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# FINANCIAL MANAGEMENT FIN 3716

LSU

GPA 3.96

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This 82 page Class Notes was uploaded by Alyce Quitzon on Tuesday October 13, 2015. The Class Notes belongs to FIN 3716 at Louisiana State University taught by G. Utete in Fall. Since its upload, it has received 20 views. For similar materials see /class/222540/fin-3716-louisiana-state-university in Finance at Louisiana State University.

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Date Created: 10/13/15

Topic 5 Bonds The following document contains practice problems for your fifth quiz The equations listed below will be printed on the front of the test You are expected to memorize any equation not printed on this first page 1 1 72 PVArmuz39tyC l C 1g 2 PV G 1 rowmgAnnuzty ig 10 J PVGrowingPerpetuity EAR 1 1 m APR m1EARquot 1 L i g Fisher 11 1 r1 p What is the price of a bond with a face value of 1000 an annual coupon rate of 7 an annually compounded yield to maturity of 5 and 10 years left to maturity Price 70 x 1 11051 005 100010510 115443 What is the price of a bond with a face value of 1000 an annual coupon rate of 4 an annually compounded yield to maturity of 8 and 16 years left to maturity Price 40 x 1 110816008 100010816 64595 What is the price of a bond with a face value of 1000 an annual coupon rate of 4 paid semiannually an annual yield to maturity of 10 compounded semiannually and 12 years left to maturity Price 20 x 1 110524005 100010524 58604 What is the price of a bond with a face value of 1000 an annual coupon rate of 6 paid semiannually an annual yield to maturity of 3 compounded semiannually and 4 years left to maturity Price 30 x 1 1101580015 100010158 111229 Bond X pays coupons semiannually What is the annual coupon rate of the bond if it has a price of 110824 a face value of 1000 an annual yield to maturity of 10 compounded semiannually and 25 years to go until maturity 110824 Cx 1 11055005 10001055 C 110824 100010551 11055005 C 75 paid semiannually Therefore the annual coupon rate is 15 Bond Y pays coupons annually What is the annual coupon rate of the bond if it has a price of 84639 a face value of 1000 an annual yield to maturity of 10 and 10 years to go until maturity 84639 C x 1 11101 010 1000110 l0 C 84639 10001101 1 11101 010 C 75 paid annually Therefore the annual coupon rate is 75 Bond 2 pays coupons semiannually What is the annual coupon rate of the bond if it has a price of 90348 a face value of 1000 an annual yield to maturity of 10 compounded semiannually and 5 years to go until maturity 90348 C x 1 11051 005 100010510 C 90348 10001051 1 11051 005 C 3750 paid semiannually Therefore the annual coupon rate is 75 Bond A has a price of 98046 a face value of 1000 an annual coupon rate of 9 paid semiannually and 5 years until maturity What is the annual yield to maturity if it is compounded semiannually The bond is selling at a discount The YTM must be higher than the annual coupon rate Let s try 95 as our plugin answer Price 45 x 1 1104751 00475 10001047510 98046 Bond B has a price of 104055 a face value of 1000 an annual coupon rate of 9 paid semiannually and 5 years until maturity What is the annual yield to maturity if it is compounded semiannually This bond is selling at a premium The YTM must be lower than the annual coupon rate Let s try 85 as our plugin answer Price 45 x 1 1104251 00425 100010425 l0 102003 This is incorrect We need a bigger difference between the coupon rate and the YTM Try 800 Price 45 x 1 11041 004 10001041 104055 There are two important concepts here The yield to maturity tells you what the risk level ofa bond is at any point in time The coupon rate tells you what the risk level of a bond was when it was issued Since the coupon rate does not change over the life of the bond the price adjusts to changing risk conditions If the YTM gt the coupon rate the bond will sell at a discount If the YTM lt the coupon rate the bond will sell at a premium We always match up our variables with the number of periods Therefore 85 per year 425 per period for instance At what tax rate would you be indifferent between a corporate bond with an 84 yield to maturity and a municipal bond with a yield to maturity of 63 Aftertax return on a corporate bond YTM x 1 T 84 x 1 T 84 x 1 T 63 T 25 Suppose you have a choice between two bonds 1 a revenue bond issued by the state of Louisiana to finance the construction ofa new building on LSU s campus This bond has a yield of 4 2 A corporate bond with a yield of 65 At what tax rate would these bonds yield identical aftertax returns Aftertax return on a corporate bond YTM x 1 T 65 x 1 T 65 x 1 T 4 T 3846 12 Bond A has an annual coupon rate of 10 paid semiannually It has 5 years to maturity and a face value of 1000 If the yield to maturity is 6 compounded semiannually what is the price of Bond A Price of Bond A 50 x 1 11031 003 100010310 117060 If you hold Bond A in the previous question from now 5 years to maturity until today s date a year from now 4 years to maturity what capital gains yield will you experience Price of Bond A in one year 50 x 1 11038003 10001038 114039 Capital Gains Yield 114039 117060117060 258 Assume the same information from the previous question Add the current yield of Bond A to the capital gains yield you calculated What is your answer and what is the significance of the number you get Current Yield Annual CouponsPo Current Yield 100117060 854 Current Yield Capital Gains Yield 854 258 596 z 600 If you own a bond only two things can happen the price can change and you can receive coupons Therefore the combination of the capital gains yield and the current yield re ects all the information about the performance of your bond investment This has to equal the yield to maturity because the YTM is the total expected level of return given the riskiness of the bond Assume the same information from the previous question As of January 1 2011 Bond A had exactly 5 years to maturity Bond A pays coupons on June 30 and December 31 of each year Now assume that today s date is December 1 2011 What is Bond A s lldirty price ie the price that includes accrued interest You may assume that there are 180 days from January 1 to June 30 and 180 days from June 30 to December 31 Clean price on December 1 2011 50 x 1 11039003 10001039 115572 Dirty price 115572 150180 x 50 119739 Assume the same information from the previous question If you are in the 39 tax bracket and Bond A is a corporate bond what is your aftertax return on this investment After tax return YTM x 1 T 600 x 1 039 366 What is the dirty price of a bond with a face value of 1000 an annual coupon rate of 6 paid semiannually an annual yield to maturity of 8 compounded semiannually and 5 years left to maturity Assume that coupons are paid on June 30 and December 30 and that there are 360 days in the year Today s date is April 30 2012 Clean price on April 30 2012 30 x 1 110410004 100010410 91889 Dirty price 91889 120180 x 30 93889 18 Bond T has a face value of 1000 an annual coupon rate of 8 one payment per year an N N 0 annually compounded yield to maturity of 12 and 6 years to maturity Calculate the capital gainloss between today s date and one year from now Calculate the current yield Verify that the capital gainloss the current yield YTM Price of Bond T 80 x 1 11126012 10001126 83554 Price of Bond T in one year 80 x 1 11125012 10001125 85581 Capital Gains Yield 85581 8355483554 2426 Current Yield 8083554 9574 Current Yield Capital Gains Yield 9574 2426 1200 Bond X has a face value of 1000 and a current price of 96568 It pays an annual coupon rate of 7 one payment per year and has 10 years to go until maturity What is its yield to maturity The bond is selling at a discount The YTM must be higher than the annual coupon rate Let s try 75 as the plugin answer Price 70 x 1 110751 0075 1000107510 96568 What is the price of a bond with a face value of 1000 an annual coupon rate of 7 paid semiannually an annual yield to maturity of 11 compounded semiannually and 9 years left to maturity Price 35 x 1 11055180055 1000105518 77508 Bond A pays coupons semiannually What is the annual coupon rate of the bond if it has a price of 94418 a face value of 1000 an annual yield to maturity of 12 compounded semiannually and 35 years to go until maturity 94418 C x 1 11067006 10001067 C 94418 100010671 11067006 C 50 paid semiannually Therefore the annual coupon rate is 10 Bond B has a price of 103911 a face value of 1000 an annual coupon rate of 2 paid semiannually and 4years until maturity What is the annual yield to maturity if it is compounded semiannually The first clue we have is that the bond is selling at a premium The YTM must be lower than the annual coupon rate Let s try 1 as our plugin answer Price 10 x 1 1100580005 100010058 103911 The YTM is 1 per year compounded semiannually 23 N l Bond C has a price of 98188 a face value of 1000 an annual coupon rate of 4 paid semiannually and 4years until maturity What is the annual yield to maturity if it is compounded semiannually This bond is selling at a discount The YTM must be higher than the annual coupon rate Let s try 45 as our plugin answer Price 20 x 1 110225800225 1000102258 98188 The YTM is 45 per year compounded semiannually At what tax rate would you be indifferent between a corporate bond with an 89 yield to maturity and a municipal bond with a yield to maturity of 623 Aftertax return on a corporate bond YTM x 1 T 89 x 1 T 89 x 1 T 623 T 30 Suppose you have a choice between two bonds 1 a revenue bond issued by East Baton Rouge Parish to finance the 39 of a 39 center 39 This bond has a yield of 47 2 A corporate bond with a yield of 71 If you are in the 32 tax bracket which bond would you prefer Aftertax return on corporate bond 71 x 1 032 483 The 483 corporate bond yield is preferable to the 47 yield municipal bond Bond D has an annual coupon rate of 7 paid annually It has 3 years to maturity and a face value of1000 If the yield to maturity is 10 compounded annually what is the price of Bond D Price of Bond D 570 x 1 11103010 10001103 92539 If you hold Bond D in the previous question from now until today s date a year from now what capital gains yield will you experience Price of Bond D in one year 70 x 1 11102010 10001102 94793 Capital Gains Yield 94793 9253992539 244 28 Assume the same information from the previous question Add the current yield of Bond D to the capital gains yield you calculated What is your answer and what is the significance of the number you get Current Yield Annual CouponsPo Current Yield 70S92539 756 Current Yield Capital Gains Yield 756 244 1000 YTM of Bond D If you own a bond only two things can happen the price can change and you can receive coupons Therefore the combination of the capital gains yield and the current yield reflects all the information about the performance of your bond investment This has to equal the yield to maturity because the YTM is the total expected level of return given the riskiness of the bond Bond E has exactly 7 years left until to maturity as ofJanuary 1 2014 The bond has a face value of 1000 an annual coupon rate of 35 paid semiannually and an annual yield to maturity of 25 compounded semiannually f coupons are paid on June 30lh and December 30 h and there are 360 days evenly divided amongst the months in the year what is the bond s dirty price as of September 30 2014 Clean price on September 30 2014 1750 x 1 1101251300125 100010125 l3 105965 Dirty price 105965 90180 x 1750 106840 Discuss how bonds differs from stocks Bond contracts promise a steady stream of payments from the issuer to the investor These payments are determined by the terms of the bond indenture In general a bond indenture will specify the periodic interest rate coupons and the amount of the face value to be repaid at maturity In the event of a liquidation bondholders will have priority over stockholders in recouping their investment from the remains of the firm Stock is an ownership claim The payments a stock investor receives occur via capital gains and dividends Although stockholders are junior to bondholders they do get to participate in all of the upside of the firm s performance The junior status of stocks and the exposure to all of the fortunes of the company both good and bad generally make stocks a more risky investment than bonds Topic 3 The time value of money The following document contains practice problems for your third quiz The equations listed below will be printed on the front of the test You are expected to memorize any equation not printed on this first page 1 1 72 PVArmuz39tyC l C 1g 2 PV G 1 rowmgAnnuzty ig 10 J PVGrowingPerpetuity EAR 1 1 m APR m1EARquot 1 L i g Fisher 11 1 r1 p You invested 6200 in an account that pays 5 simple interest How much money will you have at the end of ten years Balance Principal Interest Interest 005 x 6200 x 10 3100 Balance 6200 3100 9300 Miranda invested 10500 in an account that pays 6 simple interest per year How much money will she have at the end of four years Balance with simple interest 006 x 10500 x 4 10500 13020 You invested 1650 in an account that pays 5 simple interest How much more could you have earned over a 20year period if the interest had compounded annually Balance with simple interest 005 x 1650 x 20 1650 3300 Balance with compound interest 165010520 437794 Gain with compounding 437794 3300 107794 Tre invested 1400 in an account that pays 5 simple interest per year How much more could he have earned over a 20year period ifthe interest had compounded annually Gain with compounding 14001052 005 x 1400 x 20 1400 91462 You deposit 1000 today in an account earning 5 interest compounded annually How much will you have in the account at the end of 5 years FV 10001055 127628 What is the future value of 7189 invested for 23 years at 925 compounded annually FV 71891092523 5499988 Jordan earns a salary of 36000 What will her annual salary be twelve years from now if she is guaranteed annual raises of 36 FV 360001036 lZ 5503254 What is the present value of 150000 to be received 8 years from today if the discount rate is 11 PV 1500001118 6508897 You are guaranteed to receive 1000 five years from today If the appropriate interest rate is 5 compounded annually what is the 1000 worth to you today PV 10001055 78353 10 Your father invested a lump sum 26 years ago at 425 interest compounded annually Today he gave you the proceeds of that investment which totaled 5148079 How much did your father originally invest PV 51480791042526 1744486 Abrina needs 40000 as a down payment for a house 6 years from now She earns 25 on her savings She can either deposit one lump sum today for this purpose or she can wait a year and deposit a lump sum How much additional money must she deposit if she waits for one year rather than making the deposit today PV if she deposits the money today 4000010256 3449187 PV if she waits one year 4000010255 3535417 Additional funds needed 86230 One year ago you invested 1800 Today it is worth 192462 What rate of interest did you earn Assume annual compounding i FVPV 1 i 1924621800 1 692 Forty years ago Kerry Sauley invested all 5000 of his lemonadestand money