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

Our First Magic Number  F/P i,n  Formula is (1 + i) n  The effect of F/P is to take a present number of dollars and move them n compounding periods into the future at a rate of return (or interest rate) of i  F/P * Present Value = Future Value

Example of Use  Lanna Loaner is using student loans to finance the cost of her college education. Lanna figures she will take 5 years to graduate. She figures that she will take 12 hours each semester (except summer).  Lanna figures each semester will cost $3,645 Tuition + $1,622 Fees = $5,267  Lanna expects to spend $700/semester in books and supplies

Lanna’s Learning Legend  Lanna figures she will spend $8,000/year on dorm room in the residence hall $3,804 for a 19 meal per week plan  Lanna figures she will need $300/month for food and clothing, and socializing  Lanna figures she can save $7,000 each summer from working.

Lanna Loves Learning  Lanna arranges to get student loans sponsored by the government Future Income Tax Enhancement Agency.  One Type of Loan will be a Subsidized Stafford Loan at 3.4% interest (but government will pay the interest while she is in school)  Limit is $4,500  Another Loan is unsubsidized Stafford Loan  Limit is $6,000  Interest if 6.8% and accumulates from day of dispersement  Her Parents will use Plus Loans at 7.9% for rest. (But Lanna will get to repay)  How much debt will Lanna accumulate by the time she graduates?

Step #1  Turn the story problem into a cash flow.  Figure out what Lanna needs in loans every year  2 semesters tuition and fees  $5,267 * 2 = $10,534  2 semesters books and supplies  $700 * 2 = $1400  9 months housing  $8000  Meal Plan $3,804  9 months misc.  $300 * 9 = $2700

Continuing Step #1  Total up Lanna’s expenses  $10,534 + $1,400 + $8,000+ $3,804+$2,700 = $26,438  When Lanna starts college she probably won’t already have a pile of money saved, so she will have to take the full loan the first year - thereafter  Credit Lanna’s earnings in the summer  $26,438 - $7,000 = $19,438

Breaking Down Loans  Subsidized Stafford loan  She’ll take the $4,500 every year  Unsubsidized Stafford Loan  She’ll take the $6,000 every year  Plus Loans  She’ll take $15,938 the first year  $8,938 in subsequent years

Making my Cash Flow  First decision - Who’s perspective will I take (I have Lanna taking the loan and the Dept. of Education giving it out).  I’m going to take Lanna’s  At the beginning of each school year Lanna sees money moving into her pocket  We use the convention that money moving in our pocket is positive - money moving out is negative.

One Twist on the Script  If you borrow $100 on a plus loan you only get $96 because the government took 4% off the top to pay for administrative fees  Thus to get $15,938 the first year she’ll need to borrow  $15,938/0.96= $16,602  To get $8,938 the last three she’ll need to borrow  $8,938/.96 = $9,310

Drawing a Pretty Picture (We’ll Do the Plus Loan First) $16, Lanna Gets Her Diploma How Big a Hole will Lanna be in? $9,310 each year

Going to the Next Step  Using magic numbers to “sweep up” all the money into one pile  I’m will use F/P magic number because I want to sweep dollars from the present into one pile in the future

Apply F/P Magic Numbers Lanna Gets Her Diploma $16,602 We need to sweep this number ahead 5 interest periods into the pot of money Lanna will owe

Pick Out the Number to Use  I need an F/P magic number because I have a present dollar amount I want to sweep into the future pot.  I need it to be an F/P i, 5 because I want to sweep 5 compounding periods into the future  I need it to be an F/P 7.9, 5 because my interest rate each year is 7.9%

Apply the formula to get my Magic Number  ( ) 5 =  The formula I used is (1 + i ) n

Moving Along to My Next Number Lanna Gets Her Diploma $16,602*1,4625 $9,310 I now want to sweep this money into the future pot. F/P Magic number needed I need to move 4 compounding periods I need 7.9 % interest

Calculate My Magic Number  ( ) 4 =  Note that this number is smaller than  Reality Check - Does it make sense that if money doesn’t have as long to earn interest that it will earn less interest?  Yes so we’re probably still on the right track

Next Number Lanna Gets Her Diploma $16,602* $9,310 * I need to sweep this number 3 compounding periods into the future. How many periods do I need to sweep this one and this one

Now for the Last Step Lanna Gets Her Diploma $16,602* $9,310 * $9,310 * $9,310* $9,310 * Now we will add up all the numbers to sweep them into the pot.

Adding Up the Numbers  $16,602 * = $24,281  $9,310 * = $12,619  $9,310 * = $11,695  $9,310 * = $10,839  $9,310 * = $10,045  Total swept into the future debt pot is  $69,480

We Just Computed Our First Financial Measure  Sweeping all the money into one pot at a future time is called a Net Future Value  Also abbreviated NFV  Book likes to call it a Net Future Worth (NFW)

Of Course We Have Two More Loans to Deal With  The loan where the government pays the interest is easy  $4,500 * 5 = $22,500  Now for the $6,000 per year unsubsidized Stafford Loan  We could do 5 F/P values just like before but is there an easier way?  One Deals with Annuities (I’ll keep you in suspense about that one)  The other uses Class Assistant.

Go To the Cash Flow Analyzer Input our per year Cash flow.

Set My Interest Rate 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 every Compounding period – ie if I put 1 in then the cash flow is assumed to be annual. If I put In 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 in Time to take the NFV I Want Year 5 When Lanna Graduates. And Read Off the Answer $36,704

So How Much Debt Does Lanna Have?  $69,480 at 8% interest  $22,500 at 3.4% interest  $36,704 at 6.8% interest  Total $128,684 (a little less than the price of a house)  Disclaimer notes – this example did not consider initiation fees on the Stafford Loans, it did not consider that money is actually dispersed each semester – not once a year. It did not consider that most Plus loans start repayment while students are still in school.