Name _ Section _ ID # (Prof Alagurajah’s sections F and G; Prof King’s section D; Prof Li’s section A; Prof Tahani’s sections C and E; Prof Tissenbaum’s sections B and H) AK/ADMS 3530 Midterm Exam Fall 2007 October 21, 2007 Exam - Solutions 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 answers below, and fill in your answers on the bubble sheet Only the bubble sheet is used to determine your exam score Please note the following points: - Read the questions carefully and use your time efficiently - The 20 “Numerical Questions” are worth points each - The 10 “Conceptual Questions” are worth points each - Choose the answers that are closest to yours, because of possible rounding - Keep at least decimal places for dollar amounts in your calculations, and at least decimal places for interest rates - Interest rates are annual unless otherwise stated - Bonds pay semi-annual coupons unless otherwise stated and have a face value (or par value) of $1,000 - You may use the back of the exam paper as your scrap paper Numerical Questions (4 points each) (Q in B) You decide to sell your car and a friend has offered you $1,000 now and four annual payments of $2,000, 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 $7,000 Assuming your friend will not default on the payments and the market interest rate is 8%, should you sell your car to your friend? A) B) C) D) Yes; present value is $7,134 Yes; present value is $7,624 No; present value is $6,134 No; present value is $6,624 Solution A The PV of the annuity payment of $2,000 for years is: PV(at t=1) = 2,000 x PVIFA(8%,4) = 6,624.25 PV(at t=0) = 6,624.25/ (1.08) = 6,133.56 Finally add the initial payment $1000 today to the PV annuity at t=0 6,133.56 + 1,000 = 7,133.56 = $7,134 Page This is more than the $7,000 you would get today from the dealer Therefore you would sell your car to you friend (Q in B) Your brother bet the Toronto Maple Leafs would win their 2007 home opener and is now trying to pay off a gambling debt of $3,000 You have agreed to pay off the debt for him today, and in return he has agreed to pay you $125 per month over the next three years with payments beginning immediately What is the effective annual interest rate you are charging him? A) B) C) D) 25.14% 32.61% 35.15% 42.24% Solution C 3,000 = 125 x PVIFA(i,36) x (1+i) because it is an annuity due Solve for i using your financial calculator: i = 2.5416% EAR = (1 + im )m -1 = (1.025416)12 -1 = 35.15% (Q in B) The following cash flows have a present value of $1,922.51: $300 today, $400 at the end of year one, X at the end of year two, and $900 at the end of year three The annual interest rate is 6% What is X? A) B) C) D) $419 $450 $489 $550 Solution D Bring all cash flows to t=0: 1,922.51 = 300 + 400/(1.06)+ X/(1.06)2 + 900/(1.06)3 1,622.51 = 377.36 + X/(1.06)2 + 755.66 X/(1.06)2 = 489.49 X = 489.49 x (1.06)2 = 549.99 or $550 (Q in B) You are tired of the rising housing prices in Toronto and you have decided to move to Newfoundland and buy an ocean front property which costs $175,000 You have enough funds for a 20% down payment and you will obtain a 25-year, fixed rate mortgage at 7.50% (APR semi-annually compounded) for the rest Assuming that monthly payments begin in one month, what will be your monthly payment? A) $1,000.00 Page B) $1,024.18 C) $1,115.36 D) $1,280.87 Solution B The mortgage is on $175,000 x 80% = $140,000 The monthly interest rate is given by: (1 + im )12 = + EAR = (1 + 3.75%)² = 1.0764063, that is im = 0.615453% 140,000 = PMT x PVIFA(0.615453%,300) PMT = $1,024.18 (Q 10 in B) If $300,000 is borrowed for a home mortgage at a posted rate of 7% (APR semi-annually compounded), how much interest can be saved over the life of the mortgage by agreeing to a 20-year amortization period, rather than a 25-year amortization period? A) B) C) D) $23,400 $62,800 $76,471 $80,715 