match the duration of its assets to the duration of its liabilities? Time Payment PV RV WV , Bond Price = =Duration Duration = D = years [4 marks for table and D] Volatility = v = -D/(1+r) = /1.15 = % [1 mark for v] When yield falls by one percent, price rises by 3.416% or $33.01 New price = $ $33.01 = $ [1 mark for new price] Without duration matching, say with duration of assets much longer than duration of liabilities, a financial institution's net worth (assets less liabilities) will suffer when interest rates rise. The value of longer duration assets will fall much more than the value of shorter duration liabilities, with a resulting loss of net worth and possible insolvency. [2 marks] Question 2 (15 marks) With Canadian interest rates still at historical lows, McGraw-Hill-Ryerson (MHR) is considering whether to take advantage of its lower cost of debt and refund its old bonds. Suppose the old issue comprises $30 million, 12 percent coupon rate (paid yearly) 20-year bonds that were sold 5 years ago. A new issue of $30 million, 15- year bonds can be sold with a coupon rate of 9 percent (paid yearly). A call premium of 6 percent will be required to retire the old bonds and floatation costs of $1 million will apply to the new issue. The marginal tax rate applicable is 50% and it is expected that there will be a one month overlap during which any funds can be invested in Treasury bills yielding 8 percent. Should MHR refund?

2 2 Question 3 (15 marks) Three BAS students and you are interviewing in a roundtable for employment in a prestigious asset management firm run by George and The Man. The interviewer decides to test potential employees by presenting them with the following question: Consider two mutually exclusive projects with net costs and benefits measured by the following cash flows: Year Project A Project B $1,000 -$1, $ $ $ $1,925 0 Which project should a firm undertake? The three BAS students gave different answers. Larry: It s obvious that a firm should undertake Project A because it offers $545 more in net benefits than does Project B. Curley: I think a firm should undertake Project B because it has a higher internal rate of return: approximately 19 percent as opposed to approximately 15 percent. Moe: Actually, there is really little difference between the projects. Take any discount rate, say 11.6 percent. The NPV of each project is about $112. It doesn t matter which one we choose. You are the fourth and final student to speak. 3a. Draw a diagram of the net present value profiles of both projects. (4 marks) 3b. Provide a valid critique of Larry, Curley and Moe s answers. (8 marks) 3c. Provide a brief description of the correct method by which the projects should be evaluated. (3 marks) 3a. (4 marks) NPV Profiles NPV r NPV(A) NPV(B) 3b. Larry does not take into account the time value of money. (The opportunity cost of capital is almost never zero.) Curley needs to realize the deficiencies of the IRR and the superiority of NPV over IRR. The first deficiency of IRR is that it does not ask, if the project is done, how much will the firm s value increase or decrease. Could a shareholder maintain the planned pattern of consumption and add something to it? Second, the NPV reflects the absolute size of the project while the IRR does not. The IRR is biased against larger projects. Third, the NPV uses the opportunity cost of capital as the reinvestment rate while the IRR reinvests at the project s own IRR. Thus IRR is biased against projects with returns farther into the future and may lead to myopic decision making. Fourth, NPV also has important technical advantages. For example, when nonconventional cash flows are considered, a solution for the project s IRR may not exist; in other instances, more than one IRR may be found for a single project. Fifth, NPV answers the question, would this project increase consumption for the investor. Moe has figured out the cross-over point (Fisher IRR), but needs to take into account the opportunity cost of capital to make the cross-over point relevant for decision making. (8 marks) 3c. First, find the opportunity cost of capital to determine the required return. Then use it to calculate the NPV of cash flows of projects A and B. (3 marks)

3 3 Question 4 (32 marks) After the interview, you meet (Curious) George and The Man (with the Yellow Hat). They are financial managers who network with other managers and analysts. Hoping to work in the industry, you follow them around to impress them and their friends with your knowledge of finance. 4a. You next meet Professor Wiseman. She provides you with the following table which gives some characteristics of two risky assets - stocks and bonds. Also shown are weights in the market portfolio P, which is assumed to be mean-variance efficient, i.e., it provides the highest expected return for its level of variance. Asset Weigh in Market Portfolio P Expected Return Standard Deviation Correlation With Stocks Correlation With Bonds Stocks 0.50? Bonds 0.50? If the expected return on the market portfolio P, E(r P ) is equal to 0.10 or 10 percent, what are the expected returns on stocks and bonds? Assume the risk-free rate, r f, is equal to 0.05 or 5 percent and show all calculations clearly. (8 marks) 4b. George and The Man visit Caillou, CFA, a Canadian mutual fund manager. Caillou uses arbitrage pricing to find asset values. Suppose there are many stocks in the market and that the characteristics of stocks A and B are as follows: Stock Expected Return Standard Deviation A B Suppose that it is possible to borrow at the risk-free rate and the correlation of stocks A and B is -1. What must be the value of the risk-free rate and why? (8 marks) 4c. Assume that security returns are generated by the single-index model, R i = α i + β i R M + ε i, where R i is the excess return for security i and R M is the market s excess return. The risk-free rate is 2%. Suppose also there are 3 securities A, B and C, characterized by the following data: Security β i E(R i ) (ε i ) A % 25% B % 10% C % 20% (i) If M = 20%, help Caillou calculate the variance of returns of securities A, B and C. (6 marks) (ii) Now assume there are an infinite number of assets with return characteristics identical to those of A, B and C, respectively. If one forms a well-diversified portfolio of type A securities, what will be the mean and variance of the portfolio s excess returns? What about portfolios composed only of type B and type C stocks? (3 marks) (iii) Is there an arbitrage opportunity in the market? If so, show Caillou the money. (3 marks) 4d. Assume the correlation coefficient between the Sid Science Fund and the S&P/TSX index is What percentage of Sid Science Fund s total risk is specific or unsystematic? (4 marks) 4a. Please see assignment 1 question 2, but this is now marked out of 8 marks. 4b. Since Stock A and Stock B are perfectly negatively correlated, a risk-free portfolio can be created and the rate of return for this portfolio, in equilibrium, will be the risk-free rate. To find the proportions of this portfolio [with the proportion w A invested in Stock A and w B = (1 w A ) invested in Stock B], set the standard deviation equal to zero. With perfect negative correlation, the portfolio standard deviation is (and you must show the working steps from the formula for portfolio variance): P = Absolute value [w A A w B B ] 0 = 0.08w A [0.04 (1 w A )] w A = The expected rate of return for this risk-free portfolio is: E(r) = ( ) + ( ) = 10% Therefore, the risk-free rate is: 10% otherwise arbitrage opportunities would exist.