in a savings account Today that investment is worth 43006511 What is the average annual rate of return he earned on this investment Assume annual compounding i FVPV1 1 i 43006511500014 1 1178 You have a trust fund account that was established 21 years ago with a deposit of 1000 The total balance in the account today is 1882152 Given this information what annual rate of return did the account earn over the 21year time period Assume annual compounding i FVPV121 1 i 18821521000121 1 1500 You have a trust fund account that was established 21 years ago with a deposit of 1000 The total balance in the account today is 1882152 Given this information what annual rate of return did the account earn over the 21year time period Assume daily compounding 13 FVPV17 5 1 iDain 1882152100017 5 1 003829827642 i 003829827642 x 365 1398 16 You have a trust fund account that was established with an initial deposit of 1000 The total H H H N 53 balance in the account today is 367581 If the account earned 75 interest per year compounded annually how long ago was the account established t nFVPVn1i t ln3675811000ln1075 18 years ago You opened a savings account with an initial deposit of1000 The total balance in the account today is 110506 If the account earned 25 interest per year compounded monthly how many years ago was the account established t lnFVPVln1i t ln1105061000ln1 002512 48 months 4 years ago If the appropriate discount rate is 5 what is the present value of the following cash flows End onear Cash Flow 100 200 1 2 3 300 4 5 PV 100105 2001052 3001053 4001054 5001055 59848 If the appropriate discount rate is 6 what is the present value of the following cash flows End of Year Cash Flow 1 150 2 300 3 200 4 700 5 400 PV 150106 3001062 2001063 7001064 4001065 109395 Engler Corporation is considering a project that costs 1000 to start and generates cash flows of 100 in year 1 100 in year 2 300 in year 3 450 in year 4 and 600 in year 5 Calculate the NPV assuming a discount rate of 35 and briefly explain whether this is a good or a bad investment NPV CFO CF11i CF21i2 CF31i3 CF41i4 CF51i5 NPV 1000 100135 100135Z 3001353 4501354 6001355 47983 NPV is negative This is a bad investment N U39I N 0 N l You have just won the Louisiana State Lottery The winning prize consists of a 50000000 split into equal payments over the course of 5 yea rs If the first payment occurs next year and the discount rate is 5 compounded annually what is the present value of the lottery CF1 10000000 PVAnnuity 10000000 x 1 11055005 4329476671 You have just won the Louisiana State Lottery You will receive 1000000 divided into equal chunks over the course of 10 years starting next year If the appropriate discount rate is 10 compounded annually what is the present value of your winnings CF1 100000 PVAnnuity 100000 x 1 11101 010 61445671 Now suppose instead that the first cash flow is received immediately what is the present value of your lottery winnings now PVAnnuity Due 100000 x 1 11101 010 x 110 67590238 You recently won a lottery prize that will pay you 12000 per year for 6 years beginning immediately right now If the appropriate discount rate is 7 compounded annually what is this prize worth today PVAnnuity Due 12000 x 1 11076007 x 107 6120237 You have just won the Alabama State Lottery The winning prize consists of a cigarette lighter and steady payments of125 a month for four years The first payment is received next period If the discount rate is 65 per year compounded monthly what is the present value of the lottery CF1 125 PVAnnuity 125 x 1 11 00651248006512 527094 As part of your retirement package your employer will contribute 25 a week to your pension plan The pension plan generates an annual return of 8 compounded weekly If you plan on retiring in 50 years what is this pension plan worth to you today CF1 25 PVAnnuity 25 x 1 11 0085225 00852 1595145 You just won the grand prize in a national writing contest As your prize you will receive 2000 a month for ten years If you can earn 7 on your money annually monthly compounding what is this prize worth to you today CF1 2000 PVAnnuity 2000 x 1 11 0071212 00712 17225271 Your employer contributes 75 a week to your retirement plan Assume that you plan to work for your employer for another 20 years and that the applicable discount rate is 75 annually compounded weekly Given these assumptions what is this employee benefit worth to you today CF1 75 PVAnnuity 75 x 1 11 0075521 4 007552 4038469 Your employer contributes 50 a week to your retirement plan Assume that you work for your employer for another 20 years and that the applicable discount rate is 9 compounded weekly Given these assumptions what is this employee benefit worth to you today CF1 50 PVAnnuity 50 x 1 11 009521 4 00952 2410615 What is the present value of a cash flow stream that pays 500 next year and each year after that forever if the discount rate is 5 compounded annually PVPerpetuity 500005 10000 Consider the same cash flow stream from the previous question but now assume that the perpetuity starts at time 8 Le 8 years from now What is the present value The present value at time 0 of a perpetuity that starts at time 1 is 10000 Therefore the present value at time 7 of a perpetuity that starts at time 8 10000 in year 7 money PVolCF7 100001057 710681 Now suppose the cash flow stream in the previous question starts at time 8 and that each year the cash flows grow by 4 What is the present value of the perpetuity PV7Growing Perpetuity CF8i g PV7Growing Perpetuity 500005 004 50000 PV0CF7 500001057 3553407 You wish to establish an account that will generate a perpetual annual cash flow of 18000 starting next year Assuming a discount rate of 7 how much would you have to deposit today to achieve this goal PVPerpetuity 18000007 25714286 You wish to establish an account that will generate an annual cash flow of 18000 next year with the annual cash flows growing at 2 per year in perpetuity Assuming a discount rate of 7 how much would you have to deposit today to achieve this goal PVGrowing Perpetuity 18000007 002 360000 35 Suppose the real required rate of return is 748 and that inflation is 3 What is the nominal required return i 1r1p 1 i 10748103 1 1070 If a bank account offers an APR of 6 per year with interest compounded continuously what is the EAR EAR elAPR 1 618 You are trying to decide amongst three different car loans each with an APR of 800 Loan A is compounded semiannually loan B is compounded monthly and loan C is compounded continuously Calculate the EARs of all three loans and briefly describe which one you would choose and why Loan A An APR of800 compounded semiannually has two periods and a perperiod rate of 4 EAR for A 1042 1 816 Loan B An APR of 800 compounded monthly has twelve periods and a perperiod rate of 06667 EAR for B 100666712 1 830 Loan C Continuous compounding requires the use of the exponential function e 08 1 833 Loan A is the cheapest and so this is the one you would prefer You are trying to decide between two different savings accounts Bank A offers a 400 APR with continuous compounding Bank B offers a 425 APR with semiannual compounding Calculate the EARs of both savings accounts and briefly describe which one you would prefer and why Bank A EAR e 03904X1l 1 408 Bank B EAR 1 0042522 1 430 Since we are saving money you would prefer the higher EAR You should choose Bank B What is the APR ofa loan with a 15 EAR assuming daily compounding APR m1 EAR1m 1 APR 36511513 1 1398 Suppose a loan has an EAR of 512 with daily compounding what is its APR APR 3651051213 1 499 41 You are considering 3 credit card offers from Visa MasterCard and Discover You plan on transferring an existing balance of 1000 onto whichever card is best for you All three cards allow you to make no payment on the debt for three years and you plan on using this grace period option The Visa offers an introductory rate of 0 for the first year followed by 16 per year compounded monthly for the next two years The MasterCard offers a flat rate of 12 per year compounded weekly for all three years The Discover offers an introductory rate of 0 for the first two years and then 24 compounded continuously in the final year Calculate the resulting balance on all three cards and explain which one you would pick Visa end of year 1 balance 1000100 1000 Visa end of year 2 balance 10001 0161212 117227 Visa end of year 3 balance 1172271 0161212 137422 MasterCard end of year 1 balance 10001 0125252 112734 MasterCard end of year 2 balance 1127341 0125252 127090 MasterCard end of year 3 balance 1270901 0125252 143274 Discover end of year 1 balance 1000100 1000 Discover end of year 2 balance 1000100 1000 Discover end of year 3 balance 1000e 03924X 1 127125 The Discover card has the lowest outstanding balance at the end of year 3 You should pick this card 21 years ago a trust fund was established in your name The initial deposit was 2000 Today that fund is worth 2372646 What average annual rate of return did the fund earn Assume annual compounding i FVPV1 1 i 23726462000 l21 1 0124999 The average annual rate of return was 1250 10 years ago Kaleigh invested 123 in a savings account that paid 7 simple interest per year How much more money would Kaleigh have today if the account had earned 7 interest per year compounded monthly Balance with simple interest 123 x 007 x 10 123 20910 Balance with monthly compounding 1231 00712120 24718 Difference in balances 24718 20910 3808 Kaleigh would have 3808 more today You want to have a down payment amount of 50000 in five years in order to buy your dream home If your savings account offers an interest rate of 375 compounded continuously how much money do you need to invest today to achieve your goal PV CFe i a CFeHX PV 50000el 0390375X5 4145146 45 Your dream engagement ring costs 1057928 Savings accounts earn 75 per year compounded weekly If you your boo deposits 5000 in your his savings account today how many years will it take you him to be able to afford the ring t nFVPVn1i t ln10579285000ln1 007552 520 weeks 10 years You have a choice between two deals n deal 1 you give me 1000 today and I promise to pay you 1000 in year 1 and 2000 in year 2 The discount rate for this deal is 25 In deal 2 you give me 500 today and I promise to pay you 500 in year 1 and 1500 in year 2 The discount rate for this deal is 10 According to the NPV rule which deal is better and why NPV of deal 1 1000 1000125 20001252 1080 NPV of deal 2 500 500110 15001102 119421 Deal 2 has the higher NPV and so is the more attractive option according to the NPV rule You have just won the Alabama State Lottery The winning prize consists of a Browning trucker hat and steady payments of 199 a month for 10 years The first payment is received next period If the discount rate is 25 per year compounded monthly what is the present value of the lottery CFl 199 PVAnnuity 199 x 1 11 00251212 002512 2110960 Your employer contributes 175 a week to your retirement plan Assume that you work for your employer for another 20 years and that the applicable discount rate is 4 compounded weekly Given these assumptions what is this employee benefit worth to you today CFl 175 PVAnnuity 175 x 1 11 004521 4 00452 12524622 Harrison Construction generated a nominal return of 25 for its investors last year However they only experienced a real return of 21 Given this information what was the inflation rate last year p1i1r 1 p 125121 1 003306 The inflation rate was 331 What is the APR ofa loan with a 460 EAR assuming daily compounding APR m1 EAR1m 1 APR 3651046013 1 0044976 2 45000 51 Consider a growing annuity that lasts 12 years has an initial cash flow of 500 next year a growth rate of 5 per year and a discount rate of 10 per year compounded annually What is the present value of this annuity PVGrowing Annuity 500010 005 x 1 10511012 427785 Consider a growing annuity that lasts 7 years has an initial cash flow of 500 next year a growth rate of 4 per year and a discount rate of 45 per year compounded annually What is the present value of this annuity PVGrowing Annuity 5000045 004 x 1 10410457 330159 Topic 1 Shortterm solvencv longterm solvencv and taxes The following document contains practice problems for your first quiz The equations listed below will be printed on the front of the test You are expected to memorize any equation not printed on this first page Current ratio Current assetsCurrent liabilities Quick ratio Current assets nventoryCurrent liabilities Cash ratio CashCurrent liabilities Net working capital to total assets Net working capitalTotal assets Total debt ratio Total assets Total equityTotal assets Debt to equity ratio Total debtTotal equity Equity multiplier Total assetsTotal equity Longterm debt ratio Longterm debtLong term debt Total equity Times interest earned ratio EBITInterest Cash coverage ratio EBIT Depreciationnterest Inventory turnover Cost of goods soldInventory Days sales in inventory 365 daysInventory turnover Receivables turnover SalesAccounts receivable Days sales in receivables 365 daysReceivables turnover NWC turnover SalesNWC Fixed asset turnover SalesNet fixed assets Total asset turnover SalesTotal assets Profit margin Net incomeSales Return on assets ROA Net incomeTotal assets Return on equity ROE Net incomeTotal equity Dupont identity ROE Net incomeSales x SalesAssets x AssetsEquity Earnings per share Net incomeShares outstanding Pricetoearnings ratio Stock priceEPS Markettobook ratio Market value per shareBook value per share Tobin s Q Market value of assetsReplacement cost of assets b Net income DividendsNet income g ROE x b Company A is a web design company that has the following financial information A 2012 Assets Current Current Assets assets Assets A 2012 Income Statement costs costs 35 income 400 1 What is A s current ratio Is this number good or bad in your opinion Explain why for full credit Current ratio CACL Current ratio 21500030000 717 This current ratio is very good The shortterm assets can cover the shortterm liabilities more than seven times over 2 What is A s cash coverage ratio Is this number good or bad in your opinion Explain why for full credit Cash coverage ratio EBIT Depreciationnterest Cash coverage ratio 5589000 1100013000 43077 The cash coverage ratio is also very good The firm generates enough cash to make 2012 s loan payment 430 times over 3 Given your answers to the previous two questions would you have any additional advice about how A should be managing its liquid assets Firm A is extremely liquid The company should consider investing some of that money elsewhere in order to earn a higher rate of return 4 If A declares a dividend of 1000000 what is its retention ratio b Net Income DividendsNet Income b 3624400 10000003624400 07241 Firm A has a retention ratio of 7241 The FisherMyles Organization FMO is an apparel designer that has the following financial information 2011 assets assets assets 2011 Income Statement 50 income 5 What is FMO s quick ratio Is this number good or bad in your opinion Explain why for full credit Quick ratio CA InventoryCL 275000 105000250000 068 This number is good because it is reasonably close to 10 The company can satisfy its short term liabilities easily 6 What is FMO s total debt ratio Total