Using P/FUsing P/F

©Dr. B. C. Paul 2001 revisions 2008©Dr. B. C. Paul 2001 revisions 2008

Note – The subject covered in these slides is considered to be “common 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 knowledge” to those familiar with the subject and books or articles covering the concepts are widespread.concepts are widespread.

Does the Pot of Money Does the Pot of Money Have to be in the Future?Have to be in the Future? NoNo The U.S. Savings Bond GameThe U.S. Savings Bond Game

Many groups like to give savings bonds as prizesMany groups like to give savings bonds as prizes

Why -Why - Because a savings bond is worth its face amount Because a savings bond is worth its face amount

in the futurein the future It cost less than that todayIt cost less than that today Lets you give bigger prizes without coming up Lets you give bigger prizes without coming up

with the cashwith the cash

ExampleExample The Department of Art at SIU is sponsoring a The Department of Art at SIU is sponsoring a

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

Step #1Step #1

We need to decide what perspective we We need to decide what perspective we will look at the cash flow from (we have will look at the cash flow from (we have the Government that will issue the bond, the Government that will issue the bond, and the buyer).and the buyer).

I’m going to choose the buyer because I’m going to choose the buyer because the problem is about the Department of the problem is about the Department of Art that will buy the bondArt that will buy the bond

Setting Up My Cash FlowSetting Up My Cash Flow

0 1 2 3 4

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 NumberEnter 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?Now What Do I Do?

F/P * Present = FutureF/P * Present = Future How aboutHow about

P/F * Future = PresentP/F * Future = Present

Creating a New Magic Creating a New Magic NumberNumber

To do it with the symbol all I had to do To do it with the symbol all I had to do was flip it overwas flip it over

Turns out the same thing works with the Turns out the same thing works with the formulaformula F/P Flips to P/FF/P Flips to P/F (1 + i )(1 + i )nn Flips to 1/( 1 + i ) Flips to 1/( 1 + i )n n or (1 + i )or (1 + i )-n-n

Working Our New HeroWorking Our New Hero

We want to sweep $100 backWe want to sweep $100 back 5 compounding periods at5 compounding periods at 5.5%5.5%

(1 + 0.055)(1 + 0.055)-5 -5 = 0.76513= 0.76513

0 1 2 3 4

The Bond will cost$76.51

Doing it With Class Doing it With Class AssistantAssistant

Magic # Calculator

Enter Annual Interest Rate in %Do not use the % key during data entry

Annual Int Rate 5.51 Enter the number of compounding periods/year

in % in decimalPeriod Int Rate 5.5 0.055

Enter # Compouning Periods to Move Cash (value of n) 5The value should be an interger

F/P 1.306960006 (used to move one cash flow element n compounging period into the future)

P/F 0.765134354 (used to move one cash flow element n compounging periods back)

Annual Interest Rate

This problem said interest only Compounded one at the end of eachyear

There is my P/F value

Apply the value

$100*0.76513 = $76.51

This Same Thinking This Same Thinking Drives the Bond MarketDrives the Bond Market

0 1 2 3 4

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.

Effect of ROR on Bond Effect of ROR on Bond PricesPrices

Bond market over past 10 years has Bond market over past 10 years has generally outperformed the stock market.generally outperformed the stock market.

During that time interest rates have been During that time interest rates have been fallingfalling Has added to earnings of bond fundsHas added to earnings of bond funds What if that changes?What if that changes?

The Billy Bond Fund The Billy Bond Fund

Billy Bond Fund has bonds that mature in Billy Bond Fund has bonds that mature in 10 years and have a face value of 10 years and have a face value of $1,000,000.$1,000,000. Market was looking at low inflation 1%Market was looking at low inflation 1% Safe Rate 1.5%Safe Rate 1.5% Motivation 0.1%Motivation 0.1% RiskRisk

Mostly U.S. Gov backed so very low risk 0%Mostly U.S. Gov backed so very low risk 0% Interest Rate is 2.62%Interest Rate is 2.62%

Now Lets Use P/F to find Now Lets Use P/F to find what the bond portfolio is what the bond portfolio is worth today.worth today.

P/F (10 years, 2.62%) = 0.7721P/F (10 years, 2.62%) = 0.7721 Apply to $1,000,000 in bondsApply to $1,000,000 in bonds

$1,000,000 * 0.7721 = $772,100$1,000,000 * 0.7721 = $772,100 The bond portfolio is worth about $772,000The bond portfolio is worth about $772,000

Now Lets Try SomethingNow Lets Try Something

Inflation Picks up 3.6%Inflation Picks up 3.6% Safe Rate is still 1.5%Safe Rate is still 1.5% Motivation is still 0.1%Motivation is still 0.1% U.S. Gov. Messes up – Risk jumps to 1.5%U.S. Gov. Messes up – Risk jumps to 1.5% New interest rate is – 6.84%New interest rate is – 6.84% P/F (10 years, 6.84%) = 0.5160P/F (10 years, 6.84%) = 0.5160 Apply to bond portfolioApply to bond portfolio

$1,000,000 * 0.5160 = $516,000$1,000,000 * 0.5160 = $516,000

The ImpactThe Impact

The Bond Fund went from $772,100The Bond Fund went from $772,100 To $516,000To $516,000 Fund Lost over 33% of its valueFund Lost over 33% of its value

Now Its Your TurnNow Its Your Turn

Do Assignment #3Do Assignment #3

In Homework #1 you estimated the interest rate for a bond In Homework #1 you estimated the interest rate for a bond to build an auto assembly plant. Now you get to figure the to build an auto assembly plant. Now you get to figure the price of the bond.price of the bond.