Using F/PUsing F/P

©Dr. B. C. Paul 2001 revisions 2008, 2011©Dr. B. C. Paul 2001 revisions 2008, 2011

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.

Information on University Costs was taken from SIUC tuition and fees calculator on Information on University Costs was taken from SIUC tuition and fees calculator on Aug. 26, 2008. Board of Trustees 2008 action summaries were used for cost of Aug. 26, 2008. Board of Trustees 2008 action summaries were used for cost of housing and meal plans.housing and meal plans.

Our First Magic NumberOur First Magic Number

F/P F/P i,ni,n

Formula is (1 + i)Formula is (1 + i)nn

The effect of F/P is to take a present The effect of F/P is to take a present number of dollars and move them n number of dollars and move them n compounding periods into the future at a compounding periods into the future at a rate of return (or interest rate) of irate of return (or interest rate) of i

F/P * Present Value = Future ValueF/P * Present Value = Future Value

Example of UseExample of Use Lanna Loaner is using student loans to Lanna Loaner is using student loans to

finance the cost of her college education. finance the cost of her college education. Lanna figures she will take 5 years to Lanna figures she will take 5 years to graduate. She figures that she will take 12 graduate. She figures that she will take 12 hours each semester (except summer).hours each semester (except summer). Lanna figures each semester will cost $3,645 Lanna figures each semester will cost $3,645

Tuition + $1,622 Fees = $5,267Tuition + $1,622 Fees = $5,267 Lanna expects to spend $700/semester in Lanna expects to spend $700/semester in

books and suppliesbooks and supplies

Lanna’s Learning LegendLanna’s Learning Legend

Lanna figures she will spend $8,000/year Lanna figures she will spend $8,000/year on dorm room in the residence hall on dorm room in the residence hall $3,804 for a 19 meal per week plan$3,804 for a 19 meal per week plan

Lanna figures she will need $300/month Lanna figures she will need $300/month for food and clothing, and socializingfor food and clothing, and socializing

Lanna figures she can save $7,000 each Lanna figures she can save $7,000 each summer from working.summer from working.

Lanna Loves LearningLanna Loves Learning

Lanna arranges to get student loans sponsored by the Lanna arranges to get student loans sponsored by the government Future Income Tax Enhancement Agency. government Future Income Tax Enhancement Agency. One Type of Loan will be a Subsidized Stafford Loan at 3.4% One Type of Loan will be a Subsidized Stafford Loan at 3.4%

interest (but government will pay the interest while she is in interest (but government will pay the interest while she is in school)school) Limit is $4,500Limit is $4,500

Another Loan is unsubsidized Stafford LoanAnother Loan is unsubsidized Stafford Loan Limit is $6,000Limit is $6,000 Interest if 6.8% and accumulates from day of dispersementInterest if 6.8% and accumulates from day of dispersement

Her Parents will use Plus Loans at 7.9% for rest. (But Lanna Her Parents will use Plus Loans at 7.9% for rest. (But Lanna will get to repay)will get to repay)

How much debt will Lanna accumulate by the time she How much debt will Lanna accumulate by the time she graduates?graduates?

Step #1Step #1

Turn the story problem into a cash flow.Turn the story problem into a cash flow. Figure out what Lanna needs in loans every Figure out what Lanna needs in loans every

yearyear 2 semesters tuition and fees2 semesters tuition and fees

$5,267 * 2 = $10,534$5,267 * 2 = $10,534 2 semesters books and supplies2 semesters books and supplies $700 * 2 = $1400$700 * 2 = $1400

9 months housing9 months housing $8000$8000 Meal Plan $3,804 Meal Plan $3,804 9 months misc. 9 months misc. $300 * 9 = $2700$300 * 9 = $2700

Continuing Step #1Continuing Step #1

Total up Lanna’s expensesTotal up Lanna’s expenses $10,534 + $1,400 + $8,000+ $3,804+$2,700 = $10,534 + $1,400 + $8,000+ $3,804+$2,700 =

