SOLUTIONS – TYPE A Summer 2007 – 3530 Midterm Exam (Q6 in Type B) How much will be in an account after years if the initial deposit was $10, and which earned 10% interest compounded quarterly for the years? A) $10.77 B) $13.31 C) $13.45 D) $31.38 Solution C $10 x (1+.10/4)12 = $13.45 (Q7 in Type B) If I promise to pay you $1,800 nine years from now in return for a loan of $1,000 today, what is the effective annual interest rate for this agreement? A) 5.26% B) 6.75% C) 9.00% D) 10.00% Solution B r = (FV/PV)1/t – = (1800/1000)1/9 – = 6.75% or use your financial calculator PV=1,000; FV=1,800; t=9, solve for r (Q8 in Type B) In June 2007, the posted mortgage rate at CIBC was 6% for a 6-year term What is the monthly interest rate? Use decimal places in your calculations (Remember that mortgages are compounded semi-annually) A) 0.4939% B) 0.5000% C) 0.5061% D) 6.0900% Solution A The 6% posted rate is an APR from 3% per months The EAR is 1.032 – = 0.0609 The monthly rate is (1.0609)1/12 – = 0.004939 (Q9 in Type B) How much can be accumulated for retirement if $2,000 is deposited annually, beginning today, and the account earns 9% interest compounded annually for 40 years? A) $ 17,558 B) $506,824 C) $552,438 D) $802,876 Solution C Use you calculator PMT = 1,500 r = 9% , t = 40, find FV = 506,824 But payment starts immediately -> annuity DUE = 506,824 x 1.09 = $552,438 5 (Q10 in Type B)What is the effective annual rate on a deposit of $5,000 made ten years ago if the deposit is worth $9,948.94 today? The deposit pays interest semiannually A) 3.50% B) 6.76% C) 7.00% D) 7.12% Solution D From the formula for PV, FV, r, and t, we have r = (FV/PV)1/t – Using t=20 because of semi-annual interest, we get r = 0.035 as the 6-month rate Then (1+0.035)2 -1 = 0.0712 (Q11 in Type B)Assume your uncle recorded his salary history during a 40-year career and found that it had increased ten-fold (i.e., his salary at the end of his career was 10 times his salary at the beginning) If inflation averaged 5% annually during the period, how would you describe his purchasing power, on average? A) His purchasing power remained on par with inflation B) He “beat” inflation by nearly 1% annually C) He “beat” inflation by slightly over 2% annually D) He “beat” inflation by 5% annually Solution B For the annual increase in his nominal salary, r = (FV/PV)1/t – = (10)1/40 – = 5.93% By either the exact formula or the approximation, this is a real increase of nearly percentage point (Q12 in Type B) How much interest will be earned in the third year if $1,000 is deposited that earns 8% interest compounded annually? A) $ 70.00 B) $ 93.31 C) $105.62 D) $140.00 Solution B The deposit grows to $1000 x 1.07 = $1080 at the end of the first year, $1166.40 at the end of the second year, and $1259.71 at the end of the third year The difference between $1259.71 - $1166.40 = $93.31 (Q13 in Type B) A credit card account that charges interest at the rate of 1.25% per month would have an annually compounded rate of _ and an APR of _ A) 16.08%; 15.00% B) 14.55%; 16.08% C) 12.68%; 15.00% D) 15.00%; 14.55% Solution A (1+.0125)12 – = 16.08%; 1.25%x12 = 15% (Q14 in Type B)You decide to sell your car and someone has offered you four equal annual payments of $3,100, beginning two years from today Your alternative is to sell your car today for $9,000 cash Assuming everything else is equal, should you accept the offer of the four equal payments (the prevailing rate of interest is 10%)? A) Yes; present value is $9,510 B) Yes; present value is $11,372 C) No; present value is $8,933 D) No; present value is $7,461 Solution C The PV of the four payments PV= 3,100 / (1+0.1)^2 +3,100 / (1+0.1)^3 +3,100 / (1+0.1)^4 +3,100 / (1+0.1)^5 = $8,933 or use the annuity formula This is less than the $9,000 you would get today Therefore you would not accept the offer 10 (Q15 in Type B)How much more is a annual perpetuity of $1,000 worth than an annual annuity of the same amount for 20 years? Assume a 9% interest rate and cash flows are at end of each year A) $297.29 B) $1,486.44 C) $1,982.57 D) $2,000.00 Solution C The perpetuity is worth $1000/.09 = $11,111.11 The PV of the twenty-year annuity = C * [1/r – 1/r(1+r)^t ] = $9128.55; or use your financial calculator The difference between the perpetuity and annuity is $1982.57 11 (Q1 in Type B) Two years ago bonds were issued with 10 years until maturity, selling at par, and a 7% coupon Interest is paid semi-annually If market interest rates for that grade of bond are currently 8.25%, what will be the price of these bonds? A) $700.00 B) $916.00 C) $927.84 D) $987.50 Solution: C Using your calculator: PMT = $35, i= 8.25/2 = 4.125, n = yrs remaining x 