exam solution 3 fundamentals of corporate finance, 4th edition brealey

Name Section ID # Professor Alagurajah’s Section A (Fridays, 2.30-5.30 pm), Professor King’s Section G (Internet), Professor Kohen’s Section F (Tuesdays, 2:30-5:30 pm), Professor Li’s Section E (Wednesdays, 2:30-5:30 pm), Professor Okonkwo’s Section B (Tuesdays, 7-10 pm), Professor Patterson’s Section D (Thursdays, 4-7 pm), and Professor Tahani’s Section C (Wednesdays, 7-10 pm) AP/ADMS 3530.03 Finance Midterm Exam Fall 2009 October 25, 2009 Exam - Solution This exam consists of 30 multiple choice questions and carries a total of 100 points Choose the response which best answers each question Circle your answer below, and fill in your answers on the bubble sheet Only the bubble sheet is used to determine your exam score Please not forget to write your name and ID # both at the top of this cover page and on the bubble sheet Also please write the type of your exam (A or B) on the bubble sheet Please note the following points: 1) Read the questions carefully and use your time efficiently 2) Choose the answers that are closest to yours, because of possible rounding 3) Keep at least decimal places in your calculations and final answers, and at least decimal places for interest rates 4) The 20 “Numerical questions” are worth points each 5) The 10 “Conceptual questions” are worth points each 6) Unless otherwise stated, interest rates are annual, and bonds pay semiannual coupons and have a face value (or par value) of $1,000 7) You may use the back of the exam paper as your scrap paper Notations We may denote the PV and FV annuity factors respectively by PVIFA(r,n) and FVIFA(r,n), i.e.: − (1 + r ) − n (1 + r ) n − ; PVIFA(r , n) ≡ FVIFA(r , n) ≡ r r Numerical questions (4 points each) Your cousin just came home from a poker tournament in Las Vegas and is now trying to pay off a gambling debt of $5,000 You have agreed to pay off the debt for him today, and in return he has agreed to pay you $250 per month over the next two years with payments beginning immediately What is the effective annual interest rate you are charging him? A) 19.75% B) 19.86% C) 21.77% D) 22.26% E) 23.45% Answer C 5,000 = 250 x PVIFA (i,24) x (1+i) because it is an annuity due Solve for i using your financial calculator: i = 1.6550% EAR = (1 + im )m -1 = (1.01655)12 -1 = 21.77% Your parents are willing to pay for your MBA degree and want to put aside funds today even though you will not be entering MBA school for another years (from today) If they can earn 4.5% annually on the funds and your MBA school will cost $35,000 at the beginning of each year of the two year program, how much money they need to set aside today? A) $57,435 B) $60,020 C) $65,653 D) $67,243 E) $70,186 Answer B This is an ordinary annuity delayed for two years X = 35,000 x PVIFA(4.5%,2)/(1 +.045)2 X = $65,654.37/(1.045)2 = $60,020.03 You have inherited funds from your grandmother’s estate and want to buy a property in Florida which costs $250,000 You have enough funds for a 30% down payment and you can obtain a mortgage for the balance at a five-year, fixed rate of 5.5% (APR compounded semiannually) How much will you still owe at the end of five years assuming a 20-year amortization period? A) $147,172 B) $152,665 C) $195,625 D) $210,246 E) $224,825 Answer A The mortgage amount is $250,000 x 70% = $175,000 The monthly interest rate is given by: (1 + im )12 = + EAR = (1 + 2.75%)² => (1 + im) = 1.0453168, that is im = 0.453168% $175,000 = PMT x PVIFA(0.453168%,240) PMT = $1,197.68 After years, the outstanding mortgage (loan) will be the PV of the future remaining mortgage payments (180 payments) PV = $1,197.68 x PVIFA(0.453168%,180) = $147,171.66 You have decided to buy your first house and you have been approved for a $300,000 home mortgage The posted rate is 5.60% (APR, compounded semiannually) and you have decided to make weekly payments If the amortization period is 25 years and rates not change, how much will you pay in interest over the life of the mortgage? (assume 52 weeks in one year) A) $127,895 B) $253,618 C) $387,555 D) $553,618 E) $576,016 Answer B The weekly payment for the 25-year loan (1 + iw)52 = + EAR = (1 + 2.80%)² => (1 + iw) = 1.0106269, that is iw = 0.106269% $300,000 = PMT x PVIFA(0.106269%,1,300) PMT = $425.86 Total interest paid with the 25-year loan: 1,300 x $425.86 – $300,000 = $253,618 An Atkinson student who borrowed $7,560 has agreed to pay back the