$26,438$26,438

When Lanna starts college she probably When Lanna starts college she probably won’t already have a pile of money saved, so won’t already have a pile of money saved, so she will have to take the full loan the first she will have to take the full loan the first year - thereafteryear - thereafter

Credit Lanna’s earnings in the summerCredit Lanna’s earnings in the summer $26,438 - $7,000 = $19,438$26,438 - $7,000 = $19,438

Breaking Down LoansBreaking Down Loans

Subsidized Stafford loanSubsidized Stafford loan She’ll take the $4,500 every yearShe’ll take the $4,500 every year

Unsubsidized Stafford LoanUnsubsidized Stafford Loan She’ll take the $6,000 every yearShe’ll take the $6,000 every year

Plus LoansPlus Loans She’ll take $15,938 the first yearShe’ll take $15,938 the first year $8,938 in subsequent years$8,938 in subsequent years

Making my Cash FlowMaking my Cash Flow First decision - Who’s perspective will I First decision - Who’s perspective will I

take (I have Lanna taking the loan and the take (I have Lanna taking the loan and the Dept. of Education giving it out).Dept. of Education giving it out).

I’m going to take Lanna’sI’m going to take Lanna’s At the beginning of each school year At the beginning of each school year

Lanna sees money moving into her pocketLanna sees money moving into her pocket We use the convention that money moving in We use the convention that money moving in

our pocket is positive - money moving out is our pocket is positive - money moving out is negative.negative.

One Twist on the ScriptOne Twist on the Script

If you borrow $100 on a plus loan you If you borrow $100 on a plus loan you only get $96 because the government only get $96 because the government took 4% off the top to pay for took 4% off the top to pay for administrative feesadministrative fees Thus to get $15,938 the first year she’ll need Thus to get $15,938 the first year she’ll need

to borrowto borrow $15,938/0.96= $16,602$15,938/0.96= $16,602

To get $8,938 the last three she’ll need to To get $8,938 the last three she’ll need to borrowborrow $8,938/.96 = $9,310$8,938/.96 = $9,310

Drawing a Pretty PictureDrawing a Pretty Picture(We’ll Do the Plus Loan (We’ll Do the Plus Loan First)First)

$16,602

0 1 2 3 4

5 - Lanna Gets Her Diploma

How Big a Hole willLanna be in?

$9,310 each year

Going to the Next StepGoing to the Next Step

Using magic numbers to “sweep up” all Using magic numbers to “sweep up” all the money into one pilethe money into one pile

I’m will use F/P magic number because I I’m will use F/P magic number because I want to sweep dollars from the present want to sweep dollars from the present into one pile in the futureinto one pile in the future

Apply F/P Magic NumbersApply F/P Magic Numbers

0 1 2 3 4

5 - Lanna Gets Her Diploma

$16,602

We need to sweep this number ahead 5 interestperiods into the pot of money Lanna will owe

Pick Out the Number to Pick Out the Number to UseUse

I need an F/P magic number because I I need an F/P magic number because I have a present dollar amount I want to have a present dollar amount I want to sweep into the future pot.sweep into the future pot.

I need it to be an F/P I need it to be an F/P i, 5 i, 5 because I want because I want

to sweep 5 compounding periods into the to sweep 5 compounding periods into the futurefuture

I need it to be an F/P I need it to be an F/P 7.9, 5 7.9, 5 because my because my

interest rate each year is 7.9%interest rate each year is 7.9%

Apply the formula to get Apply the formula to get my Magic Numbermy Magic Number

(1 + 0.079) (1 + 0.079) 5 5 = 1.4625= 1.4625 The formula I used is (1 + i ) The formula I used is (1 + i ) nn

Magic # CalculatorNote - It is recommended that you go to the Magic # Calculator Tab for advice on how to use this feature