4 c. i. = β + 2 (e) M A = ( ) + 25 = B = ( ) + 10 = C = ( ) + 20 = 976 ii. If there are an infinite number of assets with identical characteristics, then a well-diversified portfolio of each type will have only systematic risk since the non-systematic risk will approach zero with large n. The mean will equal that of the individual (identical) stocks. iii. There is no arbitrage opportunity because the well-diversified portfolios all plot on the security market line (SML). Because they are fairly priced, there is no arbitrage. 4d. The R 2 of the regression is: = 0.49 Therefore, 51% of total variance is unexplained by the market; this is nonsystematic risk. Question 5 (15 marks) George and The Man send you to Asia to meet a friend. After saying ni hao to Kai-lan, you learn that she is considering investing in several Asian portfolios. 5a. Suppose portfolio returns in the Asian market can be described by a 2-factor model with intercept (3 factors including intercept). Kai-lan asks you to determine the equation that describes the equilibrium returns for the following portfolios: (9 marks) Portfolio Expected Return (%) β i1 β i2 A B C b. Assume there is a portfolio D with β D1 = What is the equilibrium return on portfolio D? What is the sensitivity of portfolio D to factor 2 β D2? What is the relationship of portfolio D to factor 2? (4 marks) 5c. Suppose there is another portfolio E with the following characteristics: Actual Return = 26%; β E1 = 2.0 and β E2 = 1.5. Would you recommend investment in portfolio E to Kai=Lan? Why? (2 marks)

5 (9 marks for part a, 4 marks for part b (1 mark each for equilibrium return and factor 2 sensitivity and 2 marks for saying portfolio D has the same systematic risk as factor 2), 2 marks for part c.

5 5 (9 marks for part a, 4 marks for part b (1 mark each for equilibrium return and factor 2 sensitivity and 2 marks for saying portfolio D has the same systematic risk as factor 2), 2 marks for part c.) Question 6 (15 marks) Next, Kai-lan sends you into the jungle to meet Diego, the animal rescuer, and his sister, Alicia, the animal scientist. In order to save baby jaguars (Go Diego Go!), Diego and Alicia need compasses and a new jeep. 6a. A cheap compass costs $2 but is good only for one year. An expensive compass costs $5 but could be used for three years. Find the equivalent annual cost of cheap and expensive compasses when the annual discount rate is 10%. Next, find the annual discount rate such that the costs of cheap and expensive compasses are equal. (Hint: Use interpolation and start with r = 20%.) 6b. Suppose the old jeep was purchased ten years ago for $50,000. This vehicle was in CCA Asset Class 8 with a revised CCA rate of 5% (straight line over 20 years). Now suppose Diego receives an offer from Handy Manny to give this vehicle a free fixin so that it is good as new. The upper- and lower-bounds for benefits and costs for the next ten years are as follows, with the jeep expected (as before) to be obsolete with a salvage value of zero after ten years: Base Case Upper-Bound Lower-Bound Annual Benefits $10,000 $12,500 $7,500 Annual Costs $ 5,000 $10,000 $2,500 With the cost of capital (WACC) at 10% and the corporate tax rate at 40% (Diego had formed a corporation to fund his animal rescue operations which, amongst other ventures, manufactures Easy Ups for toddlers), calculate the NPV of the free fixin for the base-, best- and worst-case scenarios. (P/S Expect to ride in the Rocket with the Little Einsteins on the final exam!) See Quiz 2 for the answers.

AP/ADMS 4540 Financial Management Winter Mid-term Exam

1 Name: Student ID: Section: AP/ADMS 4540 Financial Management Winter 2011 Mid-term Exam Instructor: Dr. William Lim Time Limit: 2 hours Instructions: Answer all 6 questions of this exam in the spaces