debt ratio A EA 775000 375000775000 052 Company B is an electronics store that has the following financial information B Assets Current Current Assets assets Assets B 2012 Income Statement costs costs 35 income 7 What is B s quick ratio Is this number good or bad in your opinion Explain why for full credit Quick ratio 425000 45000550000 069 Good close to 10 8 What is B s cash coverage ratio Cash coverage EBIT Depreciationnterest 1250000 15000090000 1556 times 9 What is B s level ofoperating cash flow OCF EBIT Depreciation Taxes 994000 You should understand why we add depreciation back 10 If B declares a dividend of 100000 what is the firm s retention ratio b 754000 100000754000 8674 Company C is an electronics store that has the following financial information C 2012 Assets Current Current Assets assets Assets C 2012 Income Statement costs costs 35 income 11 What is C s current ratio Is this number good or bad in your opinion Explain why for full credit CR CACL 15000600000 25 This number is terrible Company C is only able to cover 25 of its shortterm liabilities with its current assets 12 What is C s level of operating cash flow OCF EBIT Depreciation Taxes OCF 1400000 0 420000 980000 13 Briefly discuss two advantages and two disadvantages debt bonds has over equity stocks as a source of corporate financing Debt is tax advantaged relative to equity for financing purposes By issuing debt and making regular payments a firm builds a credit profile and communicates its level of responsibility to the market As long as timely payments are made debt does not confer ownership to the creditor This leaves the potential upside to the shareholders owners Excess debt can lead to liquidation ifa firm becomes insolvent Even if a firm is not liquidated the perception of potential credit problems can hurt a firm s ability to compete effectively in the marketplace Bugatti VeyronPorsche Carrera GT A firm has net working capital of 640 Long term debt is 4180 total assets are 6230 and fixed assets are 3910 What is the amount of total liabilities NWC CA CL CL CA NWC CA 640 CA Total Assets Fixed Assets 6230 3910 2320 Therefore CL 2320 640 1680 Total Liabilities Longterm Debt CL 4180 1680 5860 Your firm has total assets of 4900 fixed assets of3200 long term debt of 2900 and short term debt of 1400 What is the amount of net working capital NWC CA CL CA Total Assets Fixed Assets NWC 4900 3200 1400 300 Fuller Collision has shareholders39 equity of 141800 The firm owes a total of 126000 of which 60 is payable within 2 months The remainder is due in over a year The firm has fixed assets of 161900 What is the amount of net working capital NWC CA CL CL 06 x 126000 75600 A L E A 126000 141800 267800 Current Assets Total Assets Fixed Assets CA 267800 161900 105900 NWC 105900 75600 30300 17 N O N N N A firm has a debtequity ratio of 042 What is the total debt ratio You can solve this with algebra We have LE 042 and we want LA L 042E and so LA 042EA ALEsoA042EE142E Total debt ratio is then LA 042E142E 029577 since the Es cancel Alternatively you could just make up your own numbers like this The debtequity ratio is 042 If total debt is 42 L and total equity is 100 E then total assets are 142 A Total debt ratio 42142 029577 If a firm has a debtequity ratio of 10 what is its total debt ratio Remember Assets Liabilities Equity The debt to equity ratio LE and the total debt ratio LA Since L A E we can rewrite the debt to equity ratio as A EE 10 Therefore A E E gt A 2E gt EA 05 The total debt ratio can be rewritten as LA A EA 1 EA Since EA 05 the total debt ratio must also equal 05 Weathers Industries has sales of 546000 cost of goods sold of 295000 depreciation expense of 37000 interest expense of 15000 and a tax rate of 32 The firm paid 59000 in cash dividends What is the addition to retained earnings Sales COGS Depreciation Interest EBT 546000 295000 37000 15000 199000 Net Income 199000 X 1 032 135320 Addition to Retained Earnings Net Income Dividends 135320 59000 76320 Griffin Enterprises paid 1300 in dividends and 920 in interest this past year Common stock increased by 1200 and retained earnings decreased by 310 What is the net income for the year Net Income Addition to Retained Earnings Dividends Net Income 310 1300 990 A firm has 520 in inventory 1860 in fixed assets 190 in accounts receivables 210 in accounts payable and 70 in cash What is the amount of the current assets CA 520 190 70 780 Jessalyn39s Bakery has sales of 687000 with costs of 492000 Interest expense is 26000 and depreciation is 42000 The tax rate is 35 What is the net income Net income 687000 492000 26000 42000 x 1 35 82550 23 Kane s Equipment Rental paid 75 in dividends and 511 in interest expense The addition to retained earnings is 418 The tax rate is 35 Sales are 15900 and depreciation is 680 What are the earnings before interest and taxes We need to work backwards on this one Net income 75 418 493 Net Income EBT x 1 Tax Rate 493 EBT x 1 035 493 Therefore EBT 4931 35 75846 Earnings before interest and taxes 75846 511 126946 What is the percentage of the next dollar you earn that must be paid in taxes known as The marginal tax rate is what you pay on the next dollar of earnings Suppose for example that the tax rate applicable for the income band 20000 50000 is 25 and the tax rate from 50001 100000 is 32 If you are on pace to make 50000 this year and your employer pays you a dollar more on New Year s Eve your marginal tax rate would be 32 The average tax rate on the other hand totals up the amount taken out in taxes and divides it by your pre tax earnings Vandine Industries had sales of 843800 and cost of goods sold of 609900 The firm paid 38200 in interest and 18000 in dividends It also increased retained earnings by 62138 for the year The depreciation was 76400 What is the average tax rate You need to set up an income statement here Sales COGS Interest Expense Depreciation Earnings before Taxes EBT EBT 843800 609900 38200 76400 119300 The unknown input in this problem is the tax rate Net Income EBT Taxes Net Income Increased in Retained Earnings Dividends Remember there are only two destinations for after tax cash flows dividends and retained earnings Net Income 62138 18000 80138 Taxes EBT Net Income 119300 80138 39162 TaxesEBT average tax rate 39162119300 3283 Given the tax rates as shown below what is the average tax rate for an individual with taxable income of 311360 Income Tax Rate 0 50000 15 50001 75000 25 75001 100000 34 100001 335000 39 Tax 1550000 2525000 3425000 39211360 10468040 Average tax rate 10468040311360 3362 8 You are the president and CEO of MakeHerDance Corporation Your annual take home pay is 177000 and the IRS uses the following income tax bands Income Tax Rate 0 50000 25 50001 80000 30 80001 150000 36 150001 39 27 What is the average tax rate on your salary N 00 25 X 50000 12500 30 X 30000 9000 36 X 70000 25200 39 X 27000 10530 Total tax paid 57230 Average tax rate 57230177000 3233 Bradford Oil has total sales of 1349800 and costs of 903500 Depreciation is 42700 and the tax rate is 34 The firm does not have any interest expense What is the operating cash flow Earnings before interest and taxes 1349800 903500 42700 403600 Tax 403600 X 34 137224 Remember that OCF EBIT Depreciation Taxes Operating cash flow 403600 42700 137224 309076 Russell39s Deli has cash of 136 accounts receivable of 95 accounts payable of 210 and inventory of 409 What is the value of the quick ratio The trick here is that inventory is also a part of the current assets Quick ratio Cash Accounts Receivable nventory nventoryCurrent liabilities Quick ratio 136 95210 110 Macaluso Fitness MF is a gym that has the following financial information Fitness 2013 Assets Current Current Assets assets Assets Fitness 2013 Income Statement costs costs 400000 35 income 30 What is MF s cash coverage ratio Is this number good or bad in your opinion Explain why for full credit Cash coverage ratio EBIT Depreciationnterest Cash coverage ratio 10400000 10000025000 420 The cash coverage ratio is also very good The firm generates enough cash to make 2013 s loan payment 420 times over f MF declares a dividend of 4000000 what is its retention ratio b Net Income DividendsNet Income b 6743750 40000006743750 04069 MF has a retention ratio of 4069 What is MF s debttoequity ratio Debttoequity ratio LE 260000395000 06582 What is MF s level of operating cash flow OCF EBIT Depreciation Taxes 6868750 You should understand why we add depreciation back Toussant Enterprises has shareholders39 equity of 225000 The firm owes a total of 80000 of which 20 is payable within 6 months The remainder is due in over a year The firm has fixed assets of 175000 What is the amount of net working capital NWC CA CL CL 02 x 80000 16000 A L E A 80000 225000 305000 Current Assets Total Assets Fixed Assets CA 305000 175000 130000 NWC 130000 16000 114000 A firm has a debtequity ratio of 075 What is the total debt ratio You can solve this with algebra We have LE 075 and we want LA L 075E and so LA 075EA A L E soA 075E E 175E Total debt ratio is then LA 075E175E 04286 since the Es cancel Alternatively you could just make up your own numbers like this The debtequity ratio is 075 If total debt is 75 L and total equity is 100 E then total assets are 175 A Total debt ratio 75175 04286 Briefly describe how lowering taxes can in some cases lead to higher government revenue The Laffer curve is an economic theory that relates government revenue to taxation At a tax rate of 0 the governmentwould collect nothing Whereas at a level of 100 either economic activity would cease or taxpayers would find ways to avoid paying their dues In between these two extremes is a curvilinear relationship that peaks at an optimal tax rate Beyond this optimal point the incentive to either reduce investment or avoid paying taxes dominates the additional revenue potential of higher tax rates Therefore ifan economy is on the right hand side ofthe Laffer curve government revenues can theoretically be increased by reducing taxes 11 Your annual take home pay is 88000 and the IRS uses the following income tax bands Income Tax Rate 0 50000 25 50001 80000 30 80001 150000 36 150001 39 37 What is the average tax rate on your salary W 25 X 50000 12500 30 X 30000 9000 36 X 8000 2880 Total tax paid 24380 Average tax rate 2438088000 2770 Angelle39s Deli has cash of 150 accounts receivable of 88 accounts payable of 325 and inventory of 500 What is the value of the quick ratio The trick here is that inventory is also a part of the current assets Quick ratio Cash Accounts Receivable nventory nventoryCurrent liabilities Quick ratio 150 88325 07323 Ross Westerfield and Jordan 9th edition Chapter 3 question 1 page 81 Using the formula for NWC we get NWC CA CL CA CL NWC 3720 1370 5090 So the current ratio is Current ratio CA CL 50903720 137 times And the quick ratio is Quick ratio CA Inventory CL 5090 1950 3720 084 times Topic 6 Stocks The following document contains practice problems for your sixth quiz The equations listed below will be printed on the front of the test You are expected to memorize any equation not printed on this first page 1 1 i PVArmuity C z PVGrowingPerpetuity C 1 8 Company A is projected to pay a dividend of 150 per share starting next year This dividend will remain constant forever If the discount rate is 5 what is the price of a share of A today P0 P0 150005 3000 Company B is projected to pay a dividend of 250 per share starting next year This dividend will grow at a rate of 3 per year forever If the discount rate is 7 what is the price of a share of B today P0 Dll g P0 250007 003 6250 Company C is projected to pay an annual dividend of 200 per share next year If this dividend is expected to grow at a 5 rate per year and the discount rate is 15 what is the price of a share of C today P0 Dli g 200015 005 2000 Yesterday Company D paid its common stockholders an annual dividend of 4 per share which is expected to grow at a constant annual rate of 10 If the company s current stock price is 50 what is the stock s discount rate P0 D1l g i DlPo g i 40011050 010 1880 Company E paid a dividend of 100 per share last week The annual growth rate of dividends is projected to be 10 per year forever If the discount rate is 12 what is the price of a share of E today Do100 D1 100110 110 P0 DJl 3 P0 110012 010 5500 Company F paid a dividend of 300 last month The annual growth rate of dividends is projected to be 5 per year forever If a share of F sells for 25 today what is the discount rate Do 300 015300105 315 i D1P0 g i 31525 005 1760 7 Company G will pay a dividend of 175 next year The discount rate is 7 If a share of G sells for 9 5 0 50 today what is the growth rate of dividends 01 5175 g iD1Pol g 007 3175350 350 Company H is a pharmaceutical firm that is experiencing rapid growth Because of its growth opportunities the company will not pay any dividends for the next 5 years In the 6 h year the company will declare a dividend of 125 which will remain at this level forever If the discount rate is 4 what is the price ofa share of H today PV5Perpetuity Dsi PV5Perpetuity 125004 3125 in year5 dollars PV0Year 5 Lump Sum 31251045 2569 Company plans on paying dividends in two phases The first phase begins next year and will involve paying a dividend of 100 a share for 4 years The second phase begins in year 5 and will involve paying a dividend of 150 per year forever If the discount rate is 10 what is the price of a share of today The first phase is an annuity PVolAnnuity 100 x 1 1110401 317 The second phase is a perpetuity PV4Perpetuity D5i PV4Perpetuity 150010 1500 in year4 dollars PV0Year 4 Lump Sum 15001104 1025 P0 317 1025 1342 Company J plans on paying dividends in two phases The first phase begins next year and will involve paying a dividend of 150 a share for 3 years The second phase begins in year 4 and will involve paying a dividend of 200 with the size of the dividend growing by 1 per year forever If the discount rate is 6 what is the price of a share of today The first phase is an annuity PVAnnuity 150 x 1 11063006 401 The second phase is a growing perpetuity PV3Perpetuity D4i g PV3Perpetuity 200006 001 4000 in year3 dollars PVolYear 3 Lump Sum 40001063 3358 P0 401 3358 3759 11 Company K plans on paying dividends in two phases The first phase involves paying a dividend of 300 per share next year with the size of the dividend growing by 30 per year for the two years after that From year 3 to year 4 the dividend growth rate will slow down to 10 per year and will remain at this level forever If the discount rate is 12 what is the price ofa share of Ktoday The first phase needs to be manually calculated because the growth rate is higher than the discount rate D1 300 D2 300130 390 D3 3001302 507 PVFirst Phase 940 The second phase is a growing perpetuity D4 507110 5577 PV3Growing Perpetuity D4i g PV3Growing Perpetuity 5577012 010 27885 in year3 dollars PV0Year 3 Lump Sum 278851123 19848 P0 PVFirst Phase PVGrowing Perpetuity 20788 Company L plans on paying dividends in two phases The first phase involves paying a dividend of 140 per share next year with the size of the dividend growing by 25 per year for the two years after that From year 3 to year 4 the dividend