Fin 501 Winter 2024 Midterm 240227 B01 Solution

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Apr 3, 2024

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FIN 501 Winter 2024 NAME: _______________________________________________ DO NOT TURN THIS PAGE UNTIL THE INSTRUCTION TO BEGIN IS GIVEN. BE SURE TO PUT YOUR NAME AND STUDENT ID NUMBER ON THE TOP OF THE NEXT PAGE OF THIS EXAMINATION. REMEMBER TO SHOW ALL WORK. THIS IS AN 80 MINUTE EXAM. PLEASE FOLLOW ALL DIRECTIONS. The next page contains general instructions. There are instructions accompanying the individual questions. GOOD LUCK! Words of wisdom: "Money doesn't make you happy. I now have $50 million, but I was just as happy when I had $48 million." /Arnold Schwarzenegger/ Unofficial sponsor:
2 Name: ________________________________ Student ID Number: ________________________ Finance 501 Midterm Exam Winter 2024 Professor András Marosi February 27, 2024 50 points This exam is composed of 5 multiple choice questions and 4 multi-part word problems. Some of the sub-questions rely on information calculated in other parts of the question. Carry through errors will not be penalized. You have access to a scientific or financial calculator, and you may have one 8½×11 inch “cheat sheet” with material on both sides. This sheet must be in human handwriting or prepared using standard size fonts and may not be mechanically altered (i.e. reduced by a photocopier). Show all work. Credit will not be given for answers without supporting information. Please limit the amount of extraneous information in your answers since it makes it difficult to ascertain your understanding. Read through the exam before starting. Good luck! Part 1 Multiple Choice __________ (10) Part 2 Word Problems Question 1: __________ (4) Question 2: __________ (11) Question 3: __________ (10) Question 4: _________ (11) Total: __________ (46)
3 Part 1 Multiple Choice: Please write the letter of the best available answer in the space provided OR circle your choice in the list of possible answers. Students choosing more than one answer will get no credit for that question! (2 points each) 1. John Mather was the Chief Executive Officer (CEO) of Liquor Barn (an Alberta company). A lawsuit against Mather alleged that in 2007 (when he was still CEO) Mather and other Liquor Barn managers bought liquor stores and then flipped (i.e. resold) them to Liquor Barn at inflated prices. If true, this allegation was an example of _________________ . a. the maximization of shareholder value b. the disadvantages of partnerships c. the difference between market value and book value d. a capital budgeting problem e. an agency problem 2. Which of the following is true: _________________________ a. Compounding will typically not lead to differences between quoted and effective rates. b. The effective periodic rate is the EAR divided by the number of compounding periods per year. c. The monthly compounded APR equals twelve times the effective monthly interest rate. d. When comparing investments, it is best to rely on the quoted rates. e. With monthly compounding, the APR will be greater than the EAR. 3. Your friend has been offered a choice between $1,000,000 prize in one year (at t = 1) and $10,000,000 prize twenty years from now (at t = 20). She tells you that it does not matter which one she chooses because the future value of the two prizes is the same. Assuming she is correct, what must be the interest rate (EAR)? __________________ a. 112.20% b. 12.88% = ($10,000,000/$1,000,000) 1/19 – 1 c. 12.20% d. 10.00% e. She cannot possibly be correct ($1 million is always worth less than $10 million). f. The EAR can only be determined using trial and error (or Excel/Financial Calculator). 4. We can be sure that a bond A is more interest rate sensitive than bond B if A has _____________________ compared to B (and A and B are identical in every other respect). a. higher coupon rate and longer maturity. b. more frequent coupons and shorter maturity. c. less frequent coupons and longer maturity d. higher coupon rate and shorter maturity e. lower coupon rate and shorter maturity 5. Berk Inc.’s dividend is expected to increase by g = 4% in perpetuity and investors require an r E = 12% return on Berk stock. What is Berk Inc.’s dividend yield? a. 8% = 12% – 4% Explanation: r E = Div 1 /P 0 + g => Div 1 /P 0 = r E – g b. 4% c. 12% d. 16% e. Insufficient information (P 0 and Div 1 are unavailable).
