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ISE2014Fall 2011

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Cash Flow DiagramsF/P

P/F

P/AF/A

A/P

A/F

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Annuities are cash flows of equal value thatoccur in consecutive periods

We have 4 tools for manipulating annuities

P/AA/P

F/A

A/F

Lets work a quick refresher problem

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A graduating high school senior is planningon attending college at a cost of $40,000 foreach of the next 4 years

At an interest rate of 3%, he/she wants toknow the equivalent value of that tuition intodays dollars

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Draw a Cash Flow DiagramWhat are we given? Annuity

What are we looking for? Present Value

Setup ProblemUse P/A tool

X0 = $40,000(P/A, 3%, 4)

X0 = $40,000(3.7171)

X0 = $148,684

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Now suppose youre the proud parent of anewborn

You anticipate your child going to college for

4 years, but starting 18 years from nowLets assume college will still cost $40,000year and a similar 3% interest rate

You want to know the equivalent value ofthat tuition in todays dollars (18 years prior)

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How does this differ from the previousproblem?

Lets draw a Cash Flow Diagram to illustrate

Same annuity value for the same number ofyears, but now we want to shift it 18 yearsprior to the first payment, instead of just 1year prior

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How can we handle a situation like this?We can use multiple tools!

Each of our tools take an input and converts

it to something equivalentThe output from one tool can be the input tothe next tool still equivalent to theoriginal

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Lets go back to our Cash Flow DiagramIf we used the P/A tool, it would convert ourannuity to a single payment on year 17, lets

call that X17But were looking for the equivalent value inyear 0, lets call that X0

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After using the P/A tool and finding X17, wecan use the P/F tool to move X17 to X0X0 = $40,000(P/A,3%,4)(P/F,3%,17)

The result of our first tool, X17, is a singlecash flow on year 17

X17 becomes the input to our second tool,which shifts the single cash flow back 17years

X17

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X0 = $40,000(P/A,3%,4)(P/F,3%,17)X0 = $40,000(3.7171)(.6050)

X0 = $89,954

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Always remember that the terms presentand future are all relative

Tools can be used at any point in time

If the output of a tool is P (present), it meanspresent relative to the input of the tool

If the output of a tool is F (future), it meansfuture relative to the input of the tool

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As with many problems in our class, wecould have solved the previous problem in adifferent manner

Lets try a different method to see how theresult compares

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This time lets use the F/A toolThe F/A tool converts the annuity to a singlecash flow in year 21

Lets call this X21We can move this cash flow back to year 0by again using P/F, this time with N = 21years

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X0 = $40,000(F/A,3%,4)(P/F,3%,21)

The result of our first tool, X21, is a singlecash flow on year 21

We then use the P/F tool to shift this cash

flow back 21 periods to year 0

X21

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X0 = $40,000(F/A,3%,4)(P/F,3%,21)X0 = $40,000(4.1836)(.5375)

X0 = $89,947

Same answer as before with a smallrounding error

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Problem 4-55 in your textbookCarefully draw a cash flow diagram basedon the information were given

$3,000 payments on years 25-32Need to find equivalent single cash flow onyear 65 (X65)

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Need to convert the annuity to a single cashflow, can use P/A or F/A

Need to move that single cash flow to period

65, regardless of which tool we used first

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X65 = $3,000(P/A,10%,8)(F/P,10%,41)

X65 = $3,000(F/A,10%,8)(F/P,10%,33)

X24

X32

OR

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N = 41 and N= 33 arent in our tables, oh no!We can use linear interpolation to estimate

We have F/P table values for N = 30, N = 35

35 30 33 - 3028.1024-17.4494 X 17.4494

X 23.8412 Actual value 23.2252

=

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Interpolation adds error to the final answer,but in this class we care about your method,not the final answer

Always focus on correctly setting up yourCFD and tools

Homework problems may have N valuesthat arent in the tables, but on the exam Ill

try to avoid this

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In order to make your life easier, Ive created aspreadsheet to calculate any particular interestrate for all N values 1-100

Spreadsheet is posted on Scholar, just plug in

whatever rate you want and it will calculate atable exactly like what is in your book

You can interpolate or use the spreadsheet if

an N value isnt on the book tables

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Cash Flow DiagramsF/P

P/F

P/AF/A

A/P

A/F

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No new readingReview your tools, well continue addingcomplexity next class and work more

difficult problemHomework 2 due Wednesday Sept. 7th