growth rate will slow down to 7 per year and will remain at this level forever If the discount rate is 9 what is the price of a share of L today The first phase needs to be manually calculated because the growth rate is higher than the discount rate D1 140 D2 140125 175 D3 1401252 21875 PVFirst Phase 445 The second phase is a growing perpetuity D4 21s75107 234 PV3Growing Perpetuity D4i g PV3Growing Perpetuity 234009 007 11700 in year3 dollars PVolYear 3 Lump Sum 117001093 9035 P0 PVFirst Phase PVGrowing Perpetuity 9480 Yesterday David Marshall Corp DMC paid its common stockholders an annual dividend of200 per share Investors believe the dividend will grow at 5 forever If the market requires a 16 return on DMC s stock what is the stock s current price Do 200 01 200105 210 P0 Dll g P0 210016 005 1909 14 Yesterday the Leveque Corporation LC paid its common stockholders an annual dividend of The Hairston Corporation is a 100 per share Due to a series of new product offerings investors believe the dividend will grow at 30 per year for the next three years and then grow at a constant rate of 11 If the market requires a 22 return on LC s stock what is the stock s current price The first phase needs to be manually calculated because the growth rate is higher than the discount rate D1 100130 130 D2 1001302 169 D3 1001303 2197 PVFirst Phase 341 The second phase is a growing perpetuity D4 2197111 244 PV3Growing Perpetuity D4i g PV3Growing Perpetuity 244022 011 2218 in year3 dollars PV0Year 3 Lump Sum 22181223 1221 P0 PVFirst Phase PVGrowing Perpetuity 1562 I 1 I ing firm that I in intensity They just paid a dividend of 300 last week However given that the firm is operating in beast mode this dividend is projected to grow at 110 per year for the next five years From year 5 to year 6 the growth rate will slow down to 10 per year and continue at this rate in perpetuity If the appropriate discount rate is 55 no risk no reward and no guts no glory what is the current price of a share of Hairston stock 110 in decimals is 11 Therefore 1g 111 21 D1 300210 630 D2 3002102 1323 D3 3002103 277830 D4 3002104 583443 D5 3002105 1225230 D5 3002105110 1347753 Set up the project as a discounted cash flow stream and a growing perpetuity PVFirst 5 dividends 630155 13231552 2778301553 5834431554 12252301555 408351 PV5Growing perpetuity 1347753055 010 2995007 PVoGrowing perpetuity 29950071555 334764 Price of stock 408351 334764 743115 DamnStrong 16 Whitaker Incorporated is a pharmaceutical company that is looking to release a new drug The company just paid a dividend of200 and this dividend is projected to remain at 200 per year for the next 10 years while the company goes through the research and development phase In year 11 the drug will be released and the year 11 dividend is projected to be 50 higher than the year 10 dividend The 50 dividend growth rate will then continue on from year 11 through to year 15 Between years 15 and 16 the dividend growth rate will slow down to 1 and continue at this rate in perpetuity If the appropriate discount rate for Whitaker Incorporated is 5 what is the price of a share of the stock today The first phase is an annuity PVoAnnuity 200 x 1 11051 005 1544 The second phase needs to be manually calculated because the growth rate is higher than the discount rate D11 200150 300 D12 300150 450 D13 450150 675 D14 675150 10125 D15 10125150 151875 PVoSecond Phase 2026 The third phase is a growing perpetuity D16 151875101 1534 PV15Growing Perpetuity D15i g PV15Growing Perpetuity 1534005 001 38350 in year15 dollars PVoYear 15 Lump Sum 38350105 l5 18447 P0 PVFirst Phase PVSecond Phase PVThird Phase 22017 17 00 RD Yesterday Company 2 paid its common stockholders an annual dividend of 100 per share Due to two new product offerings investors believe the dividends will grow rapidly over the next three years taper off for three years thereafter and then rapidly for another three years when the second product is introduced before slowing down in perpetuity Specifically from years 1 through 3 the dividend will grow at a 30 rate per year From year 3 to 4 the rate will slow down to 11 per year and continue at this level until year 6 From year 6 to 7 the growth rate will be 30 per year and continue at this level until year 9 From year 9 to 10 the growth rate will slow down to 11 per year and continue at this level in perpetuity What is a share of company Z s stock worth today if the discount rate is 22 D1 5100130 5130 D2 5130130 5169 D3 169130 52197 D4 52197111 24387 D5 243867111 527070 D6 527070111 530047 D7 530047130 539061 D8 39061130 550779 D9 550779130 566013 P9 D1oi g 566013111022 011 56661 PVFuture Cash Flows 22 Discount Rate 2066 Company M paid a dividend of 100 per share last month The annual growth rate of dividends is projected to be 7 per year forever If a share of M sells for 10 today what is the discount rate and what does this number represent P0 DJl E i D1P0 g i 510010710 007 1770 The discount rate is the appropriate return for an investment that has M s level of risk Assume the same information from the previous question What is M s dividend yield Dividend yield Annual dividends per shareprice per share Dividend yield D1P0 10710 1070 Assume the same information from the previous question What will M s price be in a year Calculate the capital gain that this represents P1 DZll g D2 1001072 11449 P1 114490177 007 1070 The stock price will be in 1070 in a year Capital gains yied P1 PolPo Capital gains yield 51070 51010 700 21 Assume the same information from the previous question What is the sum of the dividend yield N U1 5 and the capital gains yield What is the significance of this number Dividend yield capital gains yield 1070 700 1770 The sum is the same as the stock M s discount rate If you own a stock only two things can happen the price can change and you can receive dividends Therefore the combination of the capital gains yield and the dividend yield reflects all the information about the performance of your stock investment This has to equal the discount rate because the discount rate is the total expected level of return given the riskiness of the stock Mac Fitness paid a dividend of 075 per share last week The annual growth rate of dividends is projected to be 3 per year forever If the discount rate is 5 what is the price of a share of Mac Fitness today D0 075 D1 075103 07725 P0 Dlll 3 P0 07725005 003 3863 Runnels Incorporated RI will pay a dividend of 125 next year The discount rate is 4 fa share of RI sells for 100 today what is the growth rate of dividends D1125 g i D1P0 g 004 125100 275 Leong Associates LA is a pharmaceutical firm that is experiencing rapid growth Because of its growth opportunities the company will not pay any dividends for the next 4 years In the 5 h year the company will declare a dividend of215 which will grow at a 7 rate per year in perpetuity If the discount rate is 10 what is the price of a share of LA today PV4Perpetuity Dsi g PV4Perpetuity 215010 007 7167 in year4 dollars PV0Year 4 Lump Sum 71671104 4895 Abadie Industrial Al has a stock price of 80 per share The annual growth rate of dividends is 10 per year and is projected to remain at this level forever If the discount rate is 1125 what was the size of the last dividend that Al paid P0 Dll g D1 P0 x i g 01 80x 01125 010 D1 100 D0 Dll g D0 100110 091 per share 26 Lauren Grant Automotive LGA plans on paying dividends in two phases The first phase begins next year and will involve paying a dividend of120 a share for 3 years The second phase begins in year 4 and will involve paying a dividend of 180 with the size of the dividend growing by 4 per year forever If the discount rate is 6 what is the price of a share of LGA today The first phase is an annuity PVAnnuity 120 x 1 11063006 321 The second phase is a growing perpetuity PV3Perpetuity D4i g PV3Perpetuity 180006 004 9000 in year3 dollars PV0Year 3 Lump Sum 90001063 7557 P0 321 7557 7878 Crain Corporation CC plans on paying dividends in three phases Next year the company will pay a dividend of 115 This dividend will grow at a rate of 75 up until year 3 From year 3 to year 4 the dividend growth rate will slow to 0 and remain at this level up until year 9 From year 9 to year 10 the dividend will grow at a 5 rate and remain at this level in perpetuity If the appropriate discount rate for CC s stock is 12 what is the price of a share today The first phase needs to be manually calculated because the growth rate is higher than the discount rate D1 115 D2 115175 201 D3 201175 352 PVoFirst Phase 115112 2011122 3521123 513 The second phase is an annuity D4 352 PV3Annuity 352 x 1 11125012 1447 PV0Second Phase 14471123 1030 The third phase is a growing perpetuity D10 352105 370 PV9Growing Perpetuity Dmi g PV9Growing Perpetuity 370012 005 5286 in year9 dollars PVoThird Phase 5286112 1906 P0 PVFirst Phase PVSecond Phase PVThird Phase 3449 28 Kaufman Associates KA paid a dividend of300 per share last month The annual growth rate N W W of dividends is projected to be 10 per year forever If a share of KA sells for 60 today what is the discount rate and what does this number represent P0 Dll 3 l D1P0 g i 30011060 010 1550 The discount rate is the appropriate return for an investment that has KA s level of risk Assume the same information from the previous question What is KA s dividend yield Dividend yield Annual dividends per shareprice per share Dividend yield D1P0 330S60 550 Assume the same information from the previous question What will KA s price be in a year Calculate the capital gain that this represents P1 Dzl g D2 3001102 363 P1 3630155 010 6600 The stock price will be in 66 in a year Capital gains yield P1 PolPo Capital gains yield 66 6060 1000 Assume the same information from the previous question What is the sum of the dividend yield and the capital gains yield What is the significance of this number Dividend yield capital gains yield 550 1000 1550 The sum is the same as the stock KA s discount rate If you own a stock only two things can happen the price can change and you can receive dividends Therefore the combination of the capital gains yield and the dividend yield refects all the information about the performance of your stock investment This has to equal the discount rate because the discount rate is the total expected level of return given the riskiness of the stock 32 Mac Fitness plans on paying dividends in two phases The first phase involves paying a dividend of 210 per share next year with the size of the dividend growing by 25 per year for the two years after that From year 3 to year 4 the dividend growth rate will slow down to 7 per year and will remain at this level forever If the discount rate is 12 what is the price of a share of Mac Fitness stock today ie the present value of all anticipated future cash flows D1 210 D2 210125 263 D3 2625125 329 PVFirst Phase 210112 2631122 3291123 631 The second phase is a growing perpetuity D4 329107 352 PV3Growing Perpetuity D4i g PV3Growing Perpetuity 352012 007 7040 in year3 dollars PV0Year 3 Lump Sum 70401123 5011 Price today PVFirst Phase PVGrowing Perpetuity 5642 Topic 2 Asset profitabilitv and market value The following document contains practice problems for your second quiz The equations listed below will be printed on the front of the test You are expected to memorize any equation not printed on this first page Current ratio Current assetsCurrent liabilities Quick ratio Current assets nventoryCurrent liabilities Cash ratio CashCurrent liabilities Net working capital to total assets Net working capitalTotal assets Total debt ratio Total assets Total equityTota assets Debt to equity ratio Total debtTotal equity Equity multiplier Total assetsTotal equity Longterm debt ratio Longterm debtLong term debt Total equity Times interest earned ratio EBlTlnterest Cash coverage ratio EBIT Depreciationnterest Inventory turnover Cost of goods soldInventory Days sales in inventory 365 daysInventory turnover Receivables turnover SalesAccounts receivable Days sales in receivables 365 daysReceivables turnover NWC turnover SalesNWC Fixed asset turnover SalesNet fixed assets Total asset turnover SalesTotal assets Profit margin Net incomeSales Return on assets ROA Net incomeTotal assets Return on equity ROE Net incomeTotal equity Dupont identity ROE Net incomeSales x SalesAssets x AssetsEquity Earnings per share Net incomeShares outstanding Pricetoearnings ratio Stock priceEPS Markettobook ratio Market value per shareBook value per share Tobin s Q Market value of assetsReplacement cost of assets b Net income DividendsNet income g ROE x b The FisherMyles Organization FMO is a manufacturer of industrial machinery ts financial statements are presented below assets assets assets 2011 Income Statement 50 income 1 What is FMO s days sales in receivables figure Is this number good or bad in your opinion Explain why for full credit 3655100000095000 3468 It takes a little over a month for FMO to be paid for sales on credit This is a good number for the heavy equipment industry 2 What is FMO s profit margin Profit margin Net IncomeSales 250000S1000000 25 3 What is FMO s return on equity ROE Net IncomeEquity 250000S375000 6666 Company X is an electronics store that has the following financial information Use the information to solve the questions below P Equot X 2012 Assets Current Current Assets assets Assets X 2012 Income Statement costs costs 35 income What is X s days sales in inventory figure Is this number good or bad in your opinion Explain why for full credit Days sales in inventory 365S160000045000 1027 days This is an excellent number It takes around 10 days for the product to move through the supply chain and be sold If X declares a dividend of 100000 what is the firm s growth rate Also given the ratios you calculated for full credit explain whether X is doing well or poorly g ROE x b 754000S925000 x 754000 100000754000 7070 X is doing extremely well 9 turns over product quickly 10 days in the cycle 9 is growing at a rapid rate 7070 is phenomenal growth Company A is an electronics store that has the following financial information Use the information to solve the questions below N A Assets Current Current Assets assets Assets A 2012 Income Statement costs costs 35 income What is A s days sales in receivables figure Is this number good or bad in your opinion Explain why for full credit Days sales in receivables 365S20000005000 09125 This number is unbelievably good On average A s customers take less than a day to pay in full for their purchases This number would be impressive regardless of the type of business we were looking at What is A s days sales in inventory figure Is this number good or bad in your opinion Explain why for full credit Days sales in inventory 365S6000005000 304 days This number is also very impressive On average it takes about 3 days for a product to move through the supply chain In other words the cellphonePCwhatever is assembled packaged and sold in 3 days In the technology and electronic industries quick turnaround is important because the products have a short shelf life 8 IfA does not pay dividends what is its growth rate Also provide an interpretation of the ratios g NIE x 100 since