2=16, FV=$1000, COMP PV Ỉ PV = $927.84 12 (Q2 in TYPE 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) 2.39% B) 4.78% C) D) 9.57% 12.17% Solution: C Using your calculator: PMT = $40, PV = - 960, 4.125, n = x = 6, FV=$1000, COMP i Ỉ i = 4.7826 x 2= 9.567 13 (Q3 in Type B) What is the current yield of the following bond: it has 10 years until maturity, sells for $1033, has a face value of $1000 and a 6% coupon rate (paid semiannually) A) 2.39% B) 4.78% C) 5.81% D) 11.62% Solution: B Current Yield = Annual coupon / Current price = $60/$1033 = 5.81% 14 (Q4 in Type B) BCE was recently been bought out by a U.S private equity firm who levered the company and now BCE is having cash flow problems Its existing bonds have the following terms: 6% coupon, $1000 face value and they mature in 10 years Bonds of equivalent risk yield 12% BCE is asking the bondholders to swap their existing bonds into year zero-coupon bonds with a face value of $1000 Assuming BCE will not be in default during the next 10 years, should existing bondholders accept the deal? A) No, because the existing bonds are worth more B) Yes, because, the zero coupon bonds are worth more C) Yes, because the zero coupon bonds have a shorter year maturity D) No, because zero coupon bonds not pay interest Solution: A Current Price of existing bonds: PMT = $30, n = 10 x = 20, FV = $1000, I = 12/2 = 6, COMP PV -> PV = $655.90 Current value of Zero-coupon bonds: PV = $1000/ (1.12)5 = $567.43 As long as BCE will not be in default of its bond payments, the bondholders should keep their existing bonds as they have a higher PV 15 (Q5 in Type B)You bought a bond with a 7% annual coupon rate four years ago when market interest rates for similar bonds was 6% The bond had an original maturity of 10 years and a par value of $1000 Today, the yield to maturity of the bond has increased to 8% annually If you sell the bond today, what would be your annual rate of return over the past years? The bond pays coupons semi-annually Assume coupons are not reinvested A) 3.50% B) 3.69% C) 7.33% D) 14.77% Solution: A Step 1, Find purchase price of bond years ago, using your calculator: PMT = $35, n = 10 x = 20, I = 6/2 = 3, FV = $1000 COMP PV -> PV = $1074.39 Step 2, find price of bond today, using your calculator: PMT = $35, n = x2 = 12, I = 8/2 = 4, FV = $1000 COMP PV -> PV = $953.07 Step 3: Find Rate of Return over the year holding period = (Coupon Interest + or - Cap gain/loss) Original price paid = (70 x 4) + ($953.07 – 1074.39) $1074.39 = 280 – 121.32 $1074.39 = 0.1477 or 14.77% over years Step 4: Annual rate of return = (1 + 1477) ¼ -1 = 3.50% 16 (Q16 in Type B) How much of a stock’s $25 price is reflected in the PVGO if it expects to earn $3 of earnings per share next year, and has a required rate of return of 14%? A) $3.57 B) $5.00 C) $21.43 D) $22.00 Solution: A If all earnings are paid out as dividends to shareholders, the stock price will be $3.00/0.14 = $21.43 This is the stock price when there is “no growth.” Therefore, the PVGO = $25.00 - $21.43 = $3.57 17 (Q17 in Type B) TD Bank’s earnings and dividends are expected to grow at a rate of 10% during the next years, at 8% in the third year, and at a constant rate of 6% thereafter If last dividend paid was $1 and the required rate of return on its common stock is 12% How much should you pay today for one share of TD Bank? A) $19.31 B) C) D) $24.66 $25.97 $28.02 Solution: A g1, g2 = 10% g3 = 8% g4 and onwards = 6% r = 12% DIV0 = 1.00 Constant Growth DDM P0 = DIV1 r–g and P3 = DIV4 r–g = DIV3 (1 +g) r-g First, Find DIV3 DIV1 = DIV0 (1 +g) = 1.00 (1.10) = 1.10 DIV2 = DIV1 (1 +g) = 1.10 (1.10) = 1.21 DIV3 = DIV2 (1 +g) = 1.21 (1.08) = 1.3068 DIV4 = DIV3 (1 +g) = 1.3068 (1.06) = 1.3852 P3 = 1.3852 / (.12-.06) =$23.09 P0 = DIV1/(1 +r)1 + DIV2 /(1 +r)2 + DIV3/(1 +r)3 + P3/(1 +r )3 = 1.10/(1.12) + 1.21/(1.12)2 + 1.3068/(1.12)3 + 23.09/(1.12)3 = 0.9821 + 0.9646 + 9302 + 16.4350 = $19.31 18 (Q18 in Type B) How much should you pay today for a stock per share that offers a constant growth rate of 9% for dividends, requires a 12% rate of return, and is expected to sell for $40 one year from now? A) $35.71 B) $38.83 C) $41.20 D) $44.80 Solution: B The easiest way to solve this problem is to realize that: Cap Gain return + Div Yield = 12% Cap Gain return = 12% - 9% = 3% P0 = P1 / (1.03) P0 = $40/(1.03) = $38.83 19 (Q19 in Type B)What should be the annual dividend yield for Year of a stock if a $4 dividend per share was just paid, the stock has an annual required rate of return of 18%, and a constant dividend growth rate of 6%? A) 6.35% B) 7.57% C) 12.00% D) 13.48% Solution: C DIV3 = DIV0 x (1 + g)3 = x (1.06)3 = $4.7641 P2 = DIV3/ (r-g) = $4.7641 / (.18 - 06) = $39.70 Ỵ annual dividend yield for Year = DIV3/P2 = $4.7641/$39.70 = 12.00% 20 (Q20 in Type B) What is the implied constant growth rate of dividends for a stock currently priced at $25, that just paid a dividend $2 per share, and has a yearly expected rate of return of 18%? A) 3.41% B) 9.26% C) 10.0% D) 13.5% Solution: B 21 (Q24 in Type B) A stream of equal cash payments lasting forever is termed: A) an annuity B) an annuity due C) an installment plan D) a perpetuity Solution D definition of a perpetuity 22 (Q25 in Type B)Given a set future value (greater than zero), which of the following will contribute to a lower present value? A) Higher discount rate B) Fewer time periods C) Less frequent discounting D) Lower discount factor Solution A The higher discount rate lowers the PV; the other three will raise the PV 23 (Q26 in Type B) If we assume that in the market place the nominal rate of interest is greater than that real rate of interest we can normally assume that A) there is deflation in the economy B) the CPI is increasing C) Price of the average home is going down D) No one wants to borrow money as the rates are too high Solution B It implies that we are in an inflationary environment and that the CPI (consumer price index) is going up 24 (Q27 in Type B) Which of the following theories is generally supported by the principles of compound interest, assuming we invest in interest bearing securities? A) B) C) D) the longer you invest the more likely your investment will grow Whether you invest for your retirement early or late in life are irrelevant The rate at which your retirement investment grows is irrelevant The later in life you invest the better off you will be Solution A Assuming a positive rate of interest the longer you invest the more your investment will grow over time 25 (Q21 in Type B) Which of the following is correct for a CCC-rated bond, compared to a BBB-rated bond? A) The CCC bond must have protective covenants B) The CCC bond must have a sinking fund provision C) The CCC bond must offer a higher coupon rate D) The CCC bond must offer a higher yield to maturity Solution: D See text p.150 26 (Q22 in Type B) Which of the following bond features would be attractive to the bond investor and allow him/her to lend funds at a lower rate? A) A call provision B) A sinking fund provision C) A subordination provision D) A zero coupon feature Solution: B See text p.150 27 (Q23 in Type B) Which of the following is correct for a bond currently selling at a premium? A) Its current yield is higher than its coupon rate B) Its current yield is lower than its coupon rate C) Its yield to maturity is higher than its coupon rate D) Its default risk is extremely low Solution: B 28 (Q28 in Type B)The maximum number of shares that a company is permitted to issue, as specified in the firm’s articles of incorporation is called: A) authorized share capital B) issued share capital C) issued and outstanding share capital D) additional paid-in capital Solution: A 29 (Q29 in Type B)Bank of Montreal had fallen upon hard times due to a rogue trader and dividends on their non-cumulative, preferred stock were not paid for three years They are now able to resume the dividend payments Which of the following is true? A) Common shareholders must now receive three years' worth of dividends B) Preferred shareholders must now receive three years' worth of dividends C) The corporation must close if preferred shareholders are not paid D) Common shareholders have not received dividends for three years Solution: D If a company omits the dividend on preferred stock, it must also omit the dividend on common stock Because the preferred shares are non-cumulative, the company does not need to pay out the last three years of dividends 30 (Q30 in Type B) The form of market efficiency that best describes the inability of professional portfolio managers to outperform the market is: A) strong-form efficiency B) semi-strong form efficiency C) weak-form efficiency D) None of the above All professional portfolio managers outperform the market Solution: B (see text p.187-188) ... efficiency B) semi-strong form efficiency C) weak-form efficiency D) None of the above All professional portfolio managers outperform the market Solution: B (see text p.1 8 7-1 88) ... of return of 18%, and a constant dividend growth rate of 6%? A) 6.35% B) 7.57% C) 12.00% D) 13.48% Solution: C DIV3 = DIV0 x (1 + g)3 = x (1.06)3 = $4.7641 P2 = DIV3/ (r-g) = $4.7641 / (.18 -. .. much of a stock’s $25 price is reflected in the PVGO if it expects to earn $3 of earnings per share next year, and has a required rate of return of 14%? A) $3.57 B) $5.00 C) $21.43 D) $22.00 Solution: