Math problems

PART I: MULTIPLE CHOICE - Choose the letter of the most correct answer for each question. Record only one answer per question. Each question is worth 2 points, 1. IS THE FOLLOWING STATEMENT TRUE or FALSE? "A financial security is a contract between the provider of funds and the user of these funds that clearly specifies the amount of money that has been provided and the terms and conditions of how the user is going to repay the provider." a. True b. False 2. IS THE FOLLOWING STATEMENT TRUE or FALSE? "A share of stock represents a loan to a business from individuals divided up into units which spreads out the risk of the loan and thus lowers its cost to the business." a. True b. False 3. IS THE FOLLOWING STATEMENT TRUE or FALSE? A consol is a bond that pays a variable monthly coupon amount and, when originally issued, is set to mature in 18 months. a. True b. False 4. IS THE FOLLOWING STATEMENT TRUE or FALSE? A convertible bond allows the security holder to convert one bond into another bond, usually with a different coupon rate or maturity date, according to current market conditions. a. True b. False 5. When the yield to maturity (YTM) for a particular bond is greater than its coupon rate, the bond is selling at: a. A premium. b. A discount. c. Par value d. The correct answer to this question cannot be determined without more information. 6. It the formula. =(D1Pn)+22 whar does 2 - represent a. the expected price opprecistion yield ffuet + common ack. b. the expected dividend yield from a common stock. c. the dividend yield from in peefered siock. d the interest payment fiven a bond. c. None of the abovebe paid one year from today increases and all other factorn remain comtant the price of the stock wiit if the Enowth rate of all funure dividends increases add all other fictess remait conctuti. the price of the stock will remain constant, the price of the stock witl a. Decteish, decresse, docresse b. Increase; increase; dectcase c. Docreasc; increase; decrease d. Increase; increase; increase e. None of the answern listed above are corroct. 8. Which of the following is correct about the equifibritam pirice of a 51,000 par vatue bond with an 8 is. coupon rate if the bond's yield to manarity (YTM) is 15 percet? (There may be mare than one correct answer for this quertion; you mast select ALL of the cocroct mswers, but ONE Y the corcect answers to receive any credit for this questiod). a. If this bond matures in one year of more, the price of the bood will be greater thin 51,000 . b. If this bopd manires in one year or mote, the prioe of the bood will be less than $1,000. c. The priee of this boad will be smaller if term time fo matarity is 20 years than if the term to maturity is 10 years. d. If this boed matires in one year or mote, the price of the boed will be manaller if the coupon payments are made semi-nzaually than if they are made anrally. e. This bond will sell for $1,000 regardless of the tirne to maturity of the boed. f. If this bond matures in ope year of mone, the prise of the bond win be latger if the cocpon payments: are made semi-annually than if they ate made anecally. 8. The price of this bond will be larger if tere time to mathariy is 20 ytars thas it the term to matarity ts 10 years. 9. Suppose that interest rates incteate. Axparaing alf other parameters that iapact tac price of boeds and stocks remain coostart, what would you expoct to happen to bood and stock price? a. Bond prices would incresse and stock prices would decrease. b. Bond prices would docrease and sock prices would decrease. c. Bond prices would decresse and stocis prices would increase. d. Bond prices would increase and stock prices would incresse. c. Stock prices would incresue. Moro information would be necded to determine the impact on bond prices. 4. The burwe is erifay at pur 4 fimerifiet ithurmation ti gercrmagromit? infumbatide yever. Cot year truen rodes. - Tite NeV af thit proiect in 11ates. x. 1139% h 4.1h2= \&. 15914 d. 12.75= Huat on: If 1 the PART II: MROBLEMS - Compute a final numerical ancwer for each of the following problemi. You ahould work out your witutions on loese leaf paper to that when I post the solution key you can camily see. What you did incomectly for any questions that you misk Lnless otherwise specifically intericted in the question, round all dotlar answers fo 2 decimal places and recoed all interest rale, coupon rate and growth rate answen as a percent ruunded to one decimal place. 21 Data for the last 8 years of stock prices and dividendi paid for Poresy. Inc. are liated below: What is the average rate of return for Poggy, Inc, stock over the 8 year time period? 22. Data for the last 8 years of stock prices and dividends paid for Poggy, Inc. are listed below: What is the standard deviation of rerumis for Poggy, Inc: stock over the 8 year time period? (Compute the standard deviation assuming this is a population of returns, not a sample - that is, use the procedure described in the textbook for calculating tike standard deviation of a series of stock returns). 23. Exactly three years ago, Marituna bought a twenty-year, $25,000 par value bond that has 6.5% coupon rate and semi-annual payments. Ste paid $20,248,25 for the bond. If the yield to maturity on this bond is currently 7.4\%, how much will Mary receive for her next eoupon payment that she expects to receive exactly 6 months from today? 24. What is the equilibrium price of a 51000 par value bond with a 8.35% coupon rate (annual payments) that matures in 8 years, assuming that this bosd's yield to maturity (YTM) is 6.85% ? 25. What is the yield to maturity (YTM) of a $1000 par value bond that current sells for $888.42, atsuming that the bond has a coupon nate of 6.4% (antual payments) aad 26 years remaining to maturity? - Mitinats to the 30 12. Fiegatai, Isc is cxpecied to pay a dividend of 32.56 eractly ose year froen today (ce., D, 2.56) and its 38. If share of common stock of the 5smson Co. offer an expected tocal sethirn of 15%, and if the growth rite in future dividends of the stock ate expected to be 390 per year forever, what as the stock i dividenid: yield (Le, DvP.)? 30. The stock of Cabhoce, Insurpocnied is tradins at 570.00 per state. The company just paid a dividend of 5500 per stare (etat is, D3=5.00 ). The geowth rate in dividents is projected to be 6 percent per yeter forever. What is Gabbor's cont of eyuity capital (ihat is, canpule the required raie of renura on the stock)? 40. Prallips, Inc, just paid a dividend of 53.25 per share on its common wock (that is, 5,3.25 ). Itvestors expeit the dividend to grow at 4546 in years 1 and 2 , they expect the dividend to grow at 25%6 in year 3 and they expect that all future dividenda (that ik, divideods in years 4,5,, infinity) to grow at a constant rate of 5% per year. If the cost of capital for Pailligh. lic. sooks is. 15 is. what is the current price of the stock? 41. IBIS Corporation has had dividends grow from 52.50 per stare to 56.00 per share over the last 10 ycars. (the 56.00 per ware dividend was paid yeterdays that is, D456.00 ). Thit compotanded aanual growth rate in dividends is expected to continue anto the fuene foecter. If the current market price of IBis's stack is $45.00 per shere, what rate of teram do invertees eypet to receive from buying IBIS stock? 42. Jasper, Inc- just puid a dividend of $1.88 per share (that is, D2=1.s3 ). If the growth rate in Jauper's dividends is expected to ahrink every year (forever) by, 6 percent (that is, 8=6,027=,06 ) and if Jarper's required rate of retum on equity is 22.6s, what is the currest cquilibrium price of Jaxper's stocic? 43. Malcolm Manufacturing. Ine jast paid a 52.00 antial droidend (that D1,D2=2.00 ). There will be no dividend payment for the next rav years (i.c. at t1 and t=2). In year three ( t3), the dividend is expected to be 55.00. The dividead will then grow at loss acrully for the next 3 years (Le., at t=4,5 - 5 and t=0) and thereafter (ic, beginting at t7 dividends witl grow at a rate of 3 pa annually forever, Assuming a required teturn of 14:4, what is the curtest price of the stock? 44. Consider a project witb the followitg cash tlow: The Payback Period of this project 2.6 years, If the WACC for thas project it 39 w, what is the project'at NPVitic, net pregent vatue)? (Nete that the cash flow foet tob a not provided to you - that is, you thist first solve for it and then wee this valoe to find the NPY of the project). 