Corporate finance final exam, Exams of Corporate Finance

Download Corporate finance final exam and more Exams Corporate Finance in PDF only on Docsity! Corporate Finance (FNCE 611/612) PLACEMENT/WAIVER EXAM – PART 1 Corporate Finance (FNCE 611/612) PLACEMENT/WAIVER EXAM–PART 1
Instructions 1. Please don’t open the exam until you are told to do so. 2. This exam is being administered under the University’s rules for academic conduct; the Code of Academic Integrity applies. 3. The exam consists of 5 multiple choice questions and 4 essay questions. 4. Use the white spaces (and backs of pages) in this question booklet as scratch paper for the multiple choice questions. Your final answers should be indicated with a pen in the appropriate boxes on page 1 of your answer sheet booklet. 5. Write your answers to the essay questions in the answer sheet booklet. You can use a pen or a pencil. If you need more answer sheets, you can request them, and they will be provided for you. Do not use the backs of answer sheets, since these back pages will not be graded. 6. IMPORTANT: Print your name and Penn ID number on the first page of your answer sheet booklet. 7. This is an open-book exam, i.e. you are free to use any course material. You are allowed to use a pocket calculator. Laptop computers and cell phones are not allowed. 8. You have two hours. The time left in the exam will be announced periodically. If you finish early, you can quietly hand in your answer sheet booklet and leave, unless there is less than ten minutes left in the exam. 9. Please stop writing when requested to. There will be a penalty of 20 points for the people who don’t. 10. Remain seated until all the answer sheet booklets (not just yours) have been collected. Corporate Finance (FNCE 611/612) PLACEMENT/WAIVER EXAM – PART 1 PART I: MULTIPLE CHOICE QUESTIONS (Total points: 25) INSTRUCTIONS: A correct answer to each of these questions is worth 5 points. An incorrect answer is worth 0. Also, for each question that you choose not to answer, you get 1 point. If you do choose to answer, write your answer clearly in the appropriate box on page 1 of your Answer Sheet Booklet. Your answers should be capital letters written with a pen. An empty box will be interpreted as a “no answer.” 1. A 10-year annuity paying $x at the beginning of every year (i.e. the first of ten payments is made today) is worth the same (today) as an annuity of $300 payable every 6 months for 10 years (20 payments), the first payment of which is due 66 months from now. If the annual interest rate (compounded annually) is 3%, find x. a. $232.73 d. $508.11 b. $502.48 e. $521.42 c. $506.23 2. A machine costing $3,000 must be replaced at the end of 8 years. The resale value of the machine at the time of replacement is $600. At what annual discount rate (compounded annually) would it be equally economical to use a similar machine costing $4,000 with a life of 8 years and a resale value of $1,900? (Assume that there is no taxes.) a. 2.4% d. 3.3% b. 2.7% e. 3.6% c. 3.0% 3. What is the present value of 15 payments of $100 each received every 18 months (the first one occuring in 18 months from now), if the annual discount rate (compounded annually) is 9%? a. $620.43 d. $951.28 b. $875.56 e. $1,209.10 c. $930.61 4. Corporate managers can maximize shareholder wealth by choosing positive NPV projects because: a. all investors have the same preferences. b. the unhappy shareholders can sell off their shares. c. given the existence of financial markets, investors will be satisfied with the same real investment decisions regardless of personal preferences. d. managers are wiser than shareholders regarding investments. e. none of the above. Corporate Finance (FNCE 611/612) PLACEMENT/WAIVER EXAM – PART 1 4. (25 points) The following bonds are traded in a well functioning market: a. Assuming that the coupon bond (bond B) makes only annual payments, what discount factors (DF1, DF2) are imbedded in these prices? NOTE: Show all your calculations; no points will be given for answers found by a sophisticated calculator. b. What are the 1-year, and 2-year spot rates (r1 and r2)? c. Suppose that you would like to purchase a two-year coupon bond with a face value of $10,000 and a coupon rate of 6% (with annual coupon payments). Since such a bond is not traded in this economy, what portfolio of bonds A and B could you form to satisfy your needs (i.e. how can you replicate this bond using the original two bonds). NOTE: Make sure to describe that portfolio clearly, i.e. what you are buying/selling. d. What is the exact yield to maturity on i. bond A; ii. bond B. NOTE: Again, show all your calculations; no points will be given for answers found by a sophisticated calculator. In particular, you will need to use the following formula for the roots of ax2 + bx + c = 0: ______ _ x = −b ± ÷b 2 − 4ac____________ . 2a Your answers should have at least two decimals, like 9.53%. BOND TYPE FACE VALUE COUPON MATURITY PRICE A Zero Coupon Bond $100 — 1 year $92.00 B Coupon Bond $100 8% 2 years $101.32 Corporate Finance (FNCE 611/612) PLACEMENT/WAIVER EXAM – PART 2 Corporate Finance (FNCE 611/612) PLACEMENT/WAIVER EXAM–PART 2