Solution C The monthly interest rate is given by: (1 + im )12 = + EAR = (1 + 3.5%)² = 1.0712250, that is im = 0.5750% The monthly payment for the 20-year loan 300,000 = PMT x PVIFA(0.5750%,240) PMT = $2,307.92 Total interest paid with the 20-year loan: 240 x 2,307.92 – 300,000 = $253,900.80 The monthly payment for the 25-year loan 300,000 = PMT’ x PVIFA(0.5750%,300) PMT’ = $2,101.24 Total interest paid with the 25-year loan: 300 x 2,101.24 – 300,000 = $330,372.00 Difference in total interest paid: $330,372.00 - $253,900.80 = $76,471.20 (Q in B) Which investment would you prefer: an account offering 10.20% APR with weekly compounding (there are 52 weeks in a year), and an account yielding 10.25% APR with quarterly compounding? Page A) B) C) D) 10.20% APR with weekly compounding 10.25% APR with quarterly compounding You would be indifferent None of the above Solution A The EAR corresponding to a 10.20% APR with weekly compounding is: 0.1020 52 EAR = (1 + ) − = 10.7273% 52 The EAR corresponding to a 10.25% APR with quarterly compounding is: 0.1025 EAR = (1 + ) − = 10.6508% Since the EAR corresponding to an APR of 10.20% with weekly compounding is higher, you would prefer this investment (Q in B) What is the present value of an 8-year annuity of $750 annually if the first payment on this annuity is to be made years from today? The interest rate is 7% per year A) B) C) D) $3,655.77 $3,911.67 $4,185.49 $4,478.47 Solution B This is an ordinary annuity delayed for two years 1 $750 × [ ] − 0.07 0.07 × (1.07 ) PV = = $3,911.67 (1.07 ) (Q in B) Compute the present value of the following set of payments for two years: payments of $500 per quarter for the first year and payments of $600 per quarter during the second year The APR is 9% with monthly compounding and payments will begin months from today A) B) C) D) $3,966.84 $3,975.71 $4,116.69 $4,161.51 Solution A 0.09 12 EAR = (1 + ) − = 9.3807% 12 The corresponding quarterly interest rate is: Page rquarter = (1 + EAR )1 / n − = (1 + 0.093807)1 / − = 2.2669% PV = $500 × [ $600 × [ 1 − ]+ 2.2669% 2.2669% × (1 + 2.2669%) 1 − ] /(1 + 9.3807%) = $3,966.84 2.2669% 2.2669% × (1 + 2.2669%) (Q in B) You are indifferent between the following two payment options: 1) pay $15,000 cash today, or 2) pay $250 monthly over the next years with the first payment starting immediately, plus a final payment ($FP) to be made years from today An APR of 8.4% is quoted with monthly compounding How much is FP? A) B) C) D) $9,456.06 $9,494.60 $12,155.45 $12,204.99 Solution C 8.4% rmonth = = 0.7% 12 PV = $250 × (1 + 0.7%) × [ 1 $ FP − = $15,000 ]+ 24 0.7% 0.7% × (1 + 0.7%) (1 + 0.7%) 36 ∴ $ FP = $[15,000 − 250 × (1 + 0.7%) × ( 1 − )] × (1 + 0.7%) 36 0.7% 0.7% × (1 + 0.7%) 24 = $12,155.45 The above result still holds when we use the EAR rather the monthly interest rate to discount the last payment $FP 10 (Q in B) You are planning to make a purchase worth $1 million in years To meet this goal, you need to draw up a savings plan The problem is that you won’t be able to make any deposit towards this savings goal in Years and from now How much is the equal amount that you have to deposit at the end of each year over the years to come (other than Years and 7) in order to finance your planned purchase? The interest rate is 7.8% compounded annually A) B) C) D) $80,750.66 $103,601.18 $104,931.79 $105,938.94 Solution B Page These deposits are a 9-year ordinary annuity with two missing cash flows that occur at the end of Years and The future value of these cash flows can be calculated as: (1 + 0.078) − $1,000,000 = $D × [ ] − $D × (1.078 ) − $D × (1.078 ) 0.078 = $D × (12.3838 − 1.5693 − 1.1621) = $D × 9.6524 $1,000,000 ∴ $D = = $103,601.18 9.6524 11 (Q 14 in B) How much should you pay for a $1,000-face value bond with 10% coupon, semi-annual payments, and five years to maturity if the interest