49. Fresla Motors needs to select an assembly line for producing their new SUV. They have two options: - Option A is a highly automated assembly line that has a large up-front cost but low maintenance cost over the years. This option will cost $5 million today with a yearly operating cost of $2 million. The assembly line will last for 5 years and be sold for $4 million in 5 years. - Option B is a cheaper alternative with less technology, a longer life, but higher operating costs. This option will cost $2 million today with an annual operating cost of $3 million. This assembly line will last for 8 years and be sold for 51 million in 8 years. The firm's cost of capital is 14%. Assume a tax rate of zero percent. The equivalent annual cost (EAC) of OntionA is S million (Round your answer to 3 decimal places; for example, record $82.213943 million as 82.214 million). 50. Fresla Motors needs to select an assembly line for producing their new SUV. They have two options: - Option A is a highly automated assembly line that has a large up-front cost but low maintenance cost over the years. This option will cost $5 million today with a yearly operating cost of $2 million. The assembly line will last for 5 years and be sold for $4 million in 5 years. - Option B is a cheaper alternative with less technology, a longer life, but higher operating costs. This option will cost $2 million today with an annual operating cost of $3 million. This assembly line will last for 8 years and be sold for $1 million in 8 years. The firm's cost of capital is 14%. Assume a tax rate of zero percent. The equivalent annual cost (EAC) of OptionB is $ million (Round your answer to 3 decimal places; for example, record $82.213943 million as 82.214 million). c. Ge divilmel yirlt frim is tweinged asect e. Nobe of the atoves. the price of the stoek will remain soncatint, the prict of the siock wiff a. Betease; decreve, dectrave h. Treteme; iscreasc, decreate c. Decreave; incicise, diterese if. Increave, incretse, itricase 6. Noce of the awaler litted above ac curnet. ta recelve amy credit for this question) b. If thin bond mature in ene year or mure the price of the byed wit be lens that 11 com. is 10 yzars. 2. This boed witt sell for \$5,000 segardless of the time so murarg of the beit. are made iemi-ammatily thay if they ace made armally. is 10 y can. it. Eond prices would increase and iboci feites would detreave b. Bond prices weuld drontse asd stock peices wodid decrnee. 6. Hond prices woaid docriase and thock peices would mertine- d. Fiond prices avould iscreave and inck prises woth increave. pritics. PART II: PROBL.EMS - Compute a fitul eumerical anwwer for cach of the following problems, You should work out your solutions on loose leaf paper so that when 1 post the sotution key yoe can tavily seet What you did incorrectly for any quettions that you tiset. Unless othervise specifically instrucied in the queition, foand all dollar anvwern to 2 decimal plases and record all interest rate, coupon rate and gowth rase amwers as a percent roended to one decimal place. 21. Data for the last 8 years of stock prices and dividends paid for Poerry, foc are listed belowil. What is the average rate of retum for Poggy, Inc, stock over the 8 yek time period? 22. Data for the last 8 years of stock prices and dividends paid for Poggy, Inc. are listed below: What is the standard deviation of retums for Poggy, Inc, sock over the 8 year time period? (Compute the standard deviation assuming this is a popalation of retums, not a sample - that is, use the procedure described in the textbook for calculating the standard deviation of a series of stock returns). 23. Exactly three years ago, Marianna bought a twenty-year, 525,000 par value boed that has 6.5% coupon rate and semi-annual payments. She paid 520,248,25 foe the bond. If the yield to maturity on this bond is currently 7.4\%, how much will Mary receive for ber next coupon payment that she expects to receive exactly 6 months from today? 24. What is the equilibrium price of a $1000 par value bond with a 8.35% coupon rate (annual payments) that matures in 8 years, assuming that this bond's yield to maturity (YTM) is 6.85% ? 25. What is the yield to maturity (YTM) of a 51000 par value bond that current sells for $888.42, assuming that the bond has a coupon rate of 6.4% (annual payments) and 26 years remaining to maturity? 