loan with monthly payments of $150 If the interest rate is stated as 10% APR monthly compounded, how long will it take to pay back the loan? A) 38.19 months B) 45.57 months C) 50.40 months D) 65.64 months E) 67.89 months Answer D $7,560 = 150 x PVIFA (10%/12,n) Solve for n using your financial calculator: PV=7,560; PMT= -150; I/Y= 10/12; FV= 0; CPT n = 65.64 months Which account would be preferred by a depositor: a 7.20% APR with weekly compounding or a 7.25% APR with quarterly compounding? A) 7.20% with weekly compounding B) 7.25% with quarterly compounding C) The depositor would be indifferent D) The time period must be known in order to select the preferred account E) None of the above Answer A The EAR of a 7.20% with weekly compounding is (1+7.20%/52)52 – = 7.4602% The EAR of a 7.25% with quarterly compounding is (1+7.25%/4)4 – = 7.4495% The 7.20% weekly compounded is the best option You decide to sell your car and a friend has offered you $1,000 now and four annual payments of $1,800, with the annual payments starting at the end of the second year Your other option is to sell the car to a dealer today for $6,450 Assuming your friend will not default on the payments and the market annual interest rate is 8%, should you sell your car to your friend? A) B) C) D) E) Yes; present value of the friend’s offer is $6,520 Yes; present value of the friend’s offer is $6,624 No; present value of the friend’s offer is $5,134 No; present value of the friend’s offer is $5,624 Both options offer the same value Answer A The PV of the annuity payment of $1,800 for years is: PV (at t=1): $1,800 x PVIFA(8%,4) = $5,962 PV (at t=0) = $5,962/ (1.08) = $5,520 Finally add the initial payment $1,000 today to the PV annuity at t=0 $(5,520 + 1,000) = $6,520 This is more than the $6,450 you would get today from the dealer Therefore you should sell your car to you friend In order to purchase a laptop at $2,450, you agree to make the following payments: $500 today, $650 in one year, X in two years, and $800 in three years The annual interest rate is 6% What is X? A) $500.00 B) $612.50 C) $665.10 D) $747.30 E) $851.34 Answer D PV = $2,450 = $500 + $650 x (1.06)-1 + X x (1.06)-2 + $800 x (1.06)-3 Ỵ X x (1.06)-2 = $665.10 Ỵ X = $747.30 How much interest is to be paid in the second year of a 6-year loan of $100,000 with payments occurring at the end of each month, and a 6% annual interest rate compounded monthly? A) $1,389 B) $1,657 C) $4,731 D) $6,000 E) $9,887 Answer C The payment on this loan is given by: PMT = $100,000 / PVIFA(0.5%,72) = $1,657.29 The residual balances at the end of year and year are given by: PV12 = $1,657.29 x PVIFA(0.5%,60) = $85,724.25 PV24 = $1,657.29 x PVIFA(0.5%,48) = $70,567.93 So the principal paid in year is: $85,724.25 - $70,567.93 = $15,156.32 And the interest paid in year 2: 12 x $1,657.29 - $15,156.32 = $4,731.16 10 Today, one year before your retirement, you forecast that your annual withdrawals will decline at a rate of 4% per year for 25 years; with the first withdrawal of $75,000 made one year from now If you earn an annual interest rate of 4%, how much money should you have in your bank account today? A) $773,547 B) $810,759 C) $937,500 D) $1,171,656 E) Undefined Answer B PV of a declining annuity (the growth rate g = -4%) is given by: ⎡ ⎛ − 4% ⎞ 25 ⎤ $75,000 PV = × ⎢1 − ⎜ ⎟ ⎥ = $810,759 4% − (−4%) ⎣⎢ ⎝ + 4% ⎠ ⎦⎥ 11 Potential investors of XYZ Corp stock are looking for a 20% expected return XYZ currently trades at $15 per share and has just paid an annual dividend of $2 per share Based on the above what is the implied growth rate in dividends for XYZ Corp.? A) 5.00% B) 5.88% C) 6.25% D) 6.67% E) 7.14% Answer B We need to solve for g, where g represents both the growth rate in dividends and the growth rate in the stock price Investors total expected return; r = 20% = D1/P0 + g Solving for g the formula becomes g = r – (D1/P0); note also that D1 = D0 (1 + g) g = r - [D0 (1 + g)]/ P0 = 20% - [$2 x (1 + g)] / $15 Ỵ g = 0.0588 or 5.88% 12 In a recent period Joshua Inc reported earnings per share (EPS) of $4 and following its policy just paid a dividend based on a payout ratio of 50% The company’s share price and dividends have grown at an average of 5% per year, and there is no reason to expect that this will change in the future You want to buy Joshua stock and have determined that the market expected return for this type of stocks is 16% If Joshua stock was trading at $18.45 