all of the net income is reinvested g 780000415000 x 1 18795 Company A has a lot of positives It moves product quickly and customers settle their bills in an extremely timely fashion On top of that it is growing at a very rapid rate 18795 This is probably the reason why the firm does not pay dividends Hartley39s Sport Store has sales of 897400 costs of goods sold of 628300 inventory of 208400 and accounts receivable of 74100 How many days on average does it take the firm to sell its inventory assuming that all sales are on credit This is a bit of a trick question because the mention of credit makes you think about the receivables turnover ratio However the question is actually asking for the inventory turnover ratio 365COGSInventory 365628300208400 12107 days Delatorre Incorporated expects sales of 437500 next year The profit margin is 48 and the firm has a 30 dividend payout ratio What is the projected increase in retained earnings Net Income 0048 x 437500 21000 The retention ratio b 70 07 x 21000 14700 The Gardere Meat Market GMM httpgooglmPNYnO has 747000 in sales The profit margin is 41 and the firm has 7500 shares of stock outstanding The market price per share is 27 What is the priceearnings ratio Interpret this number EPS Net IncomeNumber of Shares 747000 x 00417500 40836 PE ratio Share PriceEPS 2740836 661 Investors are willing to pay 661 for each dollar of GMM s current earnings Purchasing a share of GMM stock entitles you to the company s potential future earnings through either dividends or capital gains The Opelika Meat Store OMS httpgoogls5RUOh has 747000 in sales The profit margin is 41 and the firm has 7500 shares of stock outstanding The market price per share is 22 What is the priceearnings ratio Compare OMS and GMM Earnings per share 747000 x 00417500 40836 Priceearnings ratio 2240836 539 OMS and GMM are identical in terms of operations however GMM has a higher price to earnings ratio This implies that investors are more optimistic about GMM s future Ratios are not very meaningful in isolation Therefore it is always more informative to look at a company in comparison to the peer firms in its industry 13 A firm has total assets with a current book value of 68700 a current market value of 74300 and a current replacement cost of 75600 What is the value of Tobin39s Q Interpret this number Q 7430075600 098 This is a poor Tobin s Q The market s perception of the value of the firm when under the control of the present management team is lower than the cost to replicate its assets This is indicative of value destruction possibly through the agency problem Jersey Mike s has net income of150980 a priceearnings ratio of 128 and earnings per share of 087 How many shares of stock are outstanding EPS Net IncomeShares gt Shares Net IncomeEPS 150980087 173540 Rodriguez Corp has a Tobin39s Qof 96 The replacement cost of the firm39s assets is 225000 and the market value of the firm39s debt is 109000 The firm has 20000 shares of stock outstanding and a book value per share of 209 What is the market to book ratio Market Value of Assets Market Value of Liabilities Market Value of Equity Q Market Value of AssetsReplacement Cost Market Value of Assets 096 x 225000 216000 Market Value of Equity 216000 109000 107000 MarkettoBook Ratio Market Value of EquityBook Value of Equity Marketto Book Ratio 107000209 X 20000 25598 The Purple Martin has annual sales of 687400 total debt of 210000 total equity of 365000 and a profit margin of 520 What is the return on assets ROA Net IncomeAssets ROA 687400 X 00520210000 365000 622 Taylor39s Men39s Wear has a debtequity ratio of 42 sales of 749000 net income of 41300 and total debt of198400 What is the return on equity ROE Net IncomeEquity LE 042 E 198400042 47238095 ROE 4130047238095 874 A firm has a debtequity ratio of 57 a total asset turnover of 112 and a profit margin of 49 The total equity is 511640 What is the amount of the net income A L E LE 057 gt L 057 x 511640 291638 Therefore Assets 291638 511640 80329480 Total Asset Turnover SalesAssets Sales TAT x Assets gt Sales 112 x 80329480 89966778 Net Income Sales x Profit Margin 89966778 x 0049 4408372 19 Firm X has assets of 1000 equity of 500 and a return on assets of 025 What is the return on equity ROE ROAxAE05 Heroman s Flowers has accounts receivable of 3506 inventory of 4407 sales of 218640 and cost of goods sold of 169290 How many days does it take the firm to sell its inventory and collect the payment on the sale assuming that all sales are on credit Read the question carefully It is asking for the entire time that the product takes to go through the inventory cycle AND for the florist to get paid Days sales in inventory 3651692904407 9502 days Days sales in receivables 3652186403506 5853 days Total days in inventory and receivables 9502 5853 1535 days If a firm produces a 12 return on assets and also a 12 return on equity what is the firm s equity multiplier ROE Net IncomeSales x SalesAssets x AssetsEquity 012 012 X AE AE 10 A firm has net working capital of 2715 fixed assets of 22407 sales of 31350 and current liabilities of3908 How many dollars of sales are generated from every 1 in total assets Total asset turnover 313502715 22407 3908 108 Every 1 in total assets generates 108 in sales Lynch ChevroletCadillac of Auburn AL has sales of 807200 total assets of 1105100 and a profit margin of 968 The firm has a total debt ratio of 78 What is the return on equity Return on equity 0968 gtlt 8072001105100 X 1 78 3214 A firm has 160000 shares of stock outstanding sales of 1940000 net income of 126400 a priceearnings ratio of 187 and a book value per share of 792 What is the markettobook ratio Earnings per share 126400160000 079 Price per share 079 x 187 14773 Markettobook ratio 14773792 187 Buffalo Connection has a profit margin of 56 a return on assets of 125 and an equity multiplier of 149 What is the return on equity Return on equity 125 X 149 1863 using the Du Pont Identity N 9 A firm has a debtequity ratio of 57 a total asset turnover of 112 and a profit margin of 49 The total equity is 511640 What is the amount of net income Return on equity 049 x 112 x 1 057 0861616 Net income 511640 gtlt 0861616 44084 A firm has total assets with a current book value of 68700 a current market value of 74300 and a current replacement cost of79200 What is the value of Tobin39s Q Tobin39s Q 7430079200 94 Dixie Supply has total assets with a current book value of 368900 and a current replacement cost of 486200 The market value of these assets is 464800 What is the value of Tobin39s Q Tobin39s Q 464800486200 96 The Burger Hut has sales of 29000000 total assets of 43000000 and total debt of 13000000 The profit margin is 11 What is the return on equity Return on equity 11 x 2900000043000000 13000000 1063 The Home Supply Co has a current accounts receivable balance of280000 Credit sales for the year just ended were 1830000 How many days on average did it take for credit customers to pay off their accounts during this past year Receivables turnover 1830000280000 6536 times Days39 sales in receivables 3656536 5585 days VL Industries has ending inventory of 300000 and cost of goods sold for the year just ended was 1410000 On average how long does a unit of inventory sit on the shelf before it is sold Inventory turnover 1410000300000 47 times Day39s sales in inventory 36547 7766 days Coulter Supply has a total debt ratio of 052 What is the equity multiplier Debtequity ratio 521 052 1083 Equity multiplier 1 1083 2083 Rocky Mountain Foods has an equity multiplier of 155 a total asset turnover of 13 and a profit margin of 75 What is the return on equity Return on equity 075 X 13 X 155 1511 4 U1 9 l 00 Charlie39s Chicken has a debtequity ratio of 205 Return on assets is 92 and total equity is 560000 What is its net income Equity multiplier 1 205 305 Return on equity 092 x 305 2806 Net income 2806 gtlt 560000 157136 Canine Supply has sales of 2200 total assets of1400 and a debtequity ratio of05 ts return on equity is 15 What is the net income Return on equity 15 Net income2200 gtlt 22001400 x 1 050 Net income 14000 Billings Corporation has net income of 161000 a profit margin of 76 and an accounts receivable balance of 127100 What is the days39 sales in receivables Sales 161000076 2118421 Accounts receivable turnover 2118421127100 1667 times Days sales in receivables 3651667 22 days Gladstone Pavers has a longterm debt ratio of 06 and a current ratio of 16 Current liabilities are 700 sales are 4440 the profit margin is 95 and the return on equity is 195 How much does the firm have in fixed assets Current assets 16 x 700 1120 Net income 095 x 4440 42180 Total equity 42180195 21630769 06 Long term debtLong term debt 21630769 Longterm debt 32446153 Total debt 700 32446153 39446153 Total assets 39446153 21630769 61076922 Fixed assets 61076922 1120 498769 A firm has a debttotal asset ratio of 74 and a return on total assets of 13 What is the return on equity Total assets Total equityTotal assets 74 Total equity 26 Total assets Net income 13 Total assets Return on equity 13 Total assets26 Total assets 50 Y Sunny Enterprises YSE is a highend designer clothing store that has the following financial information 2013 Assets Current Current Assets assets Assets 2013 Income Statement costs costs 35 income 39 What is YSE s days sales in inventory figure Is this number good or bad in your opinion Explain why for full credit Days sales in inventory 365Inventory turnover Inventory turnover COGSInventory 8750000 3950000165000 7697 Days sales in inventory 3657697 474 days This is an excellent number On average it takes less than 5 days for the clothing to move from inventory to being sold 40 What is YSE s days sales in receivables figure Is this number good or bad in your opinion Explain why for full credit Days sales in receivables 365Receivables turnover Receivables turnover SalesAccounts receivable 32000000S223000 14350 Days sales in receivables 36514350 254 days This is also an excellent numbers Customers on credit pay in less than 3 days 10 41 4 N 43 Suppose YSE has a market value of liabilities of 750000 a market value ofequity of 1375000 and a replacement cost of assets of 1112000 Calculate YSE s Tobin s Q Tobin s Q Market value of assetsReplacement cost Market value of assets Market value of liabilities Market value of equity Market value of assets 750000 1375000 2125000 Tobin s Q 21250001112000 191 Yves Saint Laurent YSL a competitor to YSE has a market value of liabilities of 15000000 a price to earnings ratio of 25 earnings per share of 160 and 500000 shares outstanding The replacement cost of YSL s assets is 42000000 Calculate YSL s Tobin s Q and briefly discuss which is the better managed company and why PE Ratio Share priceEPS Share price PE Ratio x EPS 25 x 160 4000 per share Market value of equity 4000 x 500000 20000000 Market value of assets 15000000 20000000 35000000 Tobin s Qfor YSL 35000000S42000000 08333 YSE is a better run firm than YSL Since YSE has a Tobin s Qabove 10 the market perceives it as more valuable than the cost to replicate its assets Therefore the firm has positive intangibles eg brand reputation good management and presence of growth options YSL on the other hand is worth less than the replacement cost of its assets This is indicative ofvalue destruction possible through the agency problem The Gourgues Group has a Tobin39s Q of 155 The replacement cost of the firm39s assets is 875000 and the market value of the firm39s liabilities is 380000 The firm has 216000 shares of stock outstanding and a book value per share of 425 What is the market to book ratio Market Value of Assets Market Value of Liabilities Market Value of Equity Q Market Value of AssetsReplacement Cost Market Value of Assets 155 x 875000 1356250 Market Value of Equity 1356250 380000 976250 MarkettoBook Ratio Market Value of EquityBook Value of Equity MarkettoBook Ratio 976250425 X 216000 10635 Mac Fitness has a debtequity ratio of 34 sales of687000 net income of 131250 and total debt of 382149 What is the return on equity ROE Net IncomeEquity LE 034 E 382149034 112396765 ROE 131250112396765 1168 45 Using the same information about Mac Fitness from the previous question if the firm declares 4 9 a dividend of 13125 what is the company s growth rate g ROE x b Retention ratio 131250 13125131250 90 g 01168 x 09 10512 Brian Hogan and Friends BHF has a debtequity ratio of 32 a total asset turnover of 087 and a profit margin of 56 The total equity is 721819 What is BHF s net income A L E LE 032 gt L 032 x 721819 23098208 Therefore Assets 23098208 721819 95280108 Total Asset Turnover SalesAssets Sales TAT x Assets gt Sales 087 x 95280108 82893694 Net Income Sales x Profit Margin 82893694 x 0056 4642047 Company X has a profit margin of 88 a total asset turnover of 143 and a return on equity of 1728 What is the debtequity ratio TAT SalesA TAT x PM Net IncomeA ROE Net IncomeE 9 ROETATx PM AE 9 AE 01728143 X 0088 13732 A L E AE L EE L EE 13732 9 LE 03732 or 3732 Topic 4 Capital budgeting decisionmaking criteria The following document contains practice problems for your fourth quiz The equations listed below will be printed on the front of the test You are expected to memorize any equation not printed on this first page 1 1 74 PVArmuity C z PVGrowingPerpetuity i 8 1 Iquot S P A firm is considering investing in a new project The project will cost 100000 today and is expected to generate the following end of year cash flows If the discount rate is 10 what is project s net present value NPV Year 1 Year 2 Year 3 Year 4 25000 30000 30000 50000 NPV 100000 2500011 30000112 30000113 50000114 421078 Good project Accept A firm is considering investing in a new project The project will cost 75000 today and is expected to generate the following end of year cash flows If the discount rate is 12 what is the project s NPV Year 1 Year 2 Year 3 Year 4 10000 45000 50000 25000 NPV 75000 10000112 450001122 500001123 250001124 2127926 Good project Accept A firm is considering investing in a new project The project will cost 80000 today and is expected to generate the following end of year cash flows If the discount rate is 16 what is the project s NPV Year 1 Year 2 Year 3 Year 4 19500 30000 39000 29000 NPV 80000 19500116 300001162 390001163 290001164 10732 Good project Accept Project X requires 100000 to start In its first 30 years of operation it produces no cash flows However in year 31 the project begins to generate 50000 per year for 12 years If the appropriate discount rate is 5 what is the NPV of project X PV30Annuity 50000 x 1 110512005 44316258 PV044316258 44316258l053 10253783 NPV 10253783 100000 253783 The Kessler Corporation is deciding whether to invest in a new project that has the following characteristics The initial cost of the project is 1000000 In the project s first 10 years it will generate 50000 in cash flows per year Starting in year 11 the project will generate 60000 in cash flow and this figure will remain the same each year thereafter in perpetuity Assuming a discount rate of 10 calculate the NPV of this project and explain whether the Kessler Corporation should accept or reject it The project consists of a 10year annuity and a perpetuity PVoAnnuity 