rate is 12%? A) B) C) D) $926.40 $981.40 $1,000.00 $1,075.82 Solution A Price = $50 x PVIFA(6%,10) + $1,000 x (1.06)-10 = $926.40 12 (Q 15 in B) If you purchase a three-year, 9% coupon bond for $950 today, how much could it be sold for two years later if interest rates are expected to remain stable over the next two years? A) B) C) D) $964.95 $981.52 $1,000.00 $1,033.17 Solution B The market interest rate is given by: $950 = $45 x PVIFA(i,6) + $1,000 x (1+i)-6 i = 5.5009% Two years later, there will be only coupons left, the price will be: Price = $45 x PVIFA(5.5009%,2) + $1,000 x (1+i)-2 = $981.52 13 (Q 11 in B) What is the yield to maturity of a bond with the following characteristics? Coupon rate is 8% with semi-annual payments, current price is $960, three years until maturity A) 4.7826% Page B) 5.4867% C) 9.5652% D) 9.7939% Solution C $960 = $40 x PVIFA(i,6) + $1,000 x (1+i)-6 i = 4.7826% YTM = x i = 9.5652% 14 (Q 12 in B) A government bond carries a 6% coupon rate, pays semi-annual coupons, and has a $1,000 face value If you purchase it today at $1,015 and expect to sell it years from now at $1,040, what would be your annual rate of return if the coupons are reinvested at 4% APR semi-annually compounded? A) B) C) D) 3.1654% 6.3309% 6.9579% 27.8314% Solution B 4-year Rate of Return = [30 x FVIFA(2%,8) + 1,040 – 1,015] / 1,015 = 27.8314% The annual rate of return is (1+27.8314%)1/4 – = 6.3309% 15 (Q 13 in B) What is the coupon rate on a 6-year bond, paying semi-annual coupons, with a $1,000 face value and selling at $1,050 if the yield to maturity is 4%? A) B) C) D) 2.4728% 4.0478% 4.9456% 4.9538% Solution C $1,050 = PMT x PVIFA(2%,12) + $1,000 x (1+i)-12 PMT = $24.7280 Cpn rate = 4.9456% 16 (Q 19 in B) ABC Corp has just paid a $5 per share dividend The dividend is projected to grow at 5% per year indefinitely If the stock sells today for $65.625, what is the required rate of return on ABC stock? A) 6.25% B) 6.75% C) 13% Page D) 13.5% Solution C P0 = D1/(r - g) rearranging the formula we get r = D1/P0 + g where D1 = D0 x (1+g) = $5 x (1+ 0.05) = $5.25; P0 = $65.625; g = 5% r = $5.25/$65.625 + 0.05 r = 13% 17 (Q 20 in B) DEF corp has just paid a $2 per share dividend The dividend is projected to grow at 3% per year indefinitely If the required rate of return on the stock is 9%, then by what percentage does P1 exceed P0? A) B) C) D) 2% 3% 5.25% 9% Solution B Note that (P1 – P0) / P0 = (D2 - D1) / D1= g = 3% One can also compute the prices and their relative difference: The price P0 today P0 = D1/(r - g) = $2 × 1.03 / (0.09 - 0.03) = $2.06 / 0.06 = $34.33 per share The price P1 in one year P1 = D2/(r - g) P1 = D2/(r - g) = ($2.06 × 1.03) / (0.09 - 0.03) = $35.36 per share % increase = (P1 – P0) / P0 = ($35.6 - $34.33) / $34.33 = 3% 18 (Q 16 in B) The next year expected EPS (earnings per share) of JKL corp is $5; with a dividend payout ratio of 30%, a discount rate of 16%, and a return on equity (ROE) of 20% What is the current stock price? A) B) C) D) $60 $65 $70 $75 Solution D Page The next dividend will be $5 × 0.30 = $1.50 per share The plowback ratio is 0.70 implying a growth rate g of: g = Plowback Ratio × ROE = 0.70 × 20% = 14% From the dividend growth model, the price of a share is: Div1 $1.50 P0 = = = $75 r − g 16 − 14 19 (Q 17 in B) The dividends of XYZ corp are forecasted to grow at 20% per year for two years, after which the shares grow at a fixed rate of 6% forever If the discount rate is 15% and a dividend of $2.50 was just paid, what should be the current share price? A) B) C) D) $31.16 $33.23 $37.42 $47.77 Solution C $2.50 × 1.20 $2.50 × (1.20) $2.50 × (1.20) × (1.06) P0 = + + × 1.15 0.15 − 0.06 (1.15) (1.15) $3.00 $3.60 $3.816 P0 = + + 1.15 (1.15) (1.15) × 0.09 P0 = $37.42 20 (Q 18 in B) XYZ Inc reinvested 30% of its earnings in the corporation The stock sells for $25 today, and