on the market, you would likely A) B) C) D) E) not buy the stock because the fair value is $ 17.27 not buy the stock because the fair value is $18.18 buy the stock because the fair value is $19.09 buy the stock because the fair value is $36.36 buy the stock because the fair value is $66.67 Answer C We answer this question using the dividend discount model where the fair value of the stock can be calculated as P0 = D1 / (r – g), where the growth rate g = 5% The current dividend D0 is 50% of EPS or $2.00 therefore the expected dividend D1 = D0 (1 + g) = $2.00 (1 + 0.05) = $2.10 The fair value of the stock P0 = $2.10 / (0.16 – 0.05) = $19.09 13 ABC Corp expects its earnings and dividends to grow at 18% over the next years and 15% in the 3rd year and then at a constant rate of 6% thereafter ABC’s last dividend was $1.15 and the required rate of return on similar equity is 12% Based on the above what should be the share price of ABC today? A) $22.62 B) $26.95 C) $29.63 D) $32.53 E) $50.78 Answer B The share price today is the present value of all future dividends D1 = $1.15 x 1.18 = $1.3570 D2 = $1.3570 x 1.18 = $1.6013 D3 = $1.6013 x 1.15 = $1.8415 D4 = $1.8415 x 1.06 = $1.9520 Expected return (r) = 12% The growth rate of ABC stabilizes after the 3rd year therefore we can calculate the share price at P3 which incorporates all future dividends that will be paid in perpetuity P3 = D4 / (r – g) = 1.9520 / (0.12 – 0.06) = $32.53 Therefore the price of the stock today is the present value of D1, D2, D3 and P3: P0 = $1.3570/(1.12)1 + $1.6013/(1.12)2 + 1.8415/(1.12)3 + $32.53/(1.12)3 = $26.95 14 How much would you pay today for a stock that offers a constant growth rate of 8% for dividends and has an expected rate of return of 12%? You also know that the stock should be valued at $40 one year from now? A) $35.71 B) $37.04 C) $43.20 D) $44.80 E) $45.96 Answer B One way to solve this problem is to realize that the growth rate for dividends (8%) is the same as the growth rate for the value of the stock (i.e the expected capital gain on the stock): P0 = Div1 / (r - g) P1 = Div2 / (r - g) = Div1 x (1+g)/ (r - g) = P0 x (1+g) Ỵ P0 = P1 / (1 + g) = $40 / (1 + 8%) = $37.04 15 Julia Inc stock currently sells for $84 per share The market requires a 13% return on the firm’s stock If the company maintains a 6% growth rate in dividends, what was the most recent annual dividend? A) $5.04 B) $5.55 C) $5.88 D) $6.76 E) $10.92 Answer B One way to solve this is by solving for the expected dividend D1 P0 = D1 / (r – g) rearranging the formula to solve for D1 = P0 x (r – g) D1 = $84 x (0.13 – 0.06) = $5.88; we know that D0 = D1 / (1 + g) Therefore D0 = $5.88 / (1 + 0.06) = $5.55 16 How much should you pay for a $1,000-face value bond with 6% coupon, semi-annual payments, and years to maturity if the annual interest rate applicable to bonds of same quality and maturity is 4%? A) $887 B) $888 C) $1,000 D) $1,120 E) $1,121 Answer E Price = $30 x PVIFA(2%,14)+ $1,000 x (1.02)-14 = $1,121 17 BH Corp has bonds on the market with $1,000 par value, 14.5 years to maturity, a YTM of 9%, and a current price of $850 The bonds make semi-annual coupon payments What is the coupon rate on BH Corp Bonds? A) 3.56% B) 4.50% C) 5.50% D) 7.13% E) 9.00% Answer D P = $850 = C x PVIFA(4.5%,29) + $1,000/ (1+4.5%)29 Solving for C = $35.64; or coupon rate = × 3.564% = 7.128% 18 BDJ Inc wants to issue new 10-year bonds The company currently has 8% coupon, $1,000 face value bonds on the market that sell for $1,095, make semi-annual coupon payments and mature in 10 years What coupon rate should the company set on its new bonds if it wants to sell them at par today? A) 2.89% B) 3.34% C) 5.78% D) 6.68% E) 6.79% Answer D P = $1,095 = $40 x PVIFA(r,20) + $1,000/ (1+r)20 Solving for r = 3.34% Ỵ YTM = Coupon Rate (since the bonds sell at par) = 6.68% 19 KLY Inc existing bonds have the following terms: 8% coupon, $1,000 face value and they mature in 12 years The discount rate reflective of the default risk and maturity is 14% KLY Inc is offering the bondholders the option to swap their existing bonds into 3year zero-coupon bonds with a face value of $1,000 Assuming KLY Inc will not default during the next 12 years, should existing bondholders accept the option? A) Yes, because the zero coupon bonds have a shorter year maturity B) Yes, because, the zero coupon bonds are worth more C) Yes, because the zero coupon bonds are less sensitive to interest