Instructions PLEASE READ THESE INSTRUCTIONS 1. Please don’t open the exam until you are told to do so. 2. This exam is being administered under the University’s rules for academic conduct; the Code of Academic Integrity applies. 3. The exam consists of 5 multiple choice questions and 4 essay questions. 4. Write all of your answers in the blue booklets. If you need more booklets, you can request them, and they will be provided for you. 5. You must cross out anything that you do not wish to have marked. For the multiple choice questions, please write your letter answers with a pen. (You can do your calculations in either pen or pencil. The calculations will not be marked, only the letter answer, so no partial credit is given). For the essay questions, you may use either a pen or a pencil; partial credit may be given. 6. Important: Print your name and Penn ID number on the first page of your answer sheet booklet. Also indicate which section of the course you attend, so I can return your exam in the proper section. 7. This is an open-book exam, i.e., you are free to use any course material. You are allowed to use a pocket calculator. Laptop computers and cell phones are not allowed. 8. You have two hours. The time left in the exam will be announced periodically. If you finish early, you can quietly hand in your answer sheet booklet and leave, unless there is less than ten minutes left in the exam. 9. Please stop writing when requested to. There will be a penalty of 20 points for the people who don’t. 10. Remain seated until all the answer sheet booklets (not just yours) have been collected. Corporate Finance (FNCE 611/612) PLACEMENT/WAIVER EXAM – PART 2 PART I: MULTIPLE CHOICE QUESTIONS (Total points: 25) INSTRUCTIONS: A correct answer to each of these questions is worth 5 points. An incorrect answer is worth 0. Also, for each question that you choose not to answer, you get 1 point. If you do choose to answer, write your answer clearly on page 1 of your blue booklet. Your answers should be capital letters written with a pen. Only the final answer will be marked and there shall be no partial credit for the multiple choice questions. 1. (5 points) Suppose that the price of the stock is S0, and its annual volatility is s. Suppose also that the annual riskfree rate is rf . According to Black-Scholes, what is the price of a European put option with a strike price of Xmaturing in T years? NOTE: In the answers below, we use a. b. c. d. e. 2. (5 points) Which of the following statements are true? I. In a perfect capital market, it is advantageous for the firm to issue debt (vs. equity) to finance a project, because the cost of debt (rD) is always smaller than the cost of equity (rE). II. The reason that Modigliani and Miller’s Proposition I does not hold in the presence of corporate taxes is because levered firms pay less taxes than identical unlevered firms. III. Equity financing is always better than debt financing when the personal tax rate on equity income (tE) is smaller than the personal tax rate on interest income (tD). a. I and II d. I, II and III b. I and III e. fewer than two statements are true. c. II and III Corporate Finance (FNCE 611/612) PLACEMENT/WAIVER EXAM – PART 2 2. (10 points total) Firms A and B are both unlevered. The shares of both companies are currently trading at $100, and both offer an annual pre-tax return of 10%. In the case of firm A, the return is entirely in the form of a dividend yield (i.e., the company pays a regular annual dividend of $10 a share). In the case of firm B, the return comes entirely as capital gain (the shares appreciate by 10% a year). Suppose that an investor buys a share of each firm today, and plans to sell them in 10 years. Suppose that dividends and capital gains are both taxed at 30%. a. (5 points)What is the annual after-tax yield (rate of return) on firm A’s share over the 10-year period? b. (5 points)What is the annual after-tax yield (rate of return) on firm B’s share over the 10-year period? 