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4 Part 2 Word Problems: Please answer the questions below. Be sure to show all work. 1. (4 points) Time Value of Money Question: You will receive 12 annual payments starting with a $10,000 payment one year from today. The payments will increase at an annual growth rate of 10.25% (i.e. you will receive $11,025 at the end of year 2, $12,155.06 at the end of year 3 etc.) The interest rate is 10% ( APR , compounded semiannually ). What is the present value of this payment series? EAR = ___ 10.25% _______ . EAR = (1 + 0.1/2) 2 – 1 = 10.25% The present value of these payments is ___ $108,843.54 _ . r = g = 10.25% so: PVGA = T × C 1 /(1 + r) = 12 × $10,000/1.1025 = $108,843.54
5 2. (11 points) Mortgage Question: The Zariwnys live in Edmonton and they are interested in purchasing a house for $500,000. They are prepared to make a down payment equal to 25% of the total value of the house. Their bank offers them an interest rate of 6.0755% (APR, compounded semi-annually) on a mortgage loan with a 10-year term and a 25-year amortization. ( Reminder: The “term” of the mortgage simply refers to the length of the period for which the interest rate is fixed. Monthly payments are calculated for the full 25-year amortization regardless of the term). a. What is the monthly payment over the 10-year term of the mortgage? Down payment: 0.25 × $500,000 = $125,000 Mortgage: $500,000 – $125,000 = $375,000 EAR = (1+0.060755/2) 2 – 1 = 6.1678% EMR = (1+0.061678) 1/12 – 1 = 0.5% T = 25 ×12 = 300 C = ($375,000 × 0.005)/(1 – 1/1.005 300 ) = $2,416.13 b. What will the outstanding principal balance be at the end of the mortgage term of 10 years (right after you made the 120 th payment)? Time passed: 10 years = 10 × 12 = 120 months Remaining time: 15 years = 15 × 12 = 180 months OPB = ($2,416.13 / 0.005)(1 – 1/1.005 180 ) = $286,319.91 Continued next page!
6 Problem 2 continued: c. At the end of ten years, when the loan is renewed, the new monthly interest rate is 0.35% and the new monthly payment is $2,146.68. What is the new mortgage APR? ( Hint: One approach is to first, use EMR = 0.35% to calculate the new EAR, and then convert the EAR to an APR following the rules for Canadian mortgages. Can you think of a more efficient approach?) EAR = (1+0.0035) 12 – 1 = 4.2818% APR = 2 × [(1+0.042818) 1/2 – 1] = 4.2369% Or, use a faster approach: EAR = (1+0.0035) 6 – 1 = 2.11846% APR = 2 × 2.1409% = 4.2369% d. What is the interest portion of the 121 st mortgage payment? What is the principal portion of that payment? 121 st mortgage payment: $2,146.68 Interest portion: $286,319.91 × 0.35% = $1,002.12 Principal portion: $2,146.68 – $1,002.12 = $1,144.56
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7 3. (10 points) Bond Price and Duration Question: Five years ago, Freedom Airlines (FA), a U.S. air career, sold $25,000,000 worth of bonds with seven years until maturity. The bonds were sold at par and carry an annual coupon of 6%. A US Air (USA), a Freedom Airlines competitor, has just sold $18,000,000 worth of bonds to investors, also at par. A US Air bonds have two years until maturity and carry a coupon rate of 5% with coupons paid semi-annually . The terms of the FA and the USA bonds are the same, and they recently received identical ratings from the major bond rating agencies. a. What is your estimate of the market interest rate (EAR) on FA bonds today? (Hint: You do not need the result of part a. to solve parts b. and c. ! This is a concept question: you may need to think about it for a while, but if it takes more than 30 seconds to calculate it, you are “doing it wrong.” Try to come up with the best answer given the available information. ) USA bonds at par today with 5% semi-annual coupons: YTM USA = R C, USA = 5% USA and FA are very similar, so our best estimate of the interest rate on FA bonds is that they will have the same EAR as the USA bonds. EAR FA = EAR USA = (1 + 5%/2) 2 – 1 = 5.0625% b. Half a year (0.5) has passed since the USA bonds were originally issued. In the meantime, the yield-to- maturity of USA bonds has declined to 4%. What is the price of a single USA bond half a year after it was issued, given the above information? (Make sure you use the new interest rate!) r = YTM/2 = 4%/2 = 2% Maturity: 1.5 years or three periods Coupon: C USA = 0.05 × $1,000/2 = $25 P 0 = $25/1.02 + $25/1.02 2 + $1,025/1.02 3 = $24.51 + $24.03 + $965.88 = $1,014.42 Continued next page!