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

Annual Int Rate 7.91 Enter the number of compounding periods/year

in % in decimalPeriod Int Rate 7.9 0.079

(Please note - you must enter the number of compounding periods that moneyEnter # Compouning Periods to Move Cash (value of n) 5 is to be moved either forward or back for the F/P and P/F numbers to work)The value should be an interger (The value you enter here affects F/P and P/F but not P/A, A/P, F/A, A/F)

F/P 1.462538217 (used to move one cash flow element n compounging period into the future)

Moving Along to My Next Moving Along to My Next NumberNumber

0 1 2 3 4

5 - Lanna Gets Her Diploma

$16,602*1,4625

$9,310

I now want to sweep this money into the futurepot.

F/P Magic number needed

I need to move 4 compounding periods

I need 7.9 % interest

Calculate My Magic Calculate My Magic NumberNumber

(1 + 0.079 ) (1 + 0.079 ) 44 = 1.3555 = 1.3555 Note that this number is smaller than Note that this number is smaller than

1.46251.4625 Reality Check - Does it make sense that Reality Check - Does it make sense that

if money doesn’t have as long to earn if money doesn’t have as long to earn interest that it will earn less interest?interest that it will earn less interest? Yes so we’re probably still on the right trackYes so we’re probably still on the right track

Next NumberNext Number

0 1 2 3 4

5 - Lanna Gets Her Diploma

$16,602*1.4625

$9,310 * 1.3555

I need to sweep this number 3 compoundingperiods into the future.

How many periods do I needto sweep this one and this one

Now for the Last StepNow for the Last Step

0 1 2 3 4

5 - Lanna Gets Her Diploma

$16,602*1.4625$9,310 * 1.3555

$9,310 * 1.2562$9,310* 1.1642

$9,310 * 1.079

Now we will add up all the numbersto sweep them into the pot.

Adding Up the NumbersAdding Up the Numbers

$16,602 * 1.4625 = $24,281$16,602 * 1.4625 = $24,281 $9,310 * 1.3555 = $12,619$9,310 * 1.3555 = $12,619 $9,310 * 1.2562= $11,695$9,310 * 1.2562= $11,695 $9,310 * 1.1642 = $10,839$9,310 * 1.1642 = $10,839 $9,310 * 1.079 = $10,045$9,310 * 1.079 = $10,045

Total swept into the future debt pot isTotal swept into the future debt pot is

$69,480$69,480

We Just Computed Our We Just Computed Our First Financial MeasureFirst Financial Measure

Sweeping all the money into one pot at a Sweeping all the money into one pot at a future time is called a Net Future Valuefuture time is called a Net Future Value Also abbreviated NFVAlso abbreviated NFV Book likes to call it a Net Future Worth Book likes to call it a Net Future Worth

(NFW)(NFW)

Of Course We Have Two Of Course We Have Two More Loans to Deal WithMore Loans to Deal With

The loan where the government pays the The loan where the government pays the interest is easyinterest is easy $4,500 * 5 = $22,500$4,500 * 5 = $22,500

Now for the $6,000 per year unsubsidized Now for the $6,000 per year unsubsidized Stafford LoanStafford Loan We could do 5 F/P values just like before but is We could do 5 F/P values just like before but is

there an easier way?there an easier way? One Deals with Annuities (I’ll keep you in suspense about One Deals with Annuities (I’ll keep you in suspense about

that one)that one) The other uses Class Assistant.The other uses Class Assistant.

Go To the Cash Flow Go To the Cash Flow AnalyzerAnalyzer Cash Flow Analyzer

Note - It is recommended that you go to the Cash Flow Analyzer Tab for advice on how to use this featureWarning - This feature assumes the time interval on your cash flow and the interest compounding period are the sameIf this is not true you should see special slides about what to do if the interest compounding period and time interval are differentTo Use the NPV, IRR, PVR and Payback Period Features you must enter your interest rate for this type of investment and the number ofCompounding Periods in One Year.Enter Your Annual Interest Rate as a %, but do not use the % key during data entryEnter the number of compounding periods in one year 1Period interest rate 0.079 (in decimal form)

Cash Flow Evaluation Index Values(Warning IRR and Payback may not function properly on unconventional cash flows)NPV -25917.076IRR #DIV/0!PVR 0 NPV investmentPayback Period 0 (this value is reported to an integer # of compounding periods)

To Use the NFV Feature on this spread sheet you must enter the point in the future that money is to be discounted to.Enter # of compounding periods into future at which to take NFV

NFV -37904.714 (cash flows beyond the NFV time are discounted back to the NFV time)To Use the ERR and Modified IRR you must specify the rate of interest available in your external investments

Enter the rate of interest on external investments as a % (don't put %)Period interest rate

ERR (version 1) 0 % annualERR (version 2) 0 % annualMod. IRR #DIV/0! % annual

To Use the Total Life Cycle Cost you must specify the compounding period where the project goes into service andthe number of compounding periods that the project remains in service after starting

Start of Project LifeUseful Life

Total Life Cycle Cost -3421.2693

Enter Your Cash Flow in the Column Below (Remember to use minus signs for money flowing out of your pocket)Time zero is the current instant of time, values 1, 2 etc represent compounging period in the future

Time Cash Flow P/F Present Value Cum Cash Pback Mark Pos PV

0 -6000 1 -6000 -6000 0 01 -6000 0.926784 -5560.704356 -12000 0 02 -6000 0.858929 -5153.572156 -18000 0 03 -6000 0.796041 -4776.248522 -24000 0 04 -6000 0.737758 -4426.550994 -30000 0 05 0 0.683743 0 -30000 0 06 0 0.633682 0 -30000 0 0

Input our -6000 per yearCash flow.

Set My Interest RateSet My Interest Rate

Cash Flow AnalyzerNote - It is recommended that you go to the Cash Flow Analyzer Tab for advice on how to use this featureWarning - This feature assumes the time interval on your cash flow and the interest compounding period are the sameIf this is not true you should see special slides about what to do if the interest compounding period and time interval are differentTo Use the NPV, IRR, PVR and Payback Period Features you must enter your interest rate for this type of investment and the number ofCompounding Periods in One Year.Enter Your Annual Interest Rate as a %, but do not use the % key during data entry 6.8Enter the number of compounding periods in one year 1Period interest rate 0.068 (in decimal form)

Input My 6.8% interest

Identify it a compounding once a year

(A note about the cash flow analyzer – it assumes a cash flow event is shown everyCompounding period – ie if I put 1 in then the cash flow is assumed to be annual. If I putIn 12 it is assumed to be monthly. If I put in 365 the cash flow is assumed to be daily)

Now Tell it At What Point Now Tell it At What Point in Time to take the NFVin Time to take the NFV

To Use the NFV Feature on this spread sheet you must enter the point in the future that money is to be discounted to.Enter # of compounding periods into future at which to take NFV 5

NFV -36703.957 (cash flows beyond the NFV time are discounted back to the NFV time)

I Want Year 5 When LannaGraduates.

And Read Off the Answer $36,704

So How Much Debt Does So How Much Debt Does Lanna Have?Lanna Have?

$69,480 at 8% interest$69,480 at 8% interest $22,500 at 3.4% interest$22,500 at 3.4% interest $36,704 at 6.8% interest$36,704 at 6.8% interest Total $128,684 (a little less than the price of a Total $128,684 (a little less than the price of a

house)house) Disclaimer notes – this example did not consider initiation fees on Disclaimer notes – this example did not consider initiation fees on

the Stafford Loans, it did not consider that money is actually the Stafford Loans, it did not consider that money is actually dispersed each semester – not once a year. It did not consider dispersed each semester – not once a year. It did not consider that most Plus loans start repayment while students are still in that most Plus loans start repayment while students are still in school.school.