3. (25 points total) The Jack & Diane (JD) Corporation is considering a new 5-year project. Since this project is very different from JD’s current operations, the adjusted present value will be used to value the project. The project requires an initial investment of $750,000 in new assets, which will be depreciated straight-line to 0 over the project’s 5-year life. These assets will be worthless in five years, i.e., they will not be resold. (Assume that the depreciation tax shields can be discounted at the project discount rate). Each year for five years, the project is expected to generate pre-tax revenues of $600,000 and to require pre-tax costs of $240,000. The entire project will be financed through a 5-year bank loan with an annual rate of 10%. The principal on the loan will be repaid in equal installments of $150,000 each (i.e., each year, the company pays $150,000 in principal, and pays the interest on the outstanding loan). It is estimated that the pre-tax costs (payable at time zero) of negotiating the loan will be 4% of the amount borrowed. The project’s risk is very similar to the risk of Tommy & Gina (TG) Inc.’s assets. This firm is currently financed by 100,000 shares worth $12.50 each, and $750,000 worth of debt. The beta of TG’s stock is 1.5, and the company borrows at a rate of 11%. The riskfree rate in the economy is 8%, and the expected return on the market is 18%. The current corporate tax rate is 45% (assume that it applies to both JD and TG). Ignore personal taxes. a. (8 points)What would be the appropriate discount rate for the project, if it were all-equity financed? b. (17 points)What is the adjusted present value of the project? Corporate Finance (FNCE 611/612) PLACEMENT/WAIVER EXAM – PART 2 4. (20 points total) During the upcoming year, the stock price of Delinquent Jesters Inc. (DJ) is expected to go up to $290 or down to $170 with equal probabilities. The beta of the stock is equal to 0.75. The annual riskfree rate is 10.5%, and the expected annual return on the market is 16.5%. You are interested in replicating and pricing a European call option on DJ’s stock. The option has a strike price of $212, and will mature in one year. a. (4 points)What is the current price of DJ’s stock? b. (6 points) Using the stock and borrowing/lending (at the riskfree rate), form a portfolio that will replicate the call option. How many shares of DJ will you buy/sell, and how much money will you borrow/lend? c. (3 points) Use the portfolio derived in part (b) to price the call option. d. (4 points)What is the beta and expected return of the call option? e. (3 points) Using the result from part (d), show that the price of the call option found in part (c) can also be derived by discounting the expected cash flow of the option. Corporate Finance (FNCE 611/612) PLACEMENT/WAIVER EXAM – PART 1 ANSWERS Placement /Waiver Exam-Part 1 Answers FNCE 611/612 - Corporate Finance (FNCE 611/612) PLACEMENT/WAIVER EXAM - PART 1 ANSWERS. Therefore, alternative B is the best alternative, since it involves the lowest costs. 4. (a) (6 points) Since the price of every bond must be the sum of its discounted cash flows, the discount factors must solve: 100DF, + 92.00 (1) 8DF, + 108DF, 101.32 (2) Using (1), we have DF, = 0.92. Using this value for DF, in (2), we get _ 101.32 — 8(0.92) ll i DFy ua = 0.87, (b) (4 points) The discount factors can be written as 1 DF, = ——_. Fry Therefore, 1 = t= 5 h= DA 1 = 8.69565%, and 1 = — TR 1 =7.21125%. DF} (c) (7 points) The bond that you would like to purchase will pay 6%($10,000) = $600 at the end of the first year, and $10,600 at the end of the second year. Let us form a portfolio containing a quantity n4 of bond A, and ng of bond B. We would like this portfolio to pay $600 at the end of the first year, and $10,600 at the end of the second year. Mathematically we would like n4 and ng to satisfy: 100n4 + 8ng = 600 (1) + 108nz = 10,600 (2) Using (2), we have ng = 4g600 = 98.148148. Using this value for mg in (1), we get _ 600 — 8(98.148148) as 100 ~ Therefore, the portfolio that would replicate the 6% coupon bond would consist in selling 1.851852 units of bond A, and buying 98.148148 units of bond B. (d) (i) (3 points) The yield on a zero-coupon bond with a maturity of t years is simply the t-year spot rate. Therefore the yield y4 of bond A is y4 = 171 = 8.69565%. (ii) (5 points) The yield to maturity yg for bond B has to satisfy 108 ——+ 5 1+yp (1+yz) Solving for « using the quadratic equation formula, we find 1 —8 + \/(8)? — 4(108)(—101.32) l+yp 2(108) —1.851852. 