8 Problem 3 continued: c. Using the information and your results from part b. , calculate the duration (in years!) of a single USA bond today (0.5 years after it was issued). D = [($25/1.02) × 1 + ($25/1.02 2 ) × 2 + ($1,025/1.02 3 ) × 3] / $1,014.42 = 2.93 periods D = 2.93/2 = 1.46 years
9 4. (11 points) Equity Question: You have collected the following information about four publicly traded companies: EastJet West Air Machine Intelligence Inc. Air North Stock Price (P 0 ) $44 $30 $100 $18 Expected Earnings-per-Share at t = 1 (EPS 1 ) $4 $3 $1 $2 P/E Ratio ((P 0 /EPS 1 ) 11 10 SouthBest Airlines is expected to report $5,000,000 in earnings one year from today (Earnings 1 = $5 million at t = 1). SouthBest has 1,000,000 shares outstanding. a. Use the information above to estimate the value of a SouthBest airline share. AirNorth P/E ratio = $18/$2 = 9 Ignore AI company! => Average Industry P/E Ratio = (11 + 10 + 9)/3 = 10 SouthBest EPS 1 = $5,000,000/1,000,000 = $5 Estimated value of a SouthBest share: P 0 = $5 × 10 = $50 b. Rishi is an equity analyst who just left Barkleys Investment Bank for a job at Boldman Socks. Your job is to calculate the value of a single share of SouthBest stock based on Rishi’s incomplete notes that he left behind on his desk. Rishi’s notes (in bold): Equity cost of capital: r E = 10% Number of shares outstanding: 1,000,000 Expected Earnings in one year: Earnings 1 = $5 million Book Value of Equity: BE 0 = $62,500,000 Payout ratio: Div 1 /EPS 1 = 60% (expected to be maintained indefinitely) Return on new investment: ROE = _____________ (expected to be maintained indefinitely) Perpetual growth rate: g = ________________ (expected to be maintained indefinitely) Value per share: P 0 = ____________________ ROE = $5 million / $62,500,000 = 8% < r E = 10% (investing is a bad idea) b = 1 – 0.6 = 0.4 (reinvestment rate or plow back ratio) g = 0.4 × 0.08 = 3.2% Div 1 = 0.6 × EPS 1 = 0.6 × $5 = $3 P 0 = $3/(0.1 – 0.032) = $44.12 Continued next page!
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10 Problem 4 continued: c. Akshata is a former equity analyst at Barkleys Investment Bank. She was recently promoted to work on Barkley’s Mergers and Acquisitions team. You are reviewing her notes and realize that, compared to Rishi, she made different assumptions about the SouthBest valuation. Your job is to calculate the value of a single share of SouthBest stock based on Akshata’s incomplete notes that she left behind on her desk. Akshata’s notes (in bold): Equity cost of capital: r E = 10% Number of shares outstanding: 1,000,000 Expected Earnings in one year: Earnings 1 = $5 million Book Value of Equity: BE 0 = $62,500,000 Payout ratio: Div 1 /EPS 1 = 100% (expected to be maintained indefinitely) Return on new investment: ROE = _____________ (expected to be maintained indefinitely) Perpetual growth rate: g = ________________ (expected to be maintained indefinitely) Value per share: P 0 = ____________________ ROE = $5 million / $62,500,000 = 8% < r E = 10% (investing is a bad idea, also there is no need to repeat this calculation, can just copy result from part b.) b = 1 – 1 = 0 (reinvestment rate or plow back ratio) g = 0 × 0.08 = 0% Div 1 = 100% × EPS 1 = $5 Use perpetuity formula instead of growing perpetuity since g = 0. P 0 = $5/0.1 = $50 d. Consider all the information in Problem 4, who would you consider the better analyst: Rishi or Akshata? Briefly explain. Akshata is probably better, for two reasons: - Her valuation considers that SouthBest’s value would be higher if the company started paying out 100% of earnings as dividends. - Her valuation is more consistent with the price we would get using the average industry firms multiple.