rate risk D) No, because the existing bonds are worth more E) No, because zero coupon bonds not pay interest Answer B Current price of existing bonds: PV = $40 x PVIFA(7%,24) + $1,000 / (1 + 7%)24 = $655.92 Current value of zero-coupon bonds: PV = $1,000 / (1.14)3 = $674.97 The bondholders should accept the offer since the zero-coupon bond is worth more 20 LMN Co has 12% coupon $1,000 par value bonds making annual coupon payments with a YTM of 9% The current yield on these bonds is 9.80% How many years these bonds have left until they mature? A) years B) 10 years C) 13 years D) 14 years E) 15 years Answer C Current yield = 0.0980 = $120/P0 P0 = $120/.0980 = $1,224.49 P0 = $1,224.49 = $120 x PVIFA(9%,n) + $1,000 / (1 + 9%)n Solving for n = 13 years Conceptual questions (2 points each) 21 Which of the following is incorrect about partnerships: A) B) C) D) E) Partners have unlimited liability for themselves and their partners Partnerships are easy to start Partners are subject to double taxation Partnerships are flow-through entities All of the above statements are correct Answer C 22 The person most directly responsible for looking after the firm’s cash, raising new capital and maintaining relationships with banks and other investors who hold the firm’s securities is the: A) Controller B) Chief Financial Officer C) Treasurer D) Chief Executive Officer E) Accounts Payable Clerk Answer C 23 Given a future value (greater than zero), which of the following will contribute to a lower present value? A) B) C) D) E) More frequent discounting Lower discount rate Less time periods Both B and C are correct None of the above statements are correct Answer A 24 An infinite stream of cash flows growing at a constant rate is called a: A) B) C) D) E) Perpetuity Growing perpetuity Annuity Growing annuity None of the above Answer B 10 25 Which of the following statements about time value of money are true? A) Nominal and effective rates are the same for annual compounding only B) All else being the same: converting an annuity to an annuity due decreases the present value C) For a given dollar amount, the higher the discount rate, the higher the present value D) All of the above statements are correct E) None of the above statements are correct Answer A 26 An investor who purchases stock in a firm cannot realize a positive return on that investment if the firm pays no dividends This statement is: A) False: The investor will still receive interest payments from the investment B) True: The investor does not receive any cash flows therefore, the investment return is zero C) False: The investor may realize a capital gain from the appreciation of the stock price D) True: The dividend yield is zero E) None of the above Answer C 27 Which of the following terms is typically associated with both preferred stock and common stock? A) Dividend yield B) Voting rights C) Proxy D) Cumulative voting E) All of the above Answer A 28 Which of the following is the most correct for an A-rated bond, compared to a BBBrated bond? A) B) C) D) E) The A bond will sell for a lower price The A bond will sell for a higher price The A bond will offer a higher yield to maturity The A bond will offer a lower yield to maturity The A bond has a higher credit spread Answer D 11 29 A callable bond is a bond that: A) B) C) D) E) Can provide protection against inflation Can be converted into shares of stock of the issuing company Can be repurchased by the issuer prior to its maturity Can be sold at its nominal value Can be extended at the maturity date Answer C 30 The maximum number of shares that a company is permitted to issue, as specified in the firm’s articles of incorporation is called: A) B) C) D) E) Authorized share capital Issued share capital Issued and outstanding share capital Additional paid-in capital Firm’s capital Answer A 12 ... present value of the friend’s offer is $6,520 Yes; present value of the friend’s offer is $6,624 No; present value of the friend’s offer is $5,134 No; present value of the friend’s offer is $5,624... (1.06 )-1 + X x (1.06 )-2 + $800 x (1.06 )-3 Î X x (1.06 )-2 = $665.10 Î X = $747.30 How much interest is to be paid in the second year of a 6-year loan of $100,000 with payments occurring at the end of. .. mortgage for the balance at a five-year, fixed rate of 5.5% (APR compounded semiannually) How much will you still owe at the end of five years assuming a 20-year amortization period? A) $147,172