101.32 = € 108e? + 8% — 101.32 = 0, where « = 1l+yB" = 0.9327379. Solving for yg (ignoring the “minus” root, which has no economic meaning), we find yp = 7.26721%. Corporate Finance (FNCE 611/612) PLACEMENT/WAIVER EXAM – PART 2 ANSWERS Placement /Waiver Exam-Part 2 Answers FNCE 611/612 - Corporate Finance (FNCE 611/612) PLACEMENT/WAIVER EXAM - PART 2 ANSWERS. Letting n denote the number of shares repurchased and S' the new price per share, we must have nS = 3,750,000 (300,000 —n)S = 9,750,000 Solving for n and S$ gives n = 83,333.33 and S = 45. PART II: Essay Questions 1. (20 points total) (a) (2 points) We have D; = 130,000 and E, = 50,000 x 6.11 = 305,500, so that Vp = Dy + Ey = 435,500. (b) (3 points) The value of the equity can be obtained by discounting the after-tax earnings that will be received by the shareholders: (1 —t,)(EBIT — rpD;) Bp, =e TB This implies (1 —t,)(EBIT — rpD;) Ex (1 — 0.35)[102,000 — (0.12) (130,000)] 305,500 re = = 18.38298%. (c) (2 points) Stiphla’s weighted average cost of capital is Dr Ex ACO = (l-t)rp ce tre WACC ( rp Vi +TE Vi 130,000 305,500 = (1 ~0.35)(0.12) se apg + (0:1898298) 5 = 15.22388%. (d) (2 points) The value of the firm can also be obtained as follows: _ (1=t.)EBIT _ (1 —0.35)102,000 _ BLY = 435,500. Vn =" Wace 0.1522388 “ (e) (2 points) Let us denote by primed variables all the quantities after the new debt issue. The firm’s value will go up by the present value of its additional tax shields: Vi =Vi +t.(Df, — Dr) = 435,500 + 0.35(260,000 — 130,000) = 481,000. Corporate Finance (FNCE 611/612) PLACEMENT/WAIVER EXAM - PART 2 ANSWERS. In each of the project’s five years, the after-tax cash flows will be CF = (after-tax profits) + (depreciation tax shields) 360,000(1 — te) + ee 360,000(1 — 0.45) + 0.45(150,000) = 265,500. {I Therefore, using the discount rate r calculated in part (a), we have 265,500 1 NPV(project) = 265,500a5I0,2002 = —— = |1 — ——_| = 793,613.59. 0.2002 aa] ; Note that it could also be argued that the depreciation tax shields should be discounted at a rate lower than r, since they are not directly part of the project. For example, we could discount them at rp = 10%, since the company will benefit from these tax shields in the same years that it will benefit from the interest tax shields. They are also often discounted at ry = 8% in practice. In the first case you would then get NPV(project) = 360,000(1 — 0.45)asj0.2002 + 0.45(150,000) asjo.19 = 847,725.53. In the second case, you would get NPV(project) = 360,000(1 — 0.45) asjo,2002 + 0-45(150,000)asjo.05 = 861,355.35. The present value of the interest tax shields can be calculated using the following table: Debt outstanding Interest Year | at start of year | Interest | tax shield 1 750,000 75,000 33,750 2 600,000 60,000 27,000 3 450,000 45,000 20,250 4 300,000 30,000 13,500 5 150,000 15,000 6,750 Therefore, we have 33,750 6,750 SOON op OOD gy gp 80, 110 7 * Gage 8) PV(interest tax shields) = Finally, the after-tax issuance costs are PV (after-tax issuance costs) = 4% x 750,000 x (1 — 0.45) = 16,500. The adjusted present value of the project is therefore APV = —750,000 + 793,613.59 + 81,621.89 — 16,500 = 108,735.48. Corporate Finance (FNCE 611/612) PLACEMENT/WAIVER EXAM - PART 2 ANSWERS. 4. (20 points total) We are given 3, = 0.75, rz = 0.105, and rp, = 0.165. (a) (4 points) Using the CAPM, the expected return on the stock is rs = 17+ ('m — 17) By = 0-105 + (0.165 — 0.105) (0.75) = 0.15. We can find So, the current price of the stock, by discounting the expected cash flow from the stock at rs: _ 290(0.5) + 170(0.5) So 1.15 = 200. (b) (6 points) In the up state, the option will be exercised and will pay $290 — $212 = $78. In the down state, the option will not be exercised; the payoff is therefore zero. Let us form a portfolio by buying A shares of DJ’s stock, and by lending $B. In the up (down) state, this portfolio pays 290A + 1.105B (170A + 1.105B). We want 290A + 1.105B 78; 170A +1.105B = 0. Solving for A and B, we find A = 0.65 and B = —100. This means that the call option can be replicated by buying 0.65 shares of the stock, and borrowing $100. (c) (3 points) Since the portfolio has exactly the same payoff as the call option, its cost (200A +B) should be the price of the call option in a well-functioning market: Cy = 200A + B = 200(0.65) + (—100) = 30. (d) (4 points) Since the call option is a portfolio of the stock and riskfree borrowing, the beta of the call option, 8,, is given by 200(0.65) , —100 Bo = aq Bot aq Ber 200(0.65) —100 3g 0-78) + G5) = 3.25. The expected return r, on the call option can then be obtained using the CAPM: Te = 17+ (im — Pf) Be = 0.105 + (0.165 — 0.105) (3.25) = 0.30. (e) (3 points) The expected payoff of the call option is 78(0.5) + 0(0.5) = 39. The price of the option should therefore be 3939 Oo Tre = Ta9 =