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

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?

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

Setting Up My Cash Flow

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5

$100What I need to do is sweepthis $100 dollars back intothe here and now pot to findout how much its worth.

Enter Our Magic Number

F/P RulesOh ________F/P sweeps a present numberinto the future pot.

I want to sweep Future dollars intothe right now pot.

Now What Do I Do?

• F/P * Present = Future

• How about– P/F * Future = Present

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

Working Our New Hero

• We want to sweep $100 back– 5 compounding periods at– 5.5%

• (1 + 0.055)-5 = 0.76513

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The Bond will cost$76.51

This Same Thinking Drives the Bond Market

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Companies issue bonds worth some amountat maturity.

The bond markets evaluate what Rate of Returnis needed considering inflation, safe return, therisk of the company issuing the bond and thenconsidering when the bond matures they use aP/F factor to see what its worth today.