FI 4000 Fall 2017 Yates Exam I Page 1 of 7 Georgia State University Robinson College of Business FI 4000 Fundamentals of Valuation Dr Michael Yates INSTRUCTIONS Exam I September 26 2017 1 Please don t open the exam until you are told to do so 2 This exam is being administered under the University s rules for academic conduct the Code of Academic Integrity applies 3 No textbooks class notes or computers are allowed You are allowed to use a calculator 4 You have 2 hours and 40 minutes If you finish early you can quietly hand in your exam and leave 5 Once I instruct you to stop writing please put down your pen or pencil immediately 6 Please write your answers in the space provided after each problem If you need scratch paper you can write on the back of the exam pages but this space will not be graded unless specifically noted 7 In the case of numerical problems please draw a box around your final answer s 8 Be sure to state your assumptions clearly and show all of your calculations Please keep in mind that I can t grade what I can t read Name print FI 4000 Fall 2017 Yates Exam I Page 2 of 7 Exam Questions 1 27 points A Highgarden corporate bond has a coupon rate of 8 and a face value of 1 000 Coupons are paid semi annually and the bond s yield to maturity expressed as a bond equivalent yield BEY is 10 The bond matures in 6 years and the next coupon will be paid in exactly 6 months a 5 points Calculate the bond s price If BEY 10 then the 6 month yield is 5 40 05 1 11 0512 1000 1 0512 1 05 2 1 b 4 points Calculate the bond s effective annual yield to maturity c 4 points Two years from today immediately after a coupon payment the bond s BEY has dropped to 8 Calculate the bond s price at that time When BEY coupon rate the bond is priced at par Price 1 000 If you missed the shortcut here is the calculation If BEY 8 then the 6 month yield is 4 Two years from today the semiannual bond has 8 payments remaining 40 04 1 11 048 1000 1 048 Over two years you will collect 4 coupons for a total of 160 1000 160 911 37 911 37 the price found in part c calculate your holding period return d 5 points If you purchase the bond for the price found in part a and sell it two years later for FI 4000 Fall 2017 Yates Exam I Page 3 of 7 e 5 points Suppose that you purchase this bond 2 months prior to the next coupon payment In addition to the flat price how much accrued interest will you owe to the seller For simplicity you may assume that all months contain the same number of days If there are 2 months until the next coupon then 4 months have passed since the previous coupon 40 46 f 4 points A Casterly Rock corporate bond has the exact same cash flow timeline as the Highgarden bond However the Casterly Rock bond has a BEY of 6 Neither bond is callable What difference in the two corporations would explain the difference in their yields Casterly Rock must have lower default risk than Highgarden 2 26 points Assume the annual risk free rate is 4 The Atlanta Falcons wish to sign star quarterback Matt Ryan to a long term contract extension They have offered him three guaranteed contract options a 7 points Under option 1 they will pay him 50 million today as a signing bonus and then pay five growing annual salary payments at the end of each of the next five years Specifically they will pay him 10 million in one year and this amount will grow by 10 per year Calculate the present value of this contract 50 10 04 1 1 1 11 04 5 b 7 points Under option 2 they will pay him a flat 15 million dollars per year beginning two years from today and ending ten years from today Calculate the present value of this contract 15 04 1 11 04 9 1 041 FI 4000 Fall 2017 Yates Exam I Page 4 of 7 c 6 points Under option 3 they will pay him a constant annual perpetuity with the first cash flow occurring in one year Calculate the annual payment amount that would cause the present value of this contract to equal the present value you computed in part b 04 107 240 359 80 d 6 points Suppose that Matt expects interest rates to fall in the future Would he want to sign a contract today with a high duration or a low duration Explain He would want a high duration Falling rates cause the PV of the contract to increase making it more valuable He would want the contract whose value would increase the most if rates fall which is the one with the highest duration 3 5 points Bond A has a time to maturity of 10 years Bond B has a time to maturity of 11 years Is it possible for bond A to have a higher duration than bond B Explain Yes Time to maturity is just one of the factors that affects duration For example if bond B has a much higher coupon rate it could have a lower duration than bond A even though it has longer time to maturity FI 4000 Fall 2017 Yates 4 17 points The following table displays a portion of this week s Treasury yield curve Exam I Page 5 of 7 Maturity years 2 3 5 10 Yield 1 23 1 42 1 79 2 26 1000 1 022610 1 01423 1 01232 1 3 3 a 4 points Calculate the price today of a risk free zero coupon bond with a face value of 1 000 maturing in 10 years b 5 points Calculate the forward rate for year 3 c 6 points Assume the expectations theory of interest rates is true and that yields evolve as expected Five years from today you will purchase an investment that promises to pay a risk free cash flow of 100 000 ten years from today What fair price do you expect to pay for the investment five years from today 5 100000 The value at time 5 of 100 000 to be received at time 10 is 1 6 1 7 1 8 1 9 1 10 It can be shown rather easily that under the expectations theory 1 10 10 1 5 5 1 6 1 7 1 8 1 9 1 10 Rearranging we get 1 6 1 7 1 8 1 9 1 10 1 10 10 1 5 5 1 022610 1 01795 1 14428 Thus our equation for 5 becomes 5 100000 1 14428 d 2 points Using a more complete yield curve you calculate the forward rate for year 30 to be 4 5 If the liquidity …