26. Zeus Industry issued a bond, which pays coupon interest semi-annually and has 30 years to maturity. The bond's par value is 51,000 , the current market price is $1,059,34, and the yield to maturity is 7.50%. The bond's coupon rate is 27. Peter Parker Corp. plans to issue a $1,000 par value, semi-annual pay bond with 20 years to maturity and a coupon rate of 5.50%. The company expects the bonds to sell for $820.00. MC inc's cost of debt is estimated to be o 28. LBJ Enterprises is issuing new bonds for a capital budgeting project. The bonds will mature in 20 years and have a coupon rate of 8,50% with semi-annual coupon payments (assume a par value of $1,000 on the bond). The current yield-to-maturity for similar bonds is 6.00%. The company hopes to raise $16 million with the new issue. To raise the debt, how many bonds must the company issue? (Round to the nearest whole number). 29. Two years ago, Phutki Corp. issued a $1,000 par value, 11 percent (annual payment) coupon bond. At the time the bond was issued it had 15 years to maturity. Currently this bond is selling for $1,000 in the bond market. Phutki Corp, is now planning to issue a $1,000 par value bond with a coupon rate of 9 percent (semi-annual payments) that will mature 25 years from today. Assuming that the riskiness of the new bond is the same as the previous bond (i.e., the YTM on the new bond is equal to the current YTM on the previous bond), how much will investor's pay for this new bond? 30. Consider a Zerobond (i.e., a bond that pays no coupon payment, meaning that the coupon rate on the bond is 0% ) with a par value of $5,000 that will mature exactly 16 years from today. The current YTM of this Zerobond is 7.35%. Two years ago, the YTM of the same Zerobond was 8.61%. Calculate the dollar price increase/decrease (2 decimal places) within the last two years. If the bond falls in price, enter your answer on D2L as a negative value (i.e., put a minus sign before your number with no space between the minus sign and the number). If the bond increases in price, record the dollar amount of the increase. 31. If the expected retum on the market portfolio (i.e., Rm ) is 15%, if the risk-free rate (i.e., R1 ) is 3% and if the beta of Homton, Inc. stock is 1.95, what is the equilibrium expected rate of return on Homton's stock according to the Capital Asset Pricing Model? 32. If the beta of Braxton, Inc. stock is 0.85, the risk-free rate (R) is 4.5%, and the market risk premium is 8.9%, what is the equilibrium expected rate of retum on Braxton's stock according to the Capital Asset Pricing Model? 33. Compute the price of a company's stock that just paid a dividend of $3.25 (that is, D0=3.25 ), assuming that the growth rate in dividends is expected to be 4.5% per year forever and that the required rate of return on this stock is 18.5%. 34. Ma\&Son Company is expected to pay a dividend of $2.60 one year from today (i.e., D1=2.60 ). The company's required rate of return is 11%. If the market expects that the dividend will grow at a constant rate of 4% per year forever, Ma\&Son's stock should sell for $ today. 35. Rosas, Inc will not pay a dividend for two years. Three years from today, the company will pay out a dividend of $3.30 (i.e., D3=3.30 ). After that, the dividend will grow at 6% per year forever. If the required rate of return on Rosas' stock is 14%, the stock's current price (i.e., Po) is \$ 36. Dr. Lee plans to add Sony, Inc. stock to his investment portfolio. The stock just paid a dividend of \$1.50 (i.e., D0=1.50 ). He expects that the dividend will grow at 20% for the next two years and 4% forever after that. Assuming a discount rate of 13%, Dr. Lee knows that Sony, Inc stock is worth $ 37. Bugatti, Inc is expected to pay a dividend of $2.56 exactly one year from todey (i,e1,D,2.56) and its current stock price is 548.84. The required rate of teturn for the company's wock it 11 . If the market: expects. Bugatti's dividends to grow at it cotstant rate forever, then the growth rate mist be 38. If shares of common stoek of the Samson Co. offer an expected total return of 15 the and if the growth rate in future dividends of the stock are expected to be 3% per year forever, what is the stack's dividerd yield (i.e, D,P0) ? 39. The stock of Cabbor, Incorporated is trading at 570.00 per stare. The conpany just paid a dividend of $5.00 per share (that is, D0=5.00 ). The growth rate in dividends is projocted to be 6 percent per ytur forever, What is Cabbot's cost of equity capital (that is, compute the required rate of retum on the stock)? 40. Phillips, Ine, just paid a dividend of $3.25 per share on its common stock (that is, D; =3.25 ). Investors expect the dividend to grow at 45% in years 1 and 2, they expect the dividend to grow at 25% in year 3 and they expect that all future dividends (that is, dividends in years 4, 5, ..., infinity) to grow at a constant rate of 5% per year. If the cost of capital for. Phillips, Inc. stock is 15%, what is the current price of the stock? 41. IBIS Corporation has had dividends grow from $2.50 per share 10$6.00 per share over the last 10 years (the $6,00 per share dividend was paid yesterday; that is, D0=$6.00). This compounded annual growth rate in dividends is expected to continue into the future forever. If the current market price of IBIS's stock is $45.00 per share, what rate of return do investors expect to receive from buying IBIS stock? 42. Jazper, Ine, just paid a dividend of $1.88 per share (that is, D5=1.88 ). If the growth rate in Jazper's dividends is expected to shrink every year (forever) by 6 percent (that is, g=6.0%=.06 ) and if Jazper's required rate of return on equity is 22.6%, what is the current equilibrium price of Jaxper's stock? 43. Malcolm Manufacturing, Inc. just paid a $2.00 anmual dividend (that is, D2=2.00 ). There will be no dividend payment for the next two years (i.e, at t=1 and t=2). In year three (t=3), the dividend is expected to be $5.00. The dividend will then grow at 10% annually for the next 3 years (i.e., at t=4,t =5 and t=6 ) and thereafter (i.e., beginning at t=7 ) dividends will grow at a rate of 3% annually forever. Assuming a required return of 14%, what is the current price of the stock? 44. Consider a project with the following cash flows: The Payback Period of this project is 2.6 years. If the WACC for this project is 13%, what is the project's NPV (i.e., net present value)? (Note that the cash flow for t=0 is not provided to you - that is, you must first solve for it and then use this value to find the NPV of the project). 45. If the cost of capital for the project shown below is 3.5 percentige points less than the project's IRR (for example, if the project's IRR is 12%, the cost of capital is 8.5% ), what is the NPV of the project? 46. Panthers, Itic. has a capital structure of 20% debt and 80% equity. The tax rate is 40%. The firm's bonds currently trade in the market for $950. These face value $1,000 bonds have a coupon rate of 6%, paid semiannually, with 10 years to maturity. The firm's common stock trades for $20 per share. The fimm just paid a dividend of $2. Future dividends are expected to grow at 3% per year forever. Panther's WACC is %. Round your answer to 2 decimal places. USE THE INFORMATION BELOWTO ANSWER QUESTIONS 47 and 48 ABC Industries is considering a project that has the following cash flows: The project has a payback period of 3.5 years. The firm's cost of capital is 17%. 47. The project's net present value (NPV) is $ 48. The IRR of the project is % 49. Theile Motorn seeds to select in assedsbly line for producing their new SUV They liave two options - Option A is a highly autorated asscmbly liae that hat a large up-front cost but low mainteriance cost over the years. This optiod will cott $5 million toslay with a yearly operating cost of $2 milion. The assembly lite will last for 5 years and te sold for 54 million in 5 years. - Option B is a cheaper altemative with less technology, a longer life, but higher operativig conts. This option will cost 52 milliot today with an annual operating cost of 53 miltion. This acwembly line will last for 8 years and be sold for $1 million in 8 years. The fint's cost of capital is 14%. Assumea tax rate of zero percent. The equivaleat annual cost (EAC) of Option A is 5 million (Round your answer to 3 decimal places; for example, record $82.213943 million 3582.214 million). 50. Freala. Motors needs to seleet an assembly line for producing their new SUV. They have two optionst - Option A is a highly automated assembly line that has a large up-front cost but low maintenance cost over the years. This option will cost $5 million today with a yearly operating cost of $2. million. The assembly line twill last for 5 years and be sold for $4 million in 5 years. - Option B is a cheaper alternative with less technology, a longer life, but higher operatiryg costs. This option will cost $2 million today with an annual opcrating cost of $3 million. This assembly line witl last for 8 years and be sold for 51 million in 8 years, The firm's cost of capital is 14\%. Assame a tax rate of zero percent. The equativent anmaal cost (F.AC) of O mtion B is $ million (Round your answer to 3 decimal places; for example, record $82.213943 million as 82.214 million)