500001 11101 01 30722836 PV10Perpetuity 6000001 600000 PVoPerpetuity 6000001110 23132597 PV0Annuity PV0Perpetuity 53855433 NPV 1000000 53855433 46144567 This is a negative NPV project and should be rejected The Febles Corporation is deciding whether to invest in a new project that has the following characteristics The initial cost of the project is 500000 In the project s first 20 years it will generate 25000 in cash flows per year Starting in year 21 the project will generate 30000 in cash flow and this figure will remain the same each year thereafter in perpetuity Assuming a discount rate of 4 calculate the NPV of this project and explain whether the Febles Corporation should accept or reject it The project consists of a 20year annuity and a perpetuity PVoAnnuity 250001 11042 004 33975816 PVzoPerpetuity 30000004 750000 PVolPerpetuity 75000010420 34229021 PVoAnnuity PVoPerpetuity 68204837 NPV 500000 68204837 18204837 This is a positive NPV project and should be accepted Kennedy Industrial is an astrophysics firm that only uses the NPV rule The firm is considering whether to invest in a new project and has the following information at hand The initial cost is 995000 and the project s cash flows are CF1 CF149 0 CF150 150797749605 In other words the project costs one million dollars today and receives a payoff of around one billion five hundred and eight million dollars in 150years time If the discount rate is 5 should Kennedy Industrial accept or reject this project according to the NPV rule NPV 995000 150797749605105150 5000 The project should be accepted according to the NPV rule Given your answer to the previous question is there any additional advice you might give the CEO of the firm about how to evaluate this project The payback period on this project is terrible because the company has to wait 150 years to make 5000 The firm would be better served looking for other projects with superior cash flow streams 9 The Campo Corporation is deciding whether to invest in a new project that has the following characteristics The initial cost of the project is 1750000 In the project s first 42 years it will generate 15000 in cash flows per year Starting in year 43 the project will generate 32000 in cash flow and this figure will grow by 4 per year thereafter in perpetuity Assuming a discount rate of 12 calculate the NPV of this project and explain whether the Campo Corporation should accept it or reject it The project consists of a 42year annuity and a growing perpetuity PVoAnnuity 150001 111242012 12392909 PV42Growing Perpetuity 32000012 004 400000 PVoGrowing Perpetuity 40000011242 342691 PV0Annuity PV0Perpetuity 127356 NPV 1750000 127356 1622644 This is a negative NPV project and should be rejected Whitaker Industrial is a space exploration firm that only uses the NPV rule The company is considering whether to invest in a new project and has the following information at hand The initial cost is 627408415 Because of a special government program the project is guaranteed to receive grants in the amount of 1000000000 one billion dollars every ten years starting in year 10 and ending in year 100 CF10 CF20 CF30CF100 1000000000 You are a junior investment analyst with Brooke Moore s Common Sense Investing Fund BMCSIF If the discount rate is 10 should Whitaker Industrial accept or reject this project according to the NPV rule NPV 627408415 1BN110 I0 1BN11020 1BN11030 1BN11040 1BN11050 1BN11060 1BN11070 1BN11080 1BN11090 1BN110 I00 218 Given your answer to the previous question and your job with the BMCSIF are there any additional recommendations you might give the CEO of Whitaker Industrial The payback period and the return on this investment are very poor It takes 100 years to make 218 worth of today s money The company should look for alternatives 12 A project requires 1000000 in upfront costs In year 1 it loses 300000 These losses are expected to decline at a 10 rate per year up until year 5 In year 6 the project generates a positive cash flow of 500000 These cash flows grow at a 20 rate up until year 10 the final year of the project If the discount rate is 7 what is its net present value NPV CF1 300000 CF2 300000 x 09 270000 CF3 270000 X 09 243000 CF4 270000 x 09 218700 CF5 270000 x 09 196830 CF6 500000 CF7 500000 x 12 600000 CF8 600000 x 12 720000 CF9 720000 x 12 864000 CF10 864000 x 12 1036800 NPV 1000000 300000107 2700001072 2430001073 218700107 1968301075 5000001076 6000001077 7200001078 8640001079 10368001071 10113789 Briefly explain why the concept of the time value of money becomes less relevant as the discount rate decreases As the discount rate decreases the tradeoff between preferring money today over future cash flows becomes less severe Remember the discount rate summarizes factors such as inflation credit risk and opportunity cost In an extreme case where these risks go to zero 0 there is no difference between money in hand today over promised future cash ows A firm is considering investing in a new project The project will cost 100000 today and is expected to generate the following end of year cash flows If the firm s cost of capital is 10 what is the project s discounted payback period Year 1 25000 Year 2 30000 Year 3 30000 Year 4 50000 We are trying to make back 100000 This occurs at some point in year 4 Let X represent the present value needed to equal 100000 100000 25000110 300001102 300001103 X X 2993989 PVoCF4 500001104 3415067 XPVoCF4 29939893415067 088 The discounted payback period is 388 years 15 Project 2 requires 1249033 to start and generates the following cash flows at the end of each 0 l 9 of the five years in which it is in operation 500 2500 3750 8885 12275 If the appropriate discount rate is 7 what is this project s discounted payback period 500107 25001072 37501073 88851074 1249033 The discounted payback period is exactly 4 years Prunty Industrial is a technology firm that uses a strict 3year discounted payback rule The firm is considering whether to develop a new product line and has the following information at hand The initial cost is 170000 and the project s cash flows are CF1 25000 CF2 75000 CF3 125000 CF4 175000 CF5 225000 CF6 275000 CF7 1500000 If the discount rate is 15 should Prunty Industrial accept or reject this project according to the 3year discounted payback rule PVFirst 3 years 25000115 750001152 1250001153 16063943 The project does not make back the 170000 initial cost within its first 3 years and should be rejected according to the 3year payback rule Given your answer to the previous question is there any additional advice you might give the CEO of the firm about how to evaluate this project The project becomes extremely profitable from year 4 onwards The CEO might want to reconsider having such a strict payback rule and take into account the overall NPV Maben and Friends is a local seafood restaurant that is looking to open a new location in Lafayette Louisiana The new facility will cost 250000 to establish and is expected to be in business for 5 years In the first year of operation the store will generate 75000 in cash flows In the second year the restaurant will generate 7704930 in cash flow In the remaining years years 3 through 5 the annual cash flow will return to 75000 per year The discount rate for this project is 165 Calculate the NPV of the new branch NPV 250000 750001165 770493011652 7500011653 7500011654 7500011655 575523 Given your answer to the previous question use the trial and error method to find the IRR of this investment The NPV is negative so the IRR must be lower than 165 Try 155 NPV 250000 750001155 770493011552 7500011553 7500011554 7500011555 0 20 Agnew and Sons is a local hardware store that is looking to open a new location in Denham N N N Springs Louisiana The new store will cost 1000000 to establish and is expected to be in operation for 10 years In the first year of operation the store will generate 16714060 in cash flows Each year thereafter ie years 2 through 10 the store will generate 150000 in cash flow per year The discount rate for this project is 75 Calculate the NPV of the new store This project consists of a year 1 cash flow and then an annuity that lasts from years 2 through 10 PVCF1 167140601075 15547963 PV1Annuity 1500001 1107590075 95683305 PVolAnnuity 956833051075 89007726 PVAI cash flows 15547963 95683305 104555689 NPV 104555689 1000000 4555689 Given your answer to the previous question use the trial and error method to find the IRR of this investment The IRR is the discount rate that makes the NPV of the project equal to zero Since the project has a positive NPV at a discount rate of 75 the IRR must be higher Try 85 PVCF1 167140601085 15404664 PV1Annuity 1500001 1108590085 91785940 PVoAnnuity 917859401085 84595336 PVAI cash flows 1000000 NPV 1000000 1000000 0 IRR is 85 Consider the following two offers Offer 1 You give me 150 today and I give you back 250 in a year39s time Offer 2 You give me 100 today and I give you back 200 in a year39s time Calculate the IRRs of offers 1 and 2 and explain which is better according to the IRR criterion Offer 1 0 150 2501 inle iIRR 6667 Offer 2 0 100 2001 iIRR lIRR 100 Offer 2 has a higher IRR than Offer 1 Therefore it is preferable according to the IRR criterion Now suppose offers 1 and 2 can only be invested in the amounts stated in the previous question ie 150 for offer 1 and 100 for offer 2 Assuming the required rate of return is 10 for both which offer would you choose Briefly explain your answer NPV of Offer 1 150 250110 7727 NPV of Offer 2 100 200110 8181 Offer 2 is superior according to both the IRR and NPV criteria You should choose it 24 27 Consider the following two offers Offer 1 You give me 100 today and I give you back 175 in a year39s time Offer 2 You give me 75 today and I give you back 140 in a year39s time Calculate the IRRs of offers 1 and 2 Offer 1 0 100 1751 hm hm 75 Offer 2 0 75 140l iIRR iIRR 8667 Offer 2 has a higher IRR than Offer 1 therefore it is preferable according to the IRR criterion Now suppose offers 1 and 2 can only be invested in the amounts stated in the previous question ie 100 for offer 1 and 75 for offer 2 Assuming your required rate of return is 60 what are the NPVs of both offers and which would you choose Briefly explain your answer and make reference to the IRRs you calculated in question 3 NPV of Offer 1 100 175160 9375 NPV of Offer 2 75 140160 1250 Offer 2 is superior according to both the IRR and NPV criteria You should choose it If the problem was such that the IRR and NPV criteria gave conflicting results you would use the NPV rule as a tiebreaker A firm is considering investing in a new project The project will cost 200000 today and is expected to generate the following end of year cash flows The firm s cost of capital is 17 Is the project s IRR positive or negative Year 1 50000 Year 2 40000 Year 3 30000 Year 4 50000 Since the sum of the cash flows without discounting does not equal the initial cost the IRR is negative 50000 40000 30000 50000 170000 170000 lt 200000 therefore the IRR is negative Bonus Try 625 The Doucet Group is considering a 2year project that requires an initial investment of 800 In year 1 the project will generate 5000 of inflows CF1 5000 In year 2 the project will realize a 5000 loss CFZ 5000 If the discount rate is 10 what is the NPV of this project NPV 800 500011 5000112 38677 28 Calculate the NPV at discount rates of 25 and 400 and explain why this project appears to have two different IRRs NPV at 25 800 5000125 50001252 0 NPV at 400 800 50005 50005Z 0 The project has two IRRs because it has nonconventional cash flows Given your answer to the previous question over what range of discount rates will this project have a positive NPV For full credit sketch a graph that shows the ranges over which the NPV is positive and negative NPV on the vertical axis discount rate on the horizontal axis Hint Take a look at the slides from Chapter 9 932 and 933 N RD Between the ranges of 25 and 400 the project has a positive NPV NPV 60000 40000 20000 000 va 40000 60000 80000 100000 W W W W W The Nunez Group is considering a 2year project that requires an initial investment of 800 In year 1 the project will generate 5000 of inflows CF1 5000 In year 2 the project will realize a 5000 loss CF2 5000 If the discount rate is 29 what is the NPV of this project NPV 800 5000129 50001292 7134 Calculate the NPV at discount rates of 25 and 400 and explain why this project appears to have two different IRRs NPV at 25 and at 400 0 The project has two IRRs because it has nonconventional cash flows The NPVIRR graph is a smooth curve that crosses the axis twice Given your answer to the previous over what range of discount rates will this project have a positive NPV For full credit sketch a graph that shows the ranges over which the NPV is positive and negative NPV on the vertical axis discount rate on the horizontal axis Same graph from the Doucet Group question Project 2 requires 1000 in startup costs The project lasts 3 years and is projected to have positive cash inflows in years 1 and 3 and negative flows in year 2 Specifically CF1 6000 CF2 11000 CF3 6000 As you know the IRR criterion is the interest rate that equalizes the NPV to zero Calculate the NPV of project 2 at rates of 0 100 and 200 NPV 1000 60001 1100012 600013 0 NPV 1000 60002 1100022 600023 0 NPV 1000 60003 1100032 600033 0 The project has multiple IRRs because of the irregular cash flows A firm is considering investing in a new project The project will cost 160000 today and is expected to generate the following end of year cash flows If the firm s cost of capital is 10 what is the project s Profitability Index Yea r 1 3 5000 Yea r 2 45000 Yea r 3 5 5000 Yea r 4 105000 Profitability index 3500011o 450001102 5500011o3 1050001104160000 14 35 You would like to invest in the following project Brooke Moore your boss insists that only projects returning at least 106 in today39s dollars for every 1 invested can be accepted She also insists on applying a 14 percent discount rate to all cash flows Based on these criteria what should you do Yea r 0 98400 Yea r 1 S 55 200 Yea r 2 S 74 100 Profitability index 55200114 74100114298400 1072 Accept the project because the profitability index is greater than 106 Topic 7 Risk and Return The following document contains practice problems for your seventh quiz The equations listed below will be printed on the front of the test You are expected to memorize any equation not printed on this first page Holding Period Return HPR P1 P0 D1P0 Arithmetic Average Return ra r1 r2 r3 rnln Geometric Average Return r3 1r11r21rn1n 1 CAPM Equation is rf 3 X Elle rf Weighted Average Cost of Capital WACC iwacc BVx ib x 1 T SVx is Expected Return and Variance Sample 1 ERZZIR Z 1 039 WZUR Elz Population EU 2 HR 02 22 lt1 7Elt1ltgtgtz The table below illustrates the properties of 3 stocks A B and C under 3 different scenarios Calculate the expected return of each stock State state Fair The expected return of each stock can be calculated as a weighted average of the outcomes in each state ERA 30 of the time the good state occurs x 25 return in the good state 30 of the time the fair state occurs x 15 return in the fair state 40 of the time the bad state occurs