the next dividend will be $1.25 per share The discount rate is 7.5% What is the rate of return on XYZ Inc equity (ROE)? A) B) C) D) 7.50% 8.33% 12.5% 22.5% Solution B Page We know that P0= D1/(r-g) Therefore g = r - D1 / P0 Or g = 0.075 - 1.25/25 = 025 or 2.5% We also know that g = ROE x Plowback Ratio Or ROE = g / Plowback Ratio Therefore ROE = 0.025 / 0.3 = 0.0833 or 8.33% Page 10 Conceptual Questions (2 points each) 21 (Q 27 in B) Which of the following should be the goal of the financial manager of a corporation? A) To maximize the company profit B) To maximize the revenues on the income statement C) To maximize current market value of the stock D) To maximize market share 22 (Q 28 in B) Which of the following is correct about corporate debt? A) The risk of default is measured by bond ratings, with the higher the rating the lower the risk of default B) Because debt holders not own the firm, they normally have a voting power C) Since interest is an obligation, it cannot be treated as an expense and therefore cannot be deducted from taxable income D) The fund established to retire the debt before its maturity date is called a mutual fund 23 (Q 29 in B) Which of the following is correct for a bond currently selling at discount? A) B) C) D) Its current yield is higher than its coupon rate Its current yield is lower than its coupon rate Its yield to maturity is lower than its coupon rate If you buy one, you get another one for free 24 (Q 30 in B) A callable bond is a bond that: A) Can provide protection against inflation B) Can be converted into shares of stock in the issuing company C) Can be repurchased by the issuer prior to its maturity D) Can be sold at its nominal value 25 (Q 21 in B) Owners of common stock hope to receive compensation in the form of _ A) B) C) D) Interest and dividends Principal and capital gains Dividends and capital gains Interest and principal 26 (Q 22 in B) 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: Page 11 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) None of the above 27 (Q 23 in B) Given a set period rate, which of the following will contribute to a lower EAR? A) B) C) D) More compounding Less compounding Higher APR Continuous compounding 28 (Q 24 in B) Which of the following is correct about common stocks? A) Common equity is like debt in that it promises a series of fixed payments to investors B) Unlike bond coupon, the common stock’s dividend is paid at the discretion of the board C) For most companies, common stock is much less important than preferred stock in the firm’s capital structure D) Common shareholders can force the company to buy back their shares at a specified date 29 (Q 25 in B) For an investor to compare different opportunities (each with the same risk) with interest rates reported in different manners, you should convert each interest rate to: A) B) C) D) An annual nominal rate A monthly nominal rate An effective annual rate A daily nominal rate 30 (Q 26 in B) Which of the following is correct for a BB-rated bond, compared to a Arated bond? A) B) C) D) The BB bond will sell for a lower price The BB bond will sell for a higher price The BB bond will offer a higher yield to maturity The BB bond will offer a lower yield to maturity Page 12 ... )m -1 = (1.025416)12 -1 = 35.15% (Q in B) The following cash flows have a present value of $1,922.51: $300 today, $400 at the end of year one, X at the end of year two, and $900 at the end of. .. at a posted rate of 7% (APR semi-annually compounded), how much interest can be saved over the life of the mortgage by agreeing to a 20-year amortization period, rather than a 25-year amortization... price P0 today P0 = D1/(r - g) = $2 × 1.03 / (0.09 - 0.03) = $2.06 / 0.06 = $34.33 per share The price P1 in one year P1 = D2/(r - g) P1 = D2/(r - g) = ($2.06 × 1.03) / (0.09 - 0.03) = $35.36 per