1. Using P/F ©Dr. B. C. Paul 2001 revisions 2008, 2011 Note – The subject covered in these slides is considered to be “common knowledge” to those familiar with the subject and books or articles covering the concepts are widespread.

2. Does the Pot of Money Have to be in the Future?  No  The U.S. Savings Bond Game  Many groups like to give savings bonds as prizes  Why -  Because a savings bond is worth its face amount in the future  It cost less than that today  Lets you give bigger prizes without coming up with the cash

3. Example  The Department of Art at SIU is sponsoring a contest for High School Students. Teams will compete in making the most inspiring statue of a Saluki Dog out of beer cans (which the sponsors emptied first), toilet paper (which everyone gets fresh), and used chewing gum (the teams get to convert fresh gum to used). First prize is a $100 savings bond that matures in 5 years. The Government will pay 5.5% interest (compounded annually) on the bond. What will the Department of Art pay for the bond?

4. Step #1  We need to decide what perspective we will look at the cash flow from (we have the Government that will issue the bond, and the buyer).  I’m going to choose the buyer because the problem is about the Department of Art that will buy the bond

5. Setting Up My Cash Flow 0 1 2 3 4 5 $100 What I need to do is sweep this $100 dollars back into the here and now pot to find out how much its worth.

6. Enter Our Magic Number F/P Rules Oh ________ F/P sweeps a present number into the future pot. I want to sweep Future dollars into the right now pot.

7. Now What Do I Do?  F/P * Present = Future  How about  P/F * Future = Present

8. Creating a New Magic Number  To do it with the symbol all I had to do was flip it over  Turns out the same thing works with the formula  F/P Flips to P/F  (1 + i ) n Flips to 1/( 1 + i ) n or (1 + i ) -n

9. Working Our New Hero  We want to sweep $100 back  5 compounding periods at  5.5%  (1 + 0.055) -5 = 0.76513 0 1 2 3 4 The Bond will cost $76.51

10. Doing it With Class Assistant Annual Interest Rate This problem said interest only Compounded one at the end of each year There is my P/F value Apply the value $100*0.76513 = $76.51

11. How the FE Exam May Test Your Knowledge of P/F  How much money must be put in a savings account today at 5% interest to have $500 in 10 years?  (a)- $814  (b)- $310  (c)- $170  (d)- $307

12. Solving Using the Formula Method  Need to recognize the answer is  $500* P/F 5%,10years = answer  P/F formula is (1+i) -n  Remember to convert i from % to decimal  (1+0.05) -n  Now plug in n=10 years  (1+0.05) -10 = 0.6139 = P/F 5%,10 years

13. Solving Using the Table Look-Up Method Which table should I use? (The FE Exam booklet includes A ton so you must pick the Right one) Note this table is for 8% interest This table is for 5% interest Note the number near the Top. Clearly I want 5% interest as Indicated in the question so I will use the 5% table.

14. For My Next Trick I Will Pick the Correct Magic Number There is P/F There is 10 And P/F is 0.6139

15. And Finishing the Problem  $500 * 0.6139 = $306.96  The Exam Says  (a)- $814  (b)- $310  (c)- $170  (d)- $307  The correct answer is d - $307

16. This Same Thinking Drives the Bond Market 0 1 2 3 4 Companies issue bonds worth some amount at maturity. The bond markets evaluate what Rate of Return is needed considering inflation, safe return, the risk of the company issuing the bond and then considering when the bond matures they use a P/F factor to see what its worth today.

17. Effect of ROR on Bond Prices  Bond market over past 10 years has generally outperformed the stock market.  During that time interest rates have been falling  Has added to earnings of bond funds  What if that changes?

18. The James Bond Fund  James Bond Fund has bonds that mature in 10 years and have a face value of $1,000,000.  Market was looking at low inflation 1%  Safe Rate 1.5%  Motivation 0.1%  Risk  Mostly U.S. Gov backed so very low risk 0%  Interest Rate is 2.62%

19. Now Lets Use P/F to find what the bond portfolio is worth today.  P/F (10 years, 2.62%) = 0.7721  Apply to $1,000,000 in bonds  $1,000,000 * 0.7721 = $772,100  The bond portfolio is worth about $772,000

20. Now Lets Try Something  Inflation Picks up 3.6%  Safe Rate is still 1.5%  Motivation is still 0.1%  U.S. Gov. Messes up – Risk jumps to 1.5%  New interest rate is – 6.84%  P/F (10 years, 6.84%) = 0.5160  Apply to bond portfolio  $1,000,000 * 0.5160 = $516,000

21. The Impact  The Bond Fund went from $772,100  To $516,000  Fund Lost over 33% of its value

22. Now Its Your Turn Do Assignment #3 In Homework #1 you estimated the interest rate for a bond to build an auto assembly plant. Now you get to figure the price of the bond.