x 10 return in the bad state ERB 30 of the time the good state occurs x 50 return in the good state 30 of the time the fair state occurs x 15 return in the fair state 40 of the time the bad state occurs x 5 return in the bad state ERC 30 of the time the good state occurs x 8 return in the good state 30 of the time the fair state occurs x 4 return in the fair state 40 of the time the bad state occurs x 0 return in the bad state ERA 8 ERB 1750 ERc 360 Assume the same information from the previous question Calculate the standard deviation of each stock We use the population version of the standard deviation equation Since we are projecting into the future we are accounting for all possible outcomes ie the population Historical data on the other hand is a sample Variance A 30 good state x 25 return in the good state expected return of 82 30 fair state x 15 return in the fair state expected return of 82 40 bad state x 10 return in the bad state expected return of 82 00231 Variance B 30 good state x 50 return in the good state expected return of 17502 30 fair state x 15 return in the fair state expected return of 17502 40 bad state x 5 return in the bad state expected return of 17502 0052125 Variance C 30 good state x 8 return in the good state expected return of 3602 30 fair state x 4 return in the fair state expected return of 3602 40 bad state x 0 return in the bad state expected return of 3602 0001104 Standard deviation A 00231 1520 Standard deviation B 005212511 2283 Standard deviation C 0001104 332 Assume the same information from the previous question Now suppose A has a beta of 10 B has a beta of 15 and C has a beta of 05 If the riskfree rate is 15 which of the three stocks offers the highest rewardtorisk ratio Beta measures the systematic risk of a stock ie the portion of risk that we really care about The risk premium measures how much additional return my stock gives me over and above the risk free rate Tbills Remember every risky asset should be expected to return more than the risk free rate otherwise you would never buy it Rewardtorisk for stock A Expected return of 8 riskfree rate of 15Beta of 1 0065 In other words for each additional unit of systematic risk that I take on I can expect to be rewarded with an additional 65 return over and above the Tbill rate Rewardtorisk for stock B 1750 1515 1067 Rewardto risk for stock C 360 1505 420 Stock B has the highest rewardtorisk ratio Assume the same information from the previous question Consider a portfolio that is 10 invested in A 60 invested in B and 30 invested in C What is the portfolio s expected return You can either calculate what the portfolio does in each state or take the weighted average of the expected returns rgood 10 invested in A x 25 60 invested in B x 50 30 invested in Cx 8 3490 rfai 10 invested in Ax 15 60 invested in B x 15 30 invested in Cx 4 1170 rbad 10 invested in A x 10 60 invested in B x 5 30 invested in Cx 0 400 ERp 30 of the time the good state occurs x 3490 return in the good state 30 of the time the fair state occurs x 1170 return in the fair state 40 of the time the bad state occurs x 400 return in the bad state ERp 1238 Portfolio returns can also be calculated as a weighted average ERp 10 in A x 800 expected return 60 in B x 1750 expected return 30 in C x 360 expected return 1238 5 9 N Assume the same information from the previous question What is the portfolio s standard deviation Portfolio standard deviations are not weighted averages Population variance 033490 12382 031170 12382 04 400 12382 00260 Population standard deviation 0026011 1612 Assume the same information from the previous question What is the portfolio s beta Portfolio betas are weighted averages 10 invested in Ax 10 60 invested in B x 15 30 invested in Cx 05 115 Assume the same information from the previous question If the riskfree rate is 15 and the expected return on the market is 12 ERm 12 use the CAPM equation and the betas to calculate the expected returns on stocks A B and C Now assume that the CAPM can accurately predict what the expected return on a stock should be Plot the security market line for these three stocks Mark off the probabilistic return vs beta combinations that you calculated earlier and discuss whether you think each stock is overpriced or underpriced CAPM A rf 0 x ERm rf 15 10 x 12 15 1200 CAPM B 15 15 x 12 15 1725 CAPM C 15 05 x 12 15 675 The probabilityprojected returns were ERA 8 ERB 1750 ERc 360 A is projected to give us 8 when it should be giving us 1200 It is overpriced B is projected to give us 1750 when it should be giving us 1725 It is slightly underpriced C is projected to give us 360 when it should be giving us 675 It is overpriced 2 S DEBS 20 DEF6 1 5 100 100 500 000 CAPM Prediction Stock B CAPM Prediction 0 Stock A 0 Stock C 05 1 15 2 8 The table below illustrates the properties of 3 stocks X Y and 2 under 3 different scenarios Calculate the expected return of each stock state ReturnX ReturnY ReturnZ ERx 02 x 032 04 x 022 04 x 003 1400 ERv 02 x 057 04x 022 04x 007 1740 ERz 02 x 027 04x 014 04 x 005 1300 9 Assume the same information from the previous question Calculate the standard deviation of each stock Standard deviation X 02032 0142 04022 0142 04 003 0142 VI 1435 Standard deviation Y 2367 Standard deviation 2 807 10 Assume the same information from the previous question Now suppose A has a beta of 09 B H H H H has a beta of 20 and C has a beta of 025 If the riskfree rate is 100 which of the three stocks offers the highest rewardtorisk ratio Rewardtorisk for X 1400 10009 1444 Rewardtorisk for Y 1740 10020 820 Rewardtorisk for Z 1300 100025 4800 Stock 2 offers by far the highest rewardtorisk ratio Assume the same information from the previous question Consider a portfolio that is 40 invested in X 15 invested in Y and 45 invested in 2 What is the portfolio s expected return Portfolio returns are weighted averages 40 in X x 1400 expected return 15 in Yx 1740 expected return 45 in Z x 1300 expected return 1406 Assume the same information from the previous question What is the portfolio s standard deviation Portfolio standard deviations are not weighted averages rgood 40 X x 32 15 Y x 57 45 Z x 27 3350 rm 1840 rbad 000 Population standard deviation 023350 14062 041840 14062 04000 14062 1 1274 Assume the same information from the previous question What is the portfolio s beta Portfolio beta 04 x 09 015 x 20 045 x 025 07725 Assume the same information from the previous question If the riskfree rate is 100 and the expected return on the market is 15 ERm 15 use the CAPM equation to calculate the expected returns on stocks X Y and 2 Assuming the CAPM can accurately predict what the expected return on a stock should be compare the CAPM returns to the probabilistic return vs beta combinations that you calculated earlier and discuss whether you think each stock is overpriced or underpriced CAPM X rf 0 x ERm rf 100 09 x 15 10 1360 CAPM Y 10 20 x 15 100 2900 CAPM 2 10 025 x 15 100 450 The probabilityprojected returns were ERx 1400 ERv 1740 ERz 1300 H H H X is projected to give us 1400 when it should be giving us 1360 It is underpriced Y is projected to give us 1740 when it should be giving us 2900 It is overpriced Z is projected to give us 1300 when it should be giving us 450 It is underpriced The table below illustrates the properties of 3 stocks AX BX and CX under 3 different scenarios Calculate the expected return and standard deviation of each stock State of the world Probability of state Return AX Return BX Return CX Good 15 12 17 6 Fair 70 7 0 1 Bad 15 5 2 1 ERAX 015 x 012 07 x 007 015 x 005 595 ERBX 015 x 017 07 x 000 015 x 002 225 Ech 015 x 006 07 x 001 015 x 001 145 Standard deviation AX 492 Standard deviation BX 624 Standard deviation CX 204 Assume the same information from the previous question Now suppose AX has a beta of 12 BX has a beta of 20 and CX has a beta of 05 If the riskfree rate is 025 which of the three stocks offers the highest reward torisk ratio Rewardtorisk for AX 595 02512 475 Rewardtorisk for BX 225 02520 100 Rewardtorisk for CX 145 02505 240 Stock AX offers the highest rewardtorisk ratio Assume the same information from the previous question Consider a portfolio that is 40 invested in AX 15 invested in BX and 45 invested in CX What is the portfolio s expected return and standard deviation Portfolio returns are weighted averages 40 in AX x 595 expected return 15 in BX x 225 expected return 45 in CX x 145 expected return 337 Portfolio standard deviations are not weighted averages 351 18 Assume the same information from the previous question If the riskfree rate is 025 and the 11 N 0 expected return on the market is 12 ERm 12 use the CAPM equation to calculate the expected returns on stocks AX BX and CX Now assume that the CAPM can accurately predict what the expected return on a stock should be Discuss whether you think each stock is overpriced or underpriced CAPM AX rf 0 x ERm rf 025 12 x 12 025 1435 CAPM BX 025 20x 12 025 2375 CAPM CX 025 050 x 12 025 6125 The returns using the probability projections were as follows ERA 595 ERB 225 ERc 145 All three stocks are overpriced You are an investment analyst According to your assessment the world can be divided into 3 states good fair and bad Each state is equally likely to occur You are analyzing a particular stock and determine that it will return 12 in the good state 4 in the fair state and 12 in the bad state What is this stock s standard deviation ER 13 x 012 13 x 004 13 x 012 13333 Population standard deviation 13012 00133332 13004 00133332 13 012 00133332 998 Spansel Industries is a technology firm that has experienced the following historical returns over a six year period 2007 15 2008 7 2009 24 2010 9 2011 2 2012 64 Calculate the arithmetic simple average return and sample standard deviation of Spansel Industries over this six year period Simple average return 15 7 24 9 2 646 85 02 2810 RY L Iv 1 Sample variance 1515 852 7 852 24 852 9 852 2 852 64 852 009195 Sample standard deviation 009195 3032 Even though we have six years of data we divide by five because of the degrees of freedom correction in a sample 21 Morel Breweries is the worldwide leader in Jagerbomb sales There are three states of the world N N that may occur in the future good 70 probability fair 25 probability and bad 5 probability If the good state occurs Morel s stock will return 100 If the fair state occurs Morel s stock will return 50 If the bad state occurs Morel s stock will return 75 Calculate the firm s expected return and population standard deviation Expected return 07 x 100 025 x 50 005 x 75 7875 Population variance 07100 78752 02550 78752 005 75 78752 017047 Population standard deviation 01704711 4129 Consider Spansel Industries again If the good state occurs in the future Spansel will return 12 If the fair state occurs Spansel will return 8 If the bad state occurs Spansel will return 6 Assume the same state probabilities from the previous question Calculate the expected return and standard deviation of a portfolio that is 50 invested in Spansel and 50 invested in Morel For full credit explain why investing in this combination is superior to investing in either stock individually We first need to calculate what the portfolio does in each state of the world rgood 50 invested in Morel x 100 return from Morel 50 invested in Spansel x 12 return from Spansel 56 rm 05 x 50 05 x 8 29 rbad 05 x 75 05 x 6 405 Expected portfolio return 07 x 56 025 x 29 005 x 405 4443 Population variance 0756 44432 02529 44432 005405 44432 00514 Population standard deviation 0051411 2267 The portfolio is superior to each of the individual stocks because it reduces your exposure to firm specific risk If one company experiences an idiosyncratic shock to its earnings the effect is counterbalanced by the other stock A stock had returns of 11 percent 18 percent 21 percent 20 percent and 34 percent over the past five years What is the standard deviation of these returns These are historical returns and therefore are a sample 02 Zill1Ri 42 IV1 Simple average return 52 Sample variance 14011 00522 018 00522 021 00522 020 00522 034 00522 005767 Sample standard deviation 005767 2 2401 24 Faulkner Industries is a technology firm that has experienced the following returns in the past 3 N N N N N years 2010 11 2011 27 2012 56 Calculate the standard deviation of Faulkner Industries over this 3 year period These are historical returns and therefore are a sample 02 M21518 Rx Simple average return 24 Sample variance 12 011 0242 027 0242 056 0242 01129 Sample standard deviation 01129 2 3360 What type of risk does the standard deviation measure Total risk Total risk includes both 39 and What type of risk does beta measure Systematic risk Systematic risks are economywide Assume that we can use the CAPM equation to correctly calculate a stock39s required return SC Inc s stock has a beta of 110 The expected market return over the next year is 15 while the current riskfree rate is 5 An investment banker says that the expected return for SC is 115 Is the stock underpriced or overpriced CAPM SC Inc rf 3 x ERm rf 50 110 x 15 50 1600 The correct return for a stock as risky as SC is 1600 If it is only projected to return 115 then it is overpriced Assume that we can use the CAPM equation to correctly calculate a stock s required return DC Inc s stock has a beta of 085 The expected market return over the next year is 12 while the current riskfree rate is 6 An investment banker says the expected return for DC is 162 Is the stock underpriced or overpriced CAPM DC Inc rf 3 x ERm rf 60 085 x 12 60 1110 The correct return for a stock as risky as DC is 1110 If it is projected to return 162 then it is underpriced FC Inc s stock has a beta of 112 The expected market return over the next year is 17 while the current riskfree rate is 65 An investment banker says the expected return for FC is 1826 Is the stock underpriced or overpriced CAPM FC Inc rf 3 x ERm rf 65 112 x 17 65 1826 The correct return for a stock as risky as FC is 1826 If it is projected to return 1826 then it is neither underpriced nor overpriced It is fairly priced 30 W W 04 You have a portfolio made up of three securities Acadian Bluebonnet and Coursey Given the information below what is the portfolio s beta Stock Weight Expected Return Beta Acadian 50 12 12 Bluebonnet 20 18 21 Coursey 30 8 06 Portfolio betas are weighted averages 50 in Acadian x 12 20 in Bluebonnet x 21 30 in Coursey x 06 12 Assume the same information from the previous question If the return on Tbills is 3 which of the three stocks offers the highest rewardtorisk ratio Rewardtorisk for Acadian Expected return of 12 riskfree rate of 312 750 Rewardtorisk for Bluebonnet Expected return of 18 riskfree rate of 321 714 Rewardto risk for Coursey Expected return of 8 riskfree rate of 306 833 Coursey has the highest rewardto risk ratio Using the same information from the previous question you may now also assume the following there are two equally likely states of the world good and bad Acadian returns 24 in the good state and 0 in the bad state Bluebonnet returns 24 in the good state and 12 in the bad state Coursey returns 9 in the good state and 7 in the bad state What is the standard deviation of the portfolio with the three stocks We first need to calculate what the portfolio does in both states of the world rgood 50 in A x 24 20 invested in Bx 24 30 invested in Cx 9 1950 rbad 50 in Ax 0 20 invested in B x 12 30 invested in Cx 7 450 Expected return 05 x 1950 05 x 450 1200 Population variance 051950 12002 05450 12002 0005625 Population standard deviation 000562511 750 Consider the following information on Stocks A and B The expected market return is 15 and the riskfree rate is 45 If stocks A and B are correctly priced according to the CAPM the beta of stock A is and the beta of stock B is Hint we are assuming that the stocks are neither overpriced nor underpriced Stock A s return Stock B s return State of of State of Fair Bad The probabilistic return for stocks A and B are as follows Stock A 02 x 025 02 x 02 06 x 005 12 Stock B 02 x 03 02 x 015 06 x 000 9 The CAPM return for the stocks A and B are as follows CAPM A 0045 betaA x 015 0045 CAPM B 0045 betaB x 015 0045 Since the stocks are neither overpriced nor underpriced the probabilistic returns are the same as the CAPM returns 012 0045 betaA x 015 0045 gt betaA 07143 009 0045 betaB x 015 0045 gt betaB 04286 34 Consider the following information on Stocks land II The expected market return is 116 and the riskfree rate is 36 percent lf stocks land II are correctly priced according to the CAPM the beta of stock is are neither overpriced nor underpriced State of Economv Probability of State of Economv Stu ckl Recession 006 015 Normal 069 035 Irrational exuberance 025 043 Stock beta 403 Stock ll beta 372 and the beta of stock II is Hint we are assuming that the stocks Rate of Return if State Occurs Stock II 7035 035 045 35 Palmisano Corporation is the worldwide leader in highend jewelry There are three states of the world that may occur in the future good 60 probability fair 15 probability and bad 25 probability If the good state occurs Palmisano s stock will return 54 If the fair state occurs Palmisano s stock will return 30 If the bad state occurs Palmisano s stock will return 25 Calculate the firm s expected return Expected return 06 x 54 015 x 30 025 x 25 3065 36 Abdullah Mills is the worldwide leader in cereal sales lf Abdullah returns 17 in the good state 8 in the fair state and 1 in the bad state what is the expected return on a portfolio that is 65 invested in Palmisano stock and 35 invested in Abdullah stock You may assume that the same state probabilities from the previous question apply rgood 65 invested in Palmisano x 54 35 invested in Abdullah x 17 4105 rfalr 065 x 30 035 x 8 2230 rbad 065 x 25 035 x 1 1590 Expected portfolio return 06 x 4105 015 x 2230 025 x 1590 2400 37 Suppose you invest 1000 in a stock account today and at the end of the next 5 years the 0 account has the following balances 1200 Wear 1 800 Year 2 950 Year 3 700 Year 4 1500 Year 5 What geometric average return did you earn over the five year period r1 1200 10001000 20 r2 800 12001200 3333 r3 950 800800 1875 r4 700 950950 2632 r5 1500 700700 11429 rg 1r11r21rn1 quot 1 rg 1200666711875073682142915 1 845 You can cross check your answer by taking the original amount and growing it by the geometric average return for five years 1000108455 1500 Therefore 845 is the correct return On December 31 2007 you invested 1000 in a stock portfolio The table below shows the account balance at the end of each of the five years during which you held the investment Calculate your geometric average return over this five year period Date Account 2012 Decem ber r1 900 10001000 10 r2 1800 900900 100 r3 2250 18001800 25 M 2025 22502250 10 r5 1620 20252025 20 g 1r11r21rn1 quot1 g 092012509008015 1 1013 I39 r 1000110135 1620 Therefore 1013 is the correct return 39 On December 31 2007 you invested 1000 in stock X The table below shows the account 4 4 balance at the end of each of the five years during which you held the investment Calculate your geometric average return over this five year period Date Account r1 850 10001000 15 r2 714 850850 16 r3 357 714714 50 r4 49980 357357 40 r5 64974 4998049980 30 rg 08508405014013015 1 826 10001 008265 64982 Slightly different from 64974 because of rounding Suppose you wanted to use the data in the previous question to make a prediction about stock X s future Calculate the simple average return and the appropriate standard deviation for your prediction These are historical returns and therefore are a sample 02 M02410 RY Simple average return 220 Sample variance 14 015 00222 016 00222 050 00222 040 00222 030 00222 013642 Sample standard deviation 013642 2 3694 The sign in the brackets turns from negative to positive because 0022 0022 Suppose you invest 1000 in a stock account today and at the end of the next 5 years the account has the following balances 1200 Wear 1 750 Year 2 990 Year 3 890 Year 4 2250 Year 5 What geometric average return did you earn over the five year period Geometric average return 120062513208992528115 1 1761 4 w Nguyen and Friends is a local seafood restaurant that has experienced the following historical returns over a six year period 2007 25 2008 17 2009 42 2010 19 2011 38 2012 3 If you were an investor in Nguyen and Friends what geometric average return would you have realized over this six year period Geometric average return 12511705811906210316 1 7057 Blanchfield and Friends is a local seafood restaurant that has experienced the following returns in the past seven years 2006 112 2007 97 2008 40 2009 32 2010 17 2011 12 2012 21 If you were an investor in Blanchfield and Friends what geometric average return would you have realized over this seven year period Geometric average return 21219714006808311207917 1 1654 Fisher Corporation has a capital structure with 75 equity and 25 debt The firm s cost of equity is 12 and it pays 4 annual interest on its debt The firm s beta is 11 and it faces a marginal tax rate of 40 What is the firm s weighted average cost of capital WACC SV x is BV x ib x 1 T WACC 075 x 012 025 x 004 x 060 96 Dawud Corporation has a capital structure with 55 equity and 45 debt The firm s cost of equity is 12 and it pays 4 annual interest on its debt The firm s beta is 11 and it faces a marginal tax rate of 40 What is the firm s weighted average cost of capital WACC 055 x 012 045 x 004 x 060 768 Hernandez Corporation has a capital structure with 25 equity and 75 debt The firm s cost of equity is 12 and it pays 4 annual interest on its debt The firm s beta is 11 and it faces a marginal tax rate of 40 What is the firm s weighted average cost of capital and what does Aaron the CEO allegedly do to FIN 3716 students who cannot calculate the WACC correctly WACC 025 x 012 075 x 004 x 060 48 Aaron Hernandez The Capital Asset Pricing Model CAPM relates the expected return of a stock to the return on riskfree government securities and the stock s exposure to systematic risk Write down the CAPM equation and describe the intuition behind it In your answer you should discuss 1 the riskfree rate 2 what the market portfolio represents and 3 the meaning of beta The CAPM equation ER rf 3ERm rf n expectation every stock should return at least the risk free rate If this were not the case there would be no incentive to buy the stock because purchasing corporate securities involves taking on risk The market risk premium ERm rf reflects the performance of the economy as a whole In equilibrium one is only rewarded for taking on economywide or systematic risks Therefore the beta represents an individual stock s sensitivity to these economywide risk factors 48 Suppose you invest in stock X for two years and it returns 100 in year 1 and 100 in year 2 U1 U1 5 Calculate the simple average return on your investment and the geometric average return Explain which of the two returns simple average vs geometric average is a more accurate representation of what happened to your investment over the 2 year period Simple average return 100 1002 0 Geometric average return 20 l2 1 100 You will have lost all of your money at the end of year 2 which is a return of 100 Therefore the geometric average return is a more accurate representation of what happened to your funds Explain why investing in a portfolio of securities is superior to investing in an individual stock In your answer you should discuss the concepts of systematic and unsystematic risk You are only rewarded for taking on systematic economywide risks In a large welldiversified portfolio the unsystematic firmindustryspecific risks cancel each other out Therefore if one stock in your portfolio is doing poorly for idiosyncratic reasons the other stocks can balance out that negative performance Joseph Thrower Apparel JTA is a manufacturer of motorcycle gear The company has experienced the following historical returns over a five year period 2009 17 2010 42 2011 19 2012 38 2013 3 Calculate JTA s simple average return over the five year period Simple average return 17 42 19 38 35 82 Assume the same information from the previous question Calculate JTA s standard deviation over the five year period Take the variance calculation out to five decimal places Your final answer of the standard deviation only needs two decimal places These are historical returns and therefore are a sample 72 Zill1Ri R2 IV1 Simple average return 820 Sample variance 14017 00822 042 00822 019 00822 038 00822 003 00822 008827 Sample standard deviation 008827 2 2971 The sign in the brackets turns from negative to positive because 0082 0082 52 U1 4 U1 U1 Reiter Pilates RP is a health and wellness franchise that is expanding into Louisiana There are three states of the world that may occur in the future good 60 probability fair 30 probability and bad 10 probability If the good state occurs RP s stock will return 25 If the fair state occurs RP s stock will return 12 If the bad state occurs RP s stock will return 8 Calculate the firm s expected return and population standard deviation Expected return 06 x 25 03 x 12 01 x 8 178 Population variance 0625 1782 0312 1782 01 8 1782 001078 Population standard deviation 00107811 1038 Mac Fitness is Louisiana s leading fitness franchise There are three states of the world that may occur in the future good 60 probability fair 30 probability and bad 10 probability If the good state occurs Mac Fitness will return 30 If the fair state occurs Mac Fitness will return 15 If the bad state occurs Mac Fitness will return 25 Calculate the firm s expected return and population standard deviation Expected return 06 x 30 03 x 15 01 x 25 20 Population variance 0630 202 0315 202 01 25 202 0027 Population standard deviation 002711 1643 Assume the same information from the previous two questions If Reiter Pilates has a beta of 14 Mac Fitness has a beta of 25 and the return on Tbills is 125 which stock has a higher reward torisk ratio Given that these firms compete in the same industry explain what would likely happen in the long run Rewardtorisk for Reiter Piates Expected return of 178 riskfree rate of 12514 1182 Rewardtorisk for Mac Fitness Expected return of 20 riskfree rate of 12525 75 Reiter Pilates has a higher rewardtorisk ratio than Mac Fitness Investors would prefer RP s stock to Mac s stock Either Mac would eventually go out of business or the company would have to change its financial situation to offer a more attractive rewardtorisk ratio Suppose today s date is December 31 2013 You are an investment analyst looking at Scichowski Industries SI In your opinion the following table represents the 4 year forecast for this company The numbers in brackets represent the probability of each state Based on these forecasts what is the expected return on SI s stock for each of the next 4 years Year Good State 20 Fair State 20 Bad State 60 Expected Return Dec 2013 Dec 2014 17 12 2 Dec 2014 Dec 2015 21 16 12 Dec 2015 Dec 2016 24 14 8 Dec 2016 Dec 2017 15 10 9 U1 U1 U1 U1 Dec 2013 Dec 2014 ER 02 x 017 02 x 012 06 x 002 700 Dec 2014 Dec 2015 ER 02 x 021 02 x 016 06 x 012 146 Dec 2015 Dec 2016 ER 02 x 024 02 x 014 06 x 008 124 Dec 2016 Dec 2017 ER 02 x 015 02 x 010 06 x 009 104 Fast forward to January 1 2018 Suppose all of your predictions over the past 4 years were accurate Now you are looking at the historical performance of Scichowski Industries from the previous question What is the simple average of Sl s returns over the 4 year period Simple average return 7 146 124 1044 1110 Assume the same information from the previous question It is still January 1 2018 What is the standard deviation of the returns on Scichowski Industries over the 4 year period that you were invested in the stock These are historical returns and therefore are a sample 2 1 N 2 U N1Zi1Ri R Simple average return 1110 Sample variance 13007 01112 0146 01112 0124 01112 0104 01112 00010413 Sample standard deviation 00010413 2 323 Retifand the Super Friends RSF has a beta of144 The return on Tbills is 125 and the expected return on the market is 125 Use this information to calculate the CAPM expected return of RSF CAPM RSF rf a x ERm rf 125 144 x 125 125 1745 Assume the same information from the previous question Also assume that we can use the CAPM equation to correctly calculate a stock39s required return If an investment banker says the expect return on Retif and the Super Friends is 1324 is the stock underpriced or overpriced The correct return for a stock as risky as RSF is 1745 If it is only projected to return 1324 then it is overpriced 60 On December 31 2010 you invested 1000 in a stock portfolio The table below shows the account balance at the end of each of the three years during which you held the investment Calculate your geometric average return over this three year period Date Account r1 1200 10001000 20 r2 1080 12001200 10 r3 1242 10801080 15 fig 1r11r21rn1 1 r3 120911513 1 749 Alternatively you can solve directly for rg 10001 rg3 1242 r3 749 0 Murrah s Deli is a local seafood restaurant that has experienced the following returns in the past seven years 2007 112 2008 97 2009 40 2010 32 2011 17 2012 12 2013 21 If you were an investor in Murrah s Deli what geometric average return would you have realized over this seven year period Geometric average return 21219714006808311207917 1 1654 0 N To correctly use the weighted average cost of capital WACC equation the yield to maturity on a firm s bonds is multiplied by one minus the tax rate Why is this Debt is tax deductible Therefore the effective cost to the firm is the yield to maturity multiplied by one minus the tax rate 0 OJ Fisher Corporation has a capital structure with 75 equity and 25 debt The firm s cost of equity is 12 and it pays 4 annual interest on its debt The firm s beta is 11 and it faces a marginal tax rate of 40 What is the firm s weighted average cost of capital WACC 5v x is BV x i x 1 T WACC 075 x 012 025 x 004 x 060 96 as P Dunn Corporation has a capital structure with 55 equity and 45 debt It pays 5 annual interest on its debt The return on Tbills is 2 and the expected return on the market is 10 The firm39s beta is 145 and it faces a marginal tax rate of 40 What is the firm s weighted average cost of capital CAPM Dunn rf B x ERm rf 2 145 x 10 2 136 WACC 055 x 0136 045 x 005 x 060 883

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