FIN302: Week 5 - 9.21-9.25
FIN302: Week 5 - 9.21-9.25 FIN302
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This 7 page Class Notes was uploaded by Giulia Dias Roncoletta on Monday September 28, 2015. The Class Notes belongs to FIN302 at University of Miami taught by Frank Peterson in Summer 2015. Since its upload, it has received 148 views. For similar materials see FIN 302 - Fundamentals of Finance in Finance at University of Miami.
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Date Created: 09/28/15
Date Monday September 21 2015 Chapter Cont Chapter 7 Annuities always remember the 10 golden rules Chapter 7 quiz on friday Annuity Interest Rate payment every lease has an implicit interest rate which is the return to the dealer Deferred Annuity calculator will think it s the payment of the period before the first payment BUT that is for an ordinary annuity so you have to make extra calculations for the deferred annuity pv t1 t2 t3 t4 t5 t6 t7 t8 t9 335 410 100 100 deferred annuity 1st calculations N5 PMT100 l7 FV0 CPT PV 410 2nd calculations N3 l7 FV410 PMT 0 CPT PV 335 Or alternative Find FV of N5 then PV of N8 Growing Annuity consecutive payment that grow at constant rate g Formula PV PMTx11g n rg 1r Le 10 consecutive payments annual First 3 5000 one year from now Remaining pay increase by 3 annually It earn 8 on money what are they worth to you PV 5000 PMT 1 advanced 08 03 PMT starts on first Perpetuities annuity that never ends infinite stream of EQUAL payments on PMT1 r ie 100 Infinite pay with an annual discount 5 1st pay is one year from today 100 2000 5 of 2000 100 005 if you invested 2000 today at 005 you would get 100 payments every year If paid in advance just add one more pay Deferred Perpetuity receive perpetuity but it won t begin for a while ie 100 Infinite pay with an annual discount 5 1st pay is 6 years from today PV5 PMTs 100 2000 r 05 N5 l5 FV2000 PMT0 CPT PV 1567 if you pay this today you will receive 5 interest 100 Growing Perpetuities grows at constant rate g g can be negative on PMT1 r ie PV of infinite stream growing at 3 annually 1st pay 100 one year from today Loans form of annuity secured unsecured when the payments are made 1 discount interest amortized and balloonform of amortization Discount Loans no interim payment FV principal accumulated interest InterestOnly Loan no principle amortization no down payment borrowed 10000 pay 10000 at the end but mean while you just pay interest FullyAmortized Loans mortgage loans make payments that are the interest and a share of the loan amount payment principle interest ending balance 0 sum of principle payments loan IE Installment loan fully annual payment on 5 years 9 of 5000 N5 l9 P1 starting period PV5000 P2 ending period FV0 CPT PMT 1285 P1 1 P2 1 BAL balance 4165 ending balance year 1 PRI principle 835 how much PRI paid yr 1 INT interest 450 interest amount paid yr 1 Balloon Payment incomplete amortization leftover balance at ending period becomes the future failure in your calculator LE 6 years 625 loan 75000 PMT 14315 annual FV 15000 gt extra payment added lnterest rate conversion problems get harder next week go through on your own Date Wednesday September 23 2015 Chapter Chapter 8 Test 1 info Chapter 15 will be treated like one chapter 68 will be treated as individual chapters make sure to go over deferred annuity powerpoint interest rate conversion VERY IMPORTANT There will be no class a week from Friday Chapter 8 Bond contract between investor and issuer usually corporation tradable to public in band market very large loan raise lots of money for long period Coupon Bond most common bond no principle amortization fixed rate interest only loan pv int int int int fv semi annual interest rates kinda like an annuity all cash flows are fixed with date FV face value Terminal value of bond 3 gt 3 3 coupons the annuity components interest payments the coupon rate in an annual rate TERMS Face Value Par Value and Redemption Value how much money you ll be paid at the end Original lssue date bond was issued to the public Maturity Date Due Date Redemption Date the day you can cash out otherwise you can selltrade Coupon Rate fixed annual on face value Coupon Payment semiannually paid in USA LE 1 million bond with a 7 58 interest Coupon rate value 7625 X 1000000 2 How much would you pay depends on other market interest rates how much could i get else where what my opportunity cost Bond Valuation market value of a bond will change inversely with interest rates market demands higher return purchase price must drop vice versa IE wants to sell 10000 bond with 5 to a person who is earning 8 on their money 6 years N6 l8 PMT500 gt 5 loan interest fixed for life of the bond FV 10000 CPT PV 8613 If you paid 8613 to the bond then it will be equal to their previous investment at 8 So they wont be losing money For them to purchase the bond for you thats the highest price they ll go UNDERSTANDING BONDS gt held to maturity bond is package of fixed cash flows gt cash flow are fixed PV isn t R increases as PV decreases Why do prices fluctuate in order to be attractive to investors not risk free LE 15 years MKT RATE 2625 1000000 FV other bond value 7625 Bond w payments at 2625 aka market rate N 15x2 30 coupons paid twice a year I 26252 annual rate but paid twice so needs to be divided PV 1000000 PMT 13125 per coupon 1 000000 02625 2 13125 FV 1000000 Bond w payments at 7625 N 15x2 l 26252 PV 1666000 PMT 38000 1 000000 07625 2 38000 FV 1000000 If market value and bond value are the same then face value and present value will also be the same Even though the payments are higher at 7625 you end up paying a higher present value QUIZ ON CHAPTER 7 NEXT CLASS MIDTERM A WEEK FROM FRIDAY Date Friday September 25 2015 Chapter Cont Chapter 8 Time value money keys TVM on calc ALL BONDS ARE SEMIANNUALLY PAID IE find mkt value of a 1000 bond with 8 and 3 year remaining maturity if market rate is 12 0 t1 2 t3 t4 5 16 902 40 4o 40 40 4o 40 N 3x2 6 semi annual payments I 122 6 semiannual at market rate PV OPT 902 PMT 40 08x10002 FV 1000 Market rate would be of 8 if PV1000 but we are getting 12 so you pay 902PV Will get 12 return until it matures What if market rate decreased to 4 after you buy N 6 PMT 40 FV 1000 l 42 2 semiannually PV 1112 bid up until equals market value If you can predict lY movements you can make money out of this MKT rate lowers PV raises vice versa payment frequency determines the rate IE find the market value of a 1000 bond 10 year maturity 8 coupon rate 4 mkt rate N10x2 20 l 42 2 semiannually PMT 40 FV 1000 PV 1327 PV price of bond lowers as interest rates go up Plot bonds fluctuated risks at different fluctuate inversely to returns graph shows bond risks Lets say 8 is the bond rate we are looking at Lower rate 8 Higher rate Premium Discount BOND W 10 YEAR MATURITY BOND W 30 YEAR MATURITY N 10x2 N 30x2 l 42 42 PMT 40 PMT 40 FV1000 FV1000 PV CPT 1327 PV CPT 1697 longer the maturity higher the present value of the bond After analyzing these bonds with different interest rates for the market rate we are able to make the conclusions that 10 year maturity bonds had a 42 decline and 30 year maturity bonds had a 60 decline As bond approaches maturity the price will approach the face value bonds become less risky overtime to predict bonds predict interest rates Lower coupon rate bonds have more interest rate risk than higher coupon rate bonds duration Questions 1 greatest interest rate long term 2 If you suspect increase mkt rate what bond should you buy today short termmoney value 3 if you suspect decrease mkt rate what bond should you buy today long termsmall coupon more risky cuz takes longer to get money back independently of maturity 8 YTM yield to maturity 8 coupon rate bond price face value YTM gt